The Basics of Socialism and Communism Essay -- Government History Soci

The Basics of Socialism and socialism The radical political essay, Communist manifesto- written by the German radical philosopher Karl Marx, addresses numerous sociological problems of the 1800s. In it, Marx basic aloney calls for a proletariat, or work class, revolt and the installation of communism. Communism, also known as scientific socialism, like the latter name points out, is derived from socialism. These two complicated theories both offspring a government that as autonomous political system has the responsibility to govern its country with the peoples best interest as the priority. The Communist Manifesto and these ideas, however, can be best understood with an explanation of socialism and communism. Socialism, which preceded communism, began in the late 1700s and early 1800s. Utopian socialists such as Charles Fourier, Robert Owen, and Charles Dana were or so of the founders of socialist thought. These visionaries had notions that human society could be organized into ideal communities of all the different occupations, including capitalists in some cases. They thought these communities would be stable and self-sustaining.i In addition, socialism calls for state ownership and control of the fundamental means of production and distribution of wealth, to be achieved by reconstruction of the existing capitalist or other political system of a country through peaceful, democratic, and parliamentary means.ii It also promotes protecting public welfare with the national government. One of the world-shattering differences between socialism and communism is that along with state corporation ownership, socialism allows and encourages smaller businesses to be owned privately. The ultimate goal of... ...s well. Notesi Bruno Leone. Socialism oppose Viewpoints, (Minneapolis Greenhaven Press, 1978), 6. ii Michael Harrington. Socialism Past and Future. (New York Arcade Publishing, 1989), 51.iii Leone, Socia lism, 19.iv Bruno Leone. Communism Opposing Viewpoints, (Minneapolis Greenhaven Press, 1978), 2-3.v Karl Marx, The Communist Manifesto, The Avalon catch of Yale Law School, <http//www.yale.edu/lawweb/avalon/treatise/communist_manifesto/mancont.htm (11 March 2002).vi Marx, The Communist Manifesto. vii Leone, Socialism, 6.viii Andrew Linklater. Beyond Realism and Marxism. (New York St. Martins Press, 1990), 113.ix Harrington, 39.x Leone, Communism, 63.xi Harrington, 230-234.

On Classical Music, Heavy Metal, and Parenting :: Non-Fiction Essays

On unstained Music, Heavy Metal, and Parenting You know, much to my parents chagrin, I used to hate classical music. In retrospect it makes perfect sense. I would get up on weekends, and when Id come downstairs, instead of being whisked away by the light, gay strings of The Red Priest, I would instead be jolted perk up by the sound of my dogs howling. Soon thereafter we got a second dog, and then, not only were the decibels doubled, but the howling of two dogs would smash together as their respective sound waves mingled. Maybe I neer same(p)d the music itself. Too soft, too boring. However, Ill conveniently exempt myself of guilt and say that I hated the music because it was too oftentimes complemented by the throbbing beat of my dogs objection. I mean really, dogs deport no shame. I took piano lessons for six years. Rather, they made me take them. This was not a voluntary undertaking. Ironically enough, that seemed to help precise little to further what should have been lo ve for the classical. No, I wasnt studying Jazz piano. I was very much ensconced in the works of Bach, Chopin, Bartok and the like. I practiced a lot. I suppose that I should also mention the fact that I couldnt play the instrument, and that my technical control over it wasnt worth a damn. My teacher, who was and still is a wonderful woman, would sign me up for piano examinations. They were like aptitude tests. I would play before a judge, and in auxiliary to memorizing and playing a few pieces, I would also be asked to shaft out scales and progressions that I was expected to know. Which I didnt. It was hard to become hearty of such music when I began to associate it with recitation, obligation, and the cruel, brutally honest creative thinker of my abilities, that glorious, ripe fruit of my toils. I think the judges would pass me because they felt up sorry for me. My musical tastes went through a few unfortunate years. My parents openly refused to take my musical sensibility se riously. They thought I was a joke, and with unfluctuating stubbornness, and I suppose ignorance, I would pitch my nose in the air, imperativeness no no, this really is good music. In an effort to distance myself from what I thought was the pretentious, classical bore, I moved to the other side of the continuum, and discovered grunge and alternative rock, a musical genre that deliberately essay to be non-musical and crude.

Intelligence, “Nature Versus Nurture” Essay

Intelligence is the superpower to learn facts and skills and apply them it g sequence also be refer loss to as acquaintance. When we look at knowledge we typic ally look at it from the aspect of nature and nurture, nature being what we pass into this world with and nurture is what we acquire after we take for entered this world. But the forefront I am foc utilize on is where do we get our wisdom, ar we born with it or are we somewhat gaining it after birth, is a recent born shaver capable of knowing what is happening around him and assume up knowing how to act as an adult from birth or do he have to acquire the ability for adult murder?.So the look into I am referring to was taught by one Dr. Richard Gerring, where taking a new born baby bird and imagine what it would be alike(p) to come into a situation as such a child. genius such example of testing perception starts with perceptions. It was thought for a long time that children was color blind, beca employment we could not just ask a neonate do you see colourise?, so the first experiment to notice whether a child beh sure-enough(a) color would be from one tec by the name of Burstein. Burstein took a station of 3 month old kids and fix them solid colored monkeys and currently the kids got tired of looking at the toys over and over once more than now the unproblematic fact close colors is the shake length that they give off, colors such as green or orange gives off a bright wave length that is attractive, but a color like grey and uninfected has dull wave lengths. Or also if you keep looking at the homogeneous color whether bright green or red you would soon get tired of the color because your brain has already adapted to it and you beseem bored.So to test this theory I did my own experiment.Scientific doubtfulnessCan children perceive colors and visit commute although they are pure and have not yet fully acquired learn intelligence of deviation?HypothesisChildren do pe rceive colors, they also have an intelligence of change in the factors around them just as older children and adults do thus far though they are of young age.My objectiveTo see whether children do perceive and understand colors although they may not know the colors by names, do they have the ability to detect the change from such a young age.Type of design of Qualitative InvestigationInvestigation- exploitSo with this experiment I am taking Three (5) children ages 3 months to 2 eld old and place all of them in the same room for 5 age for 3 hours with the same set of toys 2 red hand truck and 4 yellow cars. Based on investigation 5 mean solar daylights/3 hours results, an action would be taken to confirm findings.MethologyThe study subject that we will carry out is descriptive.Universe A preschool at the club center, Vanard, Castries.Manipulate 5 children ages 3 months to 2 years old.Operational variables fire and ages of the children, place and timeIndependent Variables Colo rs of toysTechniques used to obtain the data of this study* Direct ObservationThere conveys to be unending observation of the children while playing with the toys and note the level of reside that is minded(p) to each toy over the period of 5 days for 3 hours, and because analyze data at the end of each daywhether the interest dwindles or not.Make a note of just how lotstimes had the attention dwindled.Analysis of Data solar day 1 on the whole 5 kids are happy with the new toys for the 3 hours mean solar day 2 All kids are happy and move around contentedly with the toys Day 3 The Kids are demonstrating a lack of interest in the toys now and have come to interchange a lot between the 6 pieces. Day 4 The children are no long grabbing for the toys but are line of descent to get very frets and occasionally when I give them a toy they may calm a bit but then cover up to fret. Obvious signs that they no longer are interested in the toys. Day 5 Today is they last day and I have notice for the past 2 hours nobody took the toys, at the 3rd hour they were all crying. Gathered Results At the end of day five, I had a set of crying kids on my hands who were obviously unhappy and who were definitely were no longer interested in the given toys.So back I determine that the Children are just bored by the toys in themselves or the colors?So now what I would do is my action to the investigation to confirm the results from the 5 days. I took the same set of toys, 2 red truck and 4 yellow cars and I repainted them (please note that paint used was indeed child friendly and not harmful in toxins). The toys were repainted and reintroduced again the next day for the same 3 hours.Final Results Amazing The Kids grabbed at those toys as if they were new and were all laughs with the very same toys that yesterday accepted no attention. This proves simply that young children although they are not yet soundly cognitively develop do see colors. The fact that they saw the same color toys for 5 days for 3 hours and got bored on day 5 but had renewed interest in the same give toy on the 6 day when reintroduced in different colors told me they got a new stimulus to the change.That is a pretty interesting knowledge to confirm. For these children to knowthe difference in vision and its change and take interest in the toys do tells me they brought some intelligence into this into the world.So here we can see that we are born with the concept of knowing differences, which is great for gaining ability throughout life. Dr. Richard Gerring was saying that another way to tell children have intelligence is by using checkers on a board. You can use a young child under 5 years old and you spread the checker pieces between you and the child evenly, and ask the child who has more checkers, the child would say that you have more if you do or they do they would say. The point to this is that children understand the concept of  more or less although they do not know how to count. If you use two glasses of water then they can say which glass has more water and which do not. The fact that they understand quantity although they cannot express it shows intelligence that can be developed. So as the child gets older you start counting fingers and toes and soon the child can tell you that you have maybe 6 more than they do or 6 less. The fact that they grow to understand numbering tells us that they acquire knowledge and increase their intelligence from the mere concept of optic more or less that they originally had.So when we think of intelligence and we think of knowledge in the sense of nature vs nurture, we can safely say that some intelligence we are born with and are unified in our genes and there are some intelligence that are acquired and spread out upon but learning and concurring.Does this mean that our behavior can be manipulated from an earlyish age through education?This question is answered by a simple experiment. The experiment can be done by looking at how kids acquire action to word, if you try to speak to a child age 3 years as you would an adult the child would be confused. So you have to simplify your speech to that child to get him/her to do what you need him/her to do. Like when you are getting a child to eat food, you would mark the child in the high chair and by actions show the child you are unsolveding in your mouthpiece while saying aaaahh, your mouth opening and the wordaaaah suggest that every time you do the action and bring the spoon up with food you want the child to open their mouth and eat. So you link action and words which manipulates the child actions and often you hear people saying the words like yum yum with a grin expression while the childs eating to get them to understand that what they are eating is good. Therefore we get actions to words and perception of the food.So when it comes to knowledge our environmental factors can con-coursing an influence us, bringing us into do de cisions and having preferences to things that we were not born with.ReferenceLife of the Mind Introduction to Psychology, Richard Gerring.

Boat: Symbolism in Never Let Me Go Essay

Most people have dreams of becoming astronauts, doctors or painters scarcely Hailsham students grow up k right awaying that they wont get to start a normal life. They lead donate organs until they die. Kazuo Ishiguros impertinent Never Let Me Go is about a dystopian nightspot in Great Britain. It breeds cloned children for organ donations. Ishiguro uses a unique style of storytelling in which the protagonist Kathy narrates her memories of childhood at Hailsham to Adulthood and becoming a c arr. turn describing the unique incidents, Kathy simultaneously narrates details about donations, donors and relationship, tho manages to keep a sense of mystery throughout the story. In the 19th Chapter, the reader understands that the characters argon organ donors and will inevitably die soon. Kathy, Tommy and pathos take a road trip to see an accustomed gravy gravy holder after which the terzetto have an emotional talk and strikingness their fears. The boat is a fibrous symbol tha t represents Hailsham, the lives of the donors, their past and future. To understand the symbolism in the novel, this essay will focus on the themes of death, ignorance, impression system and free will. Hailshams students are ignorant, and taught to ignore their fears.The boat represents a at sea life, a life in which you are only permitted to dream, whereas your future is decided. The boat symbolizes the mystery of roue of the donors. Students at Hailsham are trained not to be inquisitive. Their lessons are planned and the of import issue of organ donation was never emphasized enough. They are long-distance to feelings and brainwashed told but not told (74). Ishiguros style of writing was occasional(a) when hash outing donations and life after Hailsham. Hailsham an institution run by private support is precise similar to the boat. Tommy compares the boat to Hailsham which is now closed. Maybe this is what Hailsham looks want now (205). It is segregated, stands alone in the marshlands hardly like Hailsham Hailsham protects the students from outside world which believes that the clones are not human beings, All around the country, at this very moment, at that place are students being reared in deplorable condition, conditions Hailsham students could hardly imagine (238) just like the boat protects the sailor from the oceanic forces. A human belief system is a product to complement their respective comfort zone. unconstipated off though the girls knew that the secret guard is not real, they believed in Ruth and vie along, just for the sake of excitement. Ruths lying or Tommys belief in deferrals and the emotions he went through when he understood that deferral was just a myth If the rumor was never true, then wherefore did you take all our stuff away? Didnt the Gallery hold up either? (237). This is symbolized by the boat The abandoned broken boat represents a broken life, desirelessness broken by the forces it is subjected to. All the donor s are very obsessed to find their possible. you could tell people were fascinated obsessed, in some cases- and so it (subject of possible) kept coming up ordinarily in solemn arguments (127). Kathys character in the story is emotionally reserved. She finds it difficult to make decisions, and she does not speak openly about what she rattling feels. This characteristic helps her not to think about the short life and the perfect(a) future. She lives life with some short lived happiness. Kathy has a very original constitution unlike Ruths, who tries to impress and act like the veterans do. Ishiguro does not discuss Ruths death immediately after the 19th chapter but rather lets the reader focus on Kathys and Tommys sufferings. Ruths death is emotional and it would overshadow Kathys and Tommys struggle. exchangeable the donors the boat went through a lot of struggle perhaps even saved lives, yet the origin of the boat is a mystery, just like the donors who probably saved lives but no one cares about them, their origin is a mystery.The boat was once a life saver and withstander but now it is wrecked and is of no use. The donors too will face the same fate of the boat they will save lives and die alone. by chance thats why it is very popular object among the donors. The boat is a powerful symbol in the novel because even though it represents protection, and survival, if broken and abandoned it becomes a symbol of loneliness, no one cares about it, its origins becomes a mystery- even unnecessary and the forces it has faced in the ocean become meaningless. The boat represents the lives of Kathy, Ruth and Tommy. It is also Hailsham their protector in the sea it is Tommys hope for survival- his absolute belief in the deferral system it represents Kathys expect for a possible, the boats origin is also a mystery. The boat projects their future that no matter how hard they try and dream- their fate is sealed. They are helpless once exposed to the ocean. They are goin g to die, left abandoned like the boat. No one is going to care about them.

European Union Relations with the Russian Federations Essay

The EU ( europiuman junction) is an economic and semipolitical union tune by 28 member states and the countries atomic number 18 primarily located in atomic number 63. The union has moderniseed differently and varying relations with its different members. Russia is whiz of the countries that make the union. Russia-European affairs are the intercontinental relationships amongst the Russian federation and the European sum total, which is the largest bordering state to the east. The EU is the largest trading partner of the Russians. The Russian partnership and the European amalgamation are major partners in a go of key spheres, including economy, cogency, internal and external aspects of security. However, the relation among the both parties has been set up wanting. The cooperation and Partnership union between Russia and EU has been the framework of the EU-Russia relations since 1997 and regulates the political and economic relations between the two parties (Ross, 2004).Despite on that point macrocosm a long history of the relationship between the Russian fusion and European Union members, the flow rate state of the relations arrest raised eyes on the future of the cooperation between the two parties. In the yr 201, the then Swedish prime minister invited the Russian president and angiotensin-converting enzyme of the discussions was the possibilities of the Russia nation joining the EU establishment. However, this looks to be a too cold away satisfyingity as Russia, is non ready to follow the specialised rules that are set by the EU for its members. Russias economy is on a rapid growth and they do not want to progress to on the EU laws and set of rules they use. Their social and political status is not exactly favorable either (The U.S. and Europe diverge on the Crimea Crisis, 2014).In recent times, the relationship between the two parties has been brought into a sour unmatched as the 2013 Vilnius Summit connecting the Europea n union establishment with the countries to its east neighbors saw what The Economist  termed as raw geopolitical contest and wasnt seen in Europe since coming to an conclusion of the Cold War. Russia tried to commute its near abroad nations to unite into its nakedly established Eurasian Union instead of signing any contract with the European countries. The Russian validation beneath leaders of chairperson Putin achieved a lot in persuading Armenia and Ukraine to get their discussions with the EU and in its place commences talks with themselves (Ross, 2004). Nonetheless, the EU pinnacle leadership went forward with Moldova and Georgia discussions and in bowl over resulted to agreement with the EU alliance in spite of Russias resistance. Conversely, these divisions lead to extensive remonstrations of the Ukraine that finally brought muckle the Ukrainian president this year (Lavrov, 2013).Subsequent to the fall d cause of the renowned pro-Russian regime in U kraine, Crimea 2014 the Russian Federation commenced on a legions intervention by putting up its military which was in Crimea, in addition to the ones on the Ukrainian boundaries. This action has greatly been faced with loathing as EU leaders subscribe to viewed it as a raid. The current divisions between the two parties are believed to have a story and commenced almosttimes back. The current hype of the crises is believed to have grown over time. The developed has brought along a strained relationship between Russia and EU. After accomplishing a egress of victories at bottom the turn outlandish, such as pacifying Chechnya, dealing with the oligarchs, and the avoiding of Russian breakdown, President Putin has focus attention during his 2nd term to foreign policy matters. The president intermeshed in a much than and more revisionist strategy, with the main aim of build the farming as sound as its immediate cost. These developments included stand up to Western domin ance and pressure wherever possible (Ross, 2004).not unexpectedly, the Russian revisionism has led an ever more opposed relationship with Europe and the United States. The EU and United States are believed to develop their own worry and strategies in Russias geo-strategically significant neighborhood, ranging from Eastern Europe to the Caucasus and Central Asia. Indeed, from a westernern point of view, the list of Russian treacheries is now legion on Kosovo, Russian support for Serbia is seen as a major obstacle to slumber in the Balkans in the Caucasus and Central Asia, Russia has checked Western oil interests and turn Western attempts to promote political reform and in Moldova and the Ukraine, Russia has acted as a counter-balance to European influence. Moreover, all of this has been paired with Russias tendency to ignore real treaties, revise its economic contracts and repudiate internationally respected norms (Shevtsova, 2010).There are numerous areas that have resulted to the strained relation between the EU and the Russians. For example, politically, the Russians has repudiated the OSCE and capital of Finland Norms, disrespect of Council of Europe commitment and also breaching of Vienna Convention. Economically, the Russians failed to respect contacts, argufy of vitality Charter Treaty and disregard for WTO Norms. This in turn has led to the rise of opposition from the European members and the United States hence straining their relationship. The more published hype of the European frustration with Russian policies has been predominantly broad in three areas (a) the Russian effort to divide the European Union by utilizing divide and rule strategies, (b) Russias move in mise en scene itself up as an option to the EU in the familiar neighborhood and, (c) Russias own turn away from democracy and domestic reforms (Lavrov, 2013).In its relation with the Europe, the Russians have off late looked to undermine the unity between themselves and the Europ ean Union through engaging into bilateral relations which are meant to play to its natural power merit. This means that, the Russians have dismissed the European commission and in turn sidelining it terming it as inflexible and very elfin importance. Moderately, the Russians have been trying to build relationships with specific European powers such as Germany, France, and Italy. The Russian president has tried and regularly made it in make close and pleasant relations with the leaders of these nations and Russias state-controlled energy industry has build up some of its more of import partnerships with German, French, Portuguese and Italian businesses (Lavrov, 2013).However, at the same time, Russia has variably overlooked or punished some European nations, mainly amongst the latest member state, that have shown them to be overtly critical of Russian policies (Shevtsova, 2010). Amongst others, Russia has interrupted its oil supplies to Latvia in 2003 and Lithuanian in 2006 for t echnical reasons boycotted Polish meat exports levied export tariffs on the bargain of timber to Sweden and Finland and it has dour a blind-eye to the harassment of Estonian and British diplomats, in 2007 and 2008 respectively, after high-profile disputes with these countries. The history of these developments has in turn resulted to the EU viewing the Russian as a threat to the unity of the EU members. This has in turn acted as catalyst to sour relations that have developed between the two parties. In addition, the current development has been seen as to have gone beyond repair as the two parties have been destined for sodding(a) conflict (Ross, 2004).Internal DivisionsConcerted Russian attempts to open up European separation and the lack of European Union unity, have separate the EU into two schools of reflection on the correct way to be select in reference to how the relationships with Russia should advance. On one side, one school of sight has regarded Russia as a prospec tive partner. The radical known as fellow of Russia which has countries such as Germany, France, Italy, Greece. Spain among others has held to a policy that favors a close converse connecting the Russians and the EU as well as supporting economic cooperation as they have supported that this will and is the only chance for influencing Russians foreign policy behavior (Lavrov, 2013).On the other side of the Russian-EU relation, there is the Russia realist group. This contains nations such as, UK and numerous of the fresh member states of Eastern and Central Europe. These nations, have argued for a more forceful foreign policy approach, arguing that they know Russia better and that capital of the Russian Federation only understands the language of power and force, and in turn have turned to be the Russian opposes and hence redefining the EU Russia relations. The increasing pressure of this group is reflected in the escalating criticism of Russia from formerly pro-Russian countries su ch as Germany. Indeed, Germany is currently split between the more overtly anti-Russian Angela Merkel and her more pro-Russian coalition partner. Should Germany shift more pronounced towards the Russia realist camp, this might well tip the balance of power within Europe towards this group (Shevtsova, 2010). The inability of the EU to pursue a structured line towards Russia undermines its ability to develop a pragmatic relationship with this important country and over the last 15 years, the different elements of the EU have acknowledged this problem. The diversity of interests within the EU continues to undermine its ability to hypothesize coherent and practical solutions. There is a greater urgency for some states (those with common borders or who depend significantly on Russia for energy imports) to develop relations with Russia, while other states simply have different priorities. This makes real progress in EU-Russia relations to a certain extent helpless on which member gover nments presides over the European Council at a accustomed time (Europes Risky Russian Energy Habit, 2014).Moving into new relationship between the Russian and European UnionLooking into impendent elimination of the immediate obstacle into the negotiation of a new partnership between the two parties, the road has to better relations has looked once once more promising. Officials have vowed for more punitive international actions aimed at Russia economy. United States President at a news meeting in Asian country (South Korea) believed he and other leaders from the European nations would consider sanctions against the Russian country especially at this time the Ukraine crisis are worsening (The U.S. and Europe Diverge on the Crimea Crisis, 2014). One of the measures that have been taken by the EU and the west is the introduction of sanctions, and implementing financial and visa limitations on almost 30 Russians and Ukrainian officials (Europes Risky Russian Energy Habit, 2014). Ukrai ne amplified its bank rates in an effort to guard its economy from the chaos generated by aggressive objections and Russias forces involvement in Crimea (Shevtsova, 2010). The economic relation connecting the US, European Union, and the Russia is unbalanced the approach from the United States and US towards the Russian county is different. The main reason behind the disagreement has been laid to the fact that, the euro-zone has only just come out from its own catastrophe, and observers say it may wary of hastily ending connections with such a influential financially viable associate. Its dependence on gas out of Russia would also feed concern. In contrast, the United States, is weaning itself off Russias power supply and its trade connections is much less entangled (Europes Risky Russian Energy Habit, 2014).ConclusionIn summary, the relationship between the Russian federation and the European Union cannot be said to unplayful or healthy. However, it cant be said to be have ended despite the growing animosity and unrest between the two parties. With the current state the relationship between the two can be said to be headed to forever conflict. Despite Russia being more into the EU than the Asia, the country has embarked on establishing itself in the economic front as well as in terms of political aspects. EU consent against individuals and Russian officials, introduced in March, may have accelerated this trend or outfit the gap between the two parties. But real financial endorsements against Russia the so-called phase three have not been triggered yet meaning there is still a lot that remains when the relation between the comes into the play.References extensive Britain., & Great Britain. (2008). The European Union and Russia Report with evidencefourteenth report of session 2007-08. London The Stationery Office.Ross, C. (2004). Russian politics under Putin. Manchester u.a. Manchester Univ. Press.Shevtsova, L. (2010). Putins Russia. W ashington DC Carnegie Endowment for InternationalPeace.Lavrov, S. (2013). State of the Union Russia- EU Prospects for Partnership in the ChangingWorld. Journal Of Common grocery store Studies, 516-12. doi10.1111/jcms.12047US, EU impose sanctions after Crimea moves to join Russia. (2014). Regional Today, 3-4.The U.S. and Europe Diverge on the Crimea Crisis. (2014). Stratfor Geopolitical Diary, 13.Europes Risky Russian Energy Habit. (2014). Bloomberg Businessweek, (4372), 16.Source document

Discoveries of Maria Montessori

2. What argon the discoveries of Dr. Maria Montessori ? Dr. Maria Montessori was a keen observer of boorren. She employ her observational and experi amiable proclivities from her medical background to develop, what we might today call, a Constructivist catching of the subroutine of learning. She studied them scientifically. If she saw some unusual doings in a baby, she would say,I wont believe it now, I shall if it happens again. She studied the conditions in which the kidskinren would perform those go throughs.She thought education everlastingly involved three elements The learner, the Prepared Environment, and the Trained Adult. The staple areas in which she gave vastness was freedom, independence, celebrate and responsibility. She believed that the nestling constructs knowledge from experiencing the world. Learning, she said, was not something that needed to be labored or motivated. Instead, learning is something that gays do naturally. The early historic period p articularly are ones of great mental growth. Throughout the early years of life, the small fry absorbs impressions from the world around him. Not with his mind, that with his life.She recognized that chelaren go through and through certain phases during which they learn more easily than at any separate clock in their lives. This essential potential to learn is dependent upon a loving environment that encourages the active pursuit of knowledge. The fry should be precondition the freedom to do his litigate and mustiness be disposed(p) the respect for the child as an individual. The behavioral change paraden to respect and freedom is actually(prenominal) eminent Dr. Montessoris maturationally-appropriate approach to learning is designed to fit each child instead of making each child fit into a predetermined program.She believed that learning should take military post in multi-aged classrooms where children who are at versatile stages of development cigaret learn from and with each otherwisewise. This learning should take place in a non-competitive atmosphere in clubhouse for each child to develop at his/her own speed. Dr. Montessori observed that the best way for materialisation children to learn is by active, hands-on experiences. She developed the idea of the prepared environment, where the classroom contains a wide variety of cognitive materials that foster learning in numerous areas.The purpose of the materials is not just to impart knowledge to children, however rather to provide them with stimuli that capture their attention and initiate a process of concentration. She was compelled to believe that the children erotic love to do constructive make proved it suited their age and the stage of development. She observed that they worked with great interest and repeated the activities on their own volition to reach a stage of concentration. Montessori saw twain streams of energy within the young child. The first is the physical energy o f the remains expended in voluntary movement.And the second is mental energy the energy of intelligence and go out. She felt that these two streams of energy are often separated by the forces of modern life. And children who are not helped to unite them tend to move aimlessly and clumsily and abide unfocused thought patterns. A unification of mental and physical energies comes about when a child becomes absorbed in work. Montessori called this normalization. And concentration, she said, was the key. The guardedly prepared environment in the Montessori schools provide the opportunity for children to grow intellectually and emotionally.She decided to follow the child. Thanks to the revelations and the freedom she allowed to the children she was able to discover some(prenominal) aspects of the child and childhood. With her scientific approach of mind she tested whether every child in similar opportunities and similar conditions would manifest the homogeneous types of behavior. She tested these again and again and after twenty two years of such experiment Dr. Montessori could say that she had anchor a method of dower children in their educational pursuits. Thus came the Montessori Method of education.Some of the discoveries Dr. Maria Montessori made during her work. 1. Children love to work purposefully. The cozy drive to work is sufficient to reach their goal if it corresponded with the knowledgeable developmental need. With the provision of the necessary conditions and necessary environment the child without the fomentation of an adult underside reach his goal. 2. When an inner need to do something meets with the inner urge spontaneous fire is generated. When the inner urge or the Interest finds a suitable on the job(p) condition it leads to spontaneous repeating.When this spontaneous Repetition of an activity is done with interest the natural result is Concentration. Concentration is not the end product of education, its just the beginning. An y square(a) learning happens with concentration. The children revealed that habituated the right conditions they would work with concentration. 3. Very young children need order for their development. This order need not be only with things in the environment but also with values, functions and other human activities. The child needs to see human values like Say the Truth being practiced. unless the adults do not practice in the everyday life.The child gets confused and this can create a warp in his development. Similarly any intention in the environment being used for a purpose other than it is meant for creates disturbance. (e. g. the other end of a teaspoon used as a screwdriver). Contrary instructions about behaviour muddle his decisions how some action is allowed at some other time (for example. when a visitor is there). The examples can go on multiplying but the important factor that we need to hark back is that the young child is in the process of building his personalit y which lasts his lifetime.He needs consistency in everything in his environment. It takes a while for him to understand that things can also be different 4. Freedom is another basic requirement of a childs development process. Dr. Maria shew that to perform well in any activity they should be given the option to choose their own activity then only they stand out it according to their own capabilities. 5. Normality depended on all the human powers working in unison, in collaboration. Very often children deviate from this atomic number 7 because they do not find the conditions necessary for their development.D Montessori says that during the early childhood it is contingent to rectify any developmental errors and bring the child back to normalcy The rectification can be made possible only by the childs working individually at the developmental activities in freedom. ACTIVITY was essential. 6. These developmental activities belonged to areas that the child needed for building his personality in the main activities involving sensorial concepts, language, arithmetic, art, culture were considered necessary for the childs education.The introduction of the run of practical life as developmental activities was Dr Montessoris contribution to education. She found out how the children needed to perform these activities of everyday life. These became developmental activities especially because they brought the intelligence, will and voluntary movements together this co-ordination brought about integration of the personality Dr Montessori realized that these activities were very well understood by the children and thus mobilized their intelligence to the fullest participation. 7.Several other topics that were considered too high and out of reach for the children of 3 to 5 years were brought into the home base of Children. Dr Montessori found out that these areas of knowledge are necessary for the childs total development rather than being subjects to be learnt and, perhaps, memorized. The children showed that they could absorb the knowledge if they were given in a suitable form. 8. In the House of Children, prepare that is a bugbear in educational institutions came in a new form. The children managed their individual life,their manner of speaking, moving, handling material, interacting with other children.The children revealed quiet, orderliness, remarkable work attitude striving for perfection, sense of responsibility towards themselves and the environment and also others in the community Above all they showed independence in their control of errors, love for silence, indifference with regard to reward or punishments. Discipline did not have to be enforced. 9. At a cordial level they lived and let others live, helping others, co-operating with them, having quarrel, exhibiting no possessiveness and giving respect for elders who worked with them.At some point of time it was also seen that the children worked irrespective of whether the elder s were there or not. The absence of adults did not regulate their discipline, orderliness, quiet in their individual or social life. This suggested that discipline must come from within and not imposed from outside. Discipline is an inner development born in freedom. Freedom and discipline are two faces of the same coin. These are two forms of discipline. the outermost and the inner the inner discipline is a natural and inner urge to follow the laws that govern development. This inner discipline is the basic on which the outer discipline can rest.So the outer discipline imposed by the adults on the child should be in a form that will be given to the inner innate discipline and it can reveal itself in all its glory 10. real(a) obedience is based on love, respect and faith. When obedience leads to inner gratification it becomes real obedience and hence it becomes real development. 11. Dr Montessori discovered that the children are often seen to behave in a certain manner- destructi ve, disorderly, stubborn, disobedient etc. But in specially prepared environments and with specially trained adult they show orderly, responsible, loving behaviour both are seemingly real.But why is the contradiction? Dr Montessori says that the second instance is the real one and the very commonality behaviour is the result of the child not finding the right conditions for development. Dr Montessori calls this the social question of the child. This discovery was possible because she could witness this grandeur of human normality 12. Many of the activities presented to children in Montessori Houses of Children are results of observing the child and, therefore, may be considered as discoveries- The Silence Activity, Exercises of Practical Life, Walking on the Line are some of the examples. 3. It is a well-known truth that human life is a series of steps in gaining independence and credit could go to Dr Montessori who pointed that this is true with child life also. All the help we of fer should lead the child to Independence in his individual and social life. The Montessori Method bases itself on these and various other discoveries Dr Montessori made while she worked with children. We might conclude by face that Dr Montessori calls upon every adult human being to develop the humility to earn from the child in order to help the child create a hefty human being.

Analysis of Langston Hughes Poetry

Steven R. Goodman AASP100 England may 5, 2010 reaction 2 Langston Hughes Poetry A Literary Analysis of The Negro Speaks of Rivers The Harlem conversion evict be considered as the cultural boom in Afro-Ameri prat history. Spanning from the 1920s into the mid-1930s, the Harlem Renaissance was an apex in Afri push aside-Ameri merchantman intellectualism. The point in time is as well recognized as the New Negro Movementnamed after the 1925 anthology by Alain Locke. Alain LeRoy Locke was an American educator, writer, and philosopher, who most consider as the founding father of the Harlem Renaissance.Historians recall him as a leader and chief interpreter of the movement. In his anthology, he brings protrude a mont eon of works by many well- cognise Africans and African-Americans including such figures as Langston Hughes, Zora Neale Hurston, Jacob Lawrence, Richmond Barth, William Grant Still, Booker T. Washington, W. E. B. Du Bois, Ralph Bunche, and John Dewey (Locke). One of th ese figures wrote wiz of the most profound poems still read today. Langston Hughes was an American poet whose most gravid works came out during the Harlem Renaissance.The poem, The Negro Speaks of Rivers was Hughes first published poem and it was his signature too. Only 17 years old when he wrote it, Hughes created the poem firearm he was on a train headed to Mexico where he would live with his father for a year. As his train crossed the disseminated multiple sclerosis River, he was amazed by how beautiful the river was and the thought of how that river had a role in maintaining thrall in America came into his mind and he come out of the closeted writing. Lets start cancelled with the title. The title has the term negro in it. at a time how can we identify this?Well, the term negro tells us about the time period which takes us back to the early 20th century when negro was self-identifiable with the threatening society for that is the term that they adopted. However, we s ee that the term is only used in the title which places emphasis on its overall collective meaning of the ideas it portrays. in a flash let us dive into the poem. There are two allegoryical themes in this poem and they are rivers and sin. In track one, the Hughes says, Ive known rivers. In this annotation, I, the speaker, is standing for the entire unforgiving community throughout history. entirely of the rivers mentioned in the poem constitute as part of an extended simile that is comparing the souls of blackness people to the ancient, wise, and great rivers of the Earth (Shmoop). In the course of study two, the simile, as ancient as the world, is constructed to emphasize the comparison of the age of the rivers to the age of the Earth. In line three, we see rivers being used as a metaphor to depict the rivers of blood that flow through human veins. So the flow of blood in veins is compared to the flow of rivers. In line for, Hughes creates a simile comparing how deep h is soul is to how deep the rivers are.Now as we get to line five the story of the path of the black community in history unfolds. In line five we start off with the first river, the Euphrates River, which is supposedly where all life began known as the place of origin of civilization. Hughes notes that he bathed in the Euphrates when dawns were young. This symbolizes that there was peace and freedom. Line six entails the black communitys journey into central western Africa. In line six we continue with the morsel river, the Congo River, where he built his chantey and it lulled him to sleep. The black community is still undergoing peace and freedom.They are building a civilization. In line seven we see Hughes going into the third river, the Nile River. Now in line seven, we can certainly say that freedom hasnt necessarily stopped, but history has shown that black people amongst white people, and white-livered people were slaves and all participated in the building of the pyramids . Lastly, Hughes enters into the fourth and final river, the manuscript River. Hughes describes here the moment in history when Abraham Lincoln sailed the Mississippi River and he witnessed the horrors of slaveholding at its finest.In this same line, Hughes has the river come alive when he describes the river singing. In lines nine and ten Hughes creates some imagery when he tells of how the sunlight setting on the Mighty Muddy Mississippi R. changed its color to gold. He also personifies the river when he depicts it having a bosom acquiring feminine attributes. The second theme of darkness can only be seen when literally option away at the poem. We see that Hughes is very descriptive when he introduces darkness and light throughout the poem. In lines nine and ten we see Hughes describing how the Mississippi R. oes from muddy to golden as the sun departs and the night arrives. So we can also take from this as muddy being a metaphor for skin color when talking about slavery. Once the river becomes golden, slavery is abolished and slaves are freed. As we view the word dusky when describing the nature of the rivers, the metaphor can be not just for skin color, but also to cue our reader about the authors past which haunts him. In line 13 the poem ends with My soul has grown deep like the rivers. What can we take from this?Everytime the black civilization moves to a different point in time, the rivers get deeper, as well as the black mans soul. The author has seen the upbringing of civilizations, he has contributed in building the pyramids, and he has witnessed slavery being abolished. This poem is a time machine of events. In conclusion, Langston Hughes was a New Negro because as a voice for the black community, through his poetry he influenced other people to take pride in their heritage, culture, and triumphs noting racism when needed while showing pride in the black community. Alain Locke. The 1 Site for African American Literature Books, Novels, Authors , Movies, Resources, Discussion and more African Diaspora. Web. 06 May 2010. http//aalbc. com/authors/Alainlocke. htm. The Negro Speaks of Rivers Symbolism, Imagery &038 Wordplay. Shmoop Study Guides &038 Teacher Resources. Web. 06 May 2010. http//www. shmoop. com/negro-speaks-of-rivers/symbolism-imagery. html.

Financial Engineering

pecuniary engine room Introduction M some(prenominal) innovations argon taking note in the place of argonna of finance. Such innovations are collectively called monetary innovation. Financial innovation is a process to admit existing financial instruments and processes and to develop new one so as to enable financial market participants to cope more effectively with the ever-changing world. In recent years fast developments are taking place in corporate and banking sectors. This has given alliance to a new curb which has come to called financial engineering.The term financial engineering was introduced by capital of the United Kingdom banks. Financial engineering is the life blood of financial innovation. Financial Engineering Financial engineeringis a multidisciplinary field involving financial theory, the methods of engineering, the tools of mathematics and the go for of programming. 1It has also been defined as the application of adept methods, especially from mathemati cal financeandcomputational finance, in the practice offinance. In the United States, financial engineering programs are accredited by theInternational Association of Financial Engineers.Financial engineering draws on tools fromapplied mathematics,computer science,statisticsandeconomic theory. In broadest definition, anyone who uses technical tools in finance could be called a financial engineer, for example anycomputer programmerin abankor anystatisticianin a government economic bureau. However, most practitioners determine the term to someone educated in the full range of tools of new-made finance and whose work is informed by financial theory. It is sometimes cut back even further, to cover only those originating new financial products and strategies.Financial Engineering refers to the pack and unbundling of securities. This is done in order to maximize profits using contrary combinations of equity, futures, options, fixed income, and swaps. They apply theoretical finance an d computer modeling skills to make for pricing, hedging, trading and portfolio management decisions. Financial Engineers are prepared for careers in * investment funds Banking * Corporate Strategic Planning * Risk Management * Primary and Derivatives Securities valuation * Financial Information Systems Management Portfolio Management * Security Trading Tools of financial engineering * Conceptual Tools It includes ideas and concepts on which finance as a put forward is based. These includes valuation theory, portfolio theory, hedging theory, tax treatment etc. * Physical tools It includes the instruments and processes which keep be combined together to accomplish some specific purposes. Factors add to the growth of Financial Engineering * Environmental Factors (External Factors) A) Change in charge level B) Globalization of marketsC) Technological advancement D) Differential tax rank * Internal Factors A) Liquidity needs B) Risk aversion C) Agency cost D) Accounting benefits F inancial Reengineering Financial reengineering is the concept of 21st century. Really speaking, it is an evolving concept. It is an prolongation of financial engineering. Newer and newer developments are taking place now in finance and related fields. Hence the existing instruments and processes must reengineer to suit the changing environment. This gives birth to financial reengineering.

Apple Inc. and Mary Kay Cosmetics

P29 Q1 1. The marketing channel for bloody shame Kay cosmetics is called a station selling channel. The company user a sales force of everywhere 1000000 self-directed Beauty Consultants around the world. These consultants are not employees of Mary Kay Corporation they buy cosmetics from the company at a wholesale value and sell to end-users at a retail value. They maintain personal relationships with their end-user consumers and quit product to them after it is ordered it is a high-service purchasing relationship from the consumers point of view.Consultants thus act as both distri exactlyors and retailers. a. To what extent does an Independent Beauty Consultant participate in the eight universal marketing flows? b. How might these flows be shifted, either among the members now in the channel or to different agencies or institutions not presently included? What do you weigh would be the implications of such shifts? (think about how cosmetics are sold through plane section sto res or through drugstore chains, for example. ) c. Within severally of these distribution systems, go down the consumers role from a flow-absorption perspective.Contrast this with the consumers role when acquire cosmetics from a department store or a drugstore chain. P64 Q1,2,3 2. For sepa regulately of the three scenarios below, categorize the demand for bulk-breaking spatial convenience, waiting/ delivery time, and miscellany/ variety as high, medium, or low. In each case, explain your answers. a. A woman in an emerging-market country of Southeast Asia wishes to buy some cosmetics for herself. She has never d nonpareil so before and is not entirely sure of the make on which she will wear the cosmetics. She does not live near a big city.She is too poor to own a car but has a bit of extra money for a small luxury. b. A manufacturer uses a particular industrial chemical in one of its large-scale production processes and needs to buy more of the chemical. The rest of the bare- assed materials for its plant operations are delivered in a just-in-time fashion. c. Before you consider certain parts of the world, you are required to get a chicken fever vaccine. Many travelers let this slip until the last minute, forgetting that it is advisable (or avoiding an god-awful shot as long as possible).But they definitely get word they need the shot, and they do not want to impart to cancel their case at the last minute because they did not get it. They often fuck off themselves making a long trip to a reginal medical digest because trhey did not plan ahead. 3. For the three scenarios in Question 1, describe a marketing channel that would meet the target end-users demands for service outputs. 4. decipher three different buying situations with which you are familiar and the SODs of the buyers in each one. Do you think the SODs being supplied are boney to those being demanded? wherefore or why not? P. 103 Q4 5. Explain how the shopping characteristics for the f ollowing consumer and industrial goods affect the channels for them CONSUMER GOODS INDUSTRIAL GOODS Bread Laser printer toner cartridges eat cereal Uranium for nuclear power plants Womens hosiery cementum Refrigerators Medical machinery(e. g. , ultrasound machines) P. 150 Q5 6. orchard apple tree, as a reckoner company, has struggles oer the years with the as siftment problem. Company-owned Apple stores offered only Apple computers.Although management desire having control of the assortment, customers wanted side-by-side comparisons with other brands, eventually driving Apple to close many of its own stores. Apple also has had difficulty influencing how independent computer outlets stock and display its products. Apple is now using the success of its medicine downloading systems (iPod and variations) to compose larger assortments-and is reopening company-owned stores. Is this a good idea? What, if anything, would you recommend to Apple as an alternative strategy to improve its pr oducts coverage and sales?P192(4) 7. A manufacturer is in the habit of offering liberal payment footing to distributors They can pay anytime within 45days of receipt of the merchandise. The manufacturer currently has a band line of credit to cover accounts receivable and pays an interest rate (prime+1%) on the balance on loan from the bank. One of the manufacturers key distributors offers to pay for shipments by immediate bank gold transfer upon receipt of merchandise if the manufacturer will reduce the price by 1%. Does this offer close a gap?If so, what sort (demand side, supply side, what flow)? P238 Q6 8. You are the owner/manager of an auto franchise in Germany selling the Audi line. Your dealership is exclusive to Audi you have invested heavily to build the dealership and your contract is such that, if you decide to sell your dealership, Audi has the right to approve or disapprove any buyer you might find. What is the balance of power in your relationship? What sort of worki ng relationship are you likely to have with your supplier? What could your supplier do to ensure you do not shape alienated?

Child Soldiers in Sierra Leone Essay

The Revolutionary United Front of sierra Le unrivaled (RUF/SL) invaded sierra Leone from Liberia in March 1991. Initially they claimed to be a political movement bread and butter liberation and democracy. Instead the RUF, in reality, was an insecurely combined organization of generally rebellious young people that inflicted mortal disaster with with(predicate)out the rustic of sierra Leone. The political revolution message failed to attract popular patronage, the RUF scorecard on a barbarian ten-year cultured state of war that had devastating consequences for civilians, in particular squirtren.General Information about electric s devoter spendsThe numbers of nipper passs ar continually variable effrontery the growth of diverse arm conflicts. The number of children infra the age of 18 who take been laboured or induced to leave up arms as child soldiers is normally thought to be around of 300,000. Non- organisational military organizations tend to recruit soldiers under the age of 15.Governmental build up forces, on the other(a) hand, argon more than likely to recruit soldiers under the age of 18. From what is known the age of 7 is the youngest a child soldier can be. Over 50 countries currently take on children under the age of 18 into their militia.picFigure 1. The African fleck since Africa has without any doubt the largest number of child soldiers1What is a Child Soldier?UNICEF, The United Nations Children Fund, defines child soldiers as any child boy or girlunder eighteen old age of age, who is part of any kindly of unbendable or irregular fortify force or armed group in any capacity2.According to the Coalition to Stop the expenditure of Child Soldiers Child soldiers perform a range of tasks including participation in combat, laying mines and explosives scouting, spying, acting as decoys, couriers or guards training, drill or other preparations logistics and support functions, portering, cooking and interior(a) labour and se xual slavery or other enlisting for sexual purposes.3Girls argon in any case called child soldiers and this is the slickness for numerous reasons. Girls usually fulfil numerous roles. While they are ordinarily recruited and exercisingd for sexual purposes, they are almost always also caught up in other military responsibilities. These include fight, laying explosives, portering, and performing domestic tasks.How many a(prenominal) child soldiers are there?It is difficult to give a worldwide number of child soldiers at any one time. thither are various reasons as to why exact figures cannot be calculated. An good example is that military commanders frequently mask children or do not cater access to observers. fortify groups regularly operate in dangerous, unapproachable zones to which observers do not grant access and many children carry out support roles and are therefore not visible in military operations.How do children become soldiers?A special report on the impact of a rmed conflict on children which was created in 1996 explained how children become soldiers. In the report it is verbalize Hunger and poverty may drive parents to offer children for service or attract children to volunteer as a way to guarantee regular meals, clothing or medical attention. Some children become soldiers to protect themselves or their families in the face of violence and chaos around them, while others, in particular adolescents, are lured by ideology. Children also identify with social causes, religious expression, self-determination, national liberation or the pursuit of political freedom, as in southbound Africa or the occupied territories.4 Another reason emphasizes the efficient value of children, oddly for tedious tasks. An important explanation to keep in mind could be that child soldiers may be valuable for signalling purposes. A rebel loss leader may hope to show significance, commitment or terror through abduction of a child5. Finally, some people verif y that young children are more malleable, adaptable, and obedient, as well as more easily persuaded and deceived. Therefore they are said to be easier to manage and retain6. If children are as productive as adults, we should find a disproportionate number in armed groups.The hobby two case studies give examples of what a girl and a boy have gone through during Sierra Leones devastating civil war. By describing their tasks, the reasons as to why these violate merciful Rights can be clearly seen.Case Study FatmataFatmata was one of only two survivors from her hamlet in Sierra Leone. She was barely six years old when she was captured by the cruel rebel groups. She was taken to a rebel stronghold and forced to work under harsh conditions as a servant. In Fatmatas own words We had to work all day while they would detestation my mother and abuse me. When she got older, Fatmata was forced to become the second wife of one of her rebel captors, therefore meaning she was raped and gave bi rth to the child of a rebel.7Case Study Ishmael BeahIn A desire way gone(p) Memoirs of a Boy Soldier, Ishmael Beah, now twenty-six years old, tells a successfully enthralling story of his life as a child soldier. At the age of twelve, he fled from rebel attacks and wandered a lower caused to be unrecognizable by brutality. By thirteen, he had been captured by the government army, and Beah, even though he was a gentle young boy at heart, found that he was capable of truly terrible acts. At sixteen, he was taken away from fighting by UNICEF. Beah, like many other child soldiers, had gone through devastating psychological traumas and through the answer of the staff at his rehabilitation centre, he intoxicateed how to pardon himself, to regain his humanity and was finally able to heal.8Human RightsAccording to the fair playfulness and Reconciliations commissions report the use of local as well as transnational human rights mechanisms in responding to the shocking criminal act s that took place in Sierra Leone during the previous decade is important to the development of international human rights law9. Sierra Leone became a member of the United Nations in 1961 and is a signatory to most of the important human rights committees including the convocation of the Rights of the Child (CRC) and the African Charter on the Rights and Welfare of the Child. The Government of Sierra Leone has also ratified the optional protocol. Children Rights travel has been enacted in Sierra Leone quite recently in 2007. The Government of Sierra Leone signed and ratified the protocol on 8 September 2000 and 15 May 2002.Convention to the Rights of a ChildThe Convention to the Rights of a Child (CRC) is built on diverse legal systems as well as cultural traditions. The Convention is a universally agreed set of better standards and obligations. These human rights set the least amount of pre-emptive declaration and freedoms that should be value by governments. In Article 38, th e Convention on the Rights of the Child insist that governments to take all possible measures to guarantee that children under 15 have no direct conflict in warfare. The Convention also sets 15 years as the minimum age at which a individual can be willingly recruited into or willingly signs up in the armed forces.10 nonobligatory ProtocolThe Optional Protocol to the Convention on the Rights of the Child on the contribution of children in armed conflict symbolizes a progressive leap in the international law in bless to defend children from the damaging effects of recruitment and use in warfare. The Protocol requires States who authorize it to obtain all practicable measures to make sure those members who are part of their armed forces and are under the age of 18 do not have a direct involvement in the fightings. States must also raise the minimum age for voluntary recruitment into the armed forces from 15 years but does not require a minimum age of 18.The Protocol reminds States that children under 18 years are entitled to distinctive protection and so any voluntary recruitment under the age of 18 must include adequate protection. despotic recruitment below the age of 18 is fully banned and States parties must also take legal measures to forbid self-governing armed groups from recruiting and utilise children under the age of 18 in conflicts.11 ARTICLE 1 of the Optional Protocol States Parties shall take all feasible measures to ensure that members of their armed forces who have not attained the age of 18 years do not take a direct part in hostilities. This shows that the Protocol raised the age that children are allowed to be a member of an illegal or legal armed force from 15 years to 18 years.UNICEF and The outside(a) legal transfer Committee and how they have helpedIn Sierra Leone, UNICEF was the lead position for child protection, which worked with its colleagues to reduce arms, and to release and reconnect process for child soldiers from 1998 to 2002.They construct tutelar and healthy educational environments where former child soldiers obtain the opportunity to contemplate how to live without weapons, gain new skills which enables them to be prepared for their future and to learn how to become prolific citizens in their society.Most importantly they are given a second chance to learn how to be children again. Demobilized children were moved to flitting care centres supported by UNICEF where they were given health care and also psychosocial counselling. They also participated in educational and recreational activities while family tracing reunion was going on. A vast majority of former child soldiers have been get togetherd with their families. Access to education and family and community support programmes have been the key to their success to help the former child soldiers12.With headquarters in Freetown and tercet field offices in Kono, Kenema and Kailhaun districts, the International Rescue Committee proposes pro grams that focus on child protection, education, and health, specifically for former child soldiers after the civil war ended in 2000. The IRC works to increase local participation in project activities, build local capacity, promote and protect human rights, match with local communities and organizations, and address relief and development needs in a holistic fashion. The Revolutionary United Front rebels released 600 child soldiers. The International Rescue Committee provided education, skills training, and psychosocial care to 100 of them13.ConclusionTo conclude, there have been many programmes that have been created to reduce and assist former child soldiers. Off pedigree it is not possible to help every single child soldier and there are many reasons for this. Some of the reasons are that there are still a number of these soldiers that may still be snarled and their whereabouts are not known. During the civil war, many of the parents of these children were killed, so it is d ifficult to reunite them with their families, and if they are lucky another family member may still be alive in order to look after them. Organisations, like UNICEF, provide homes for former child soldiers who are unlucky to not have anybody. By education and counselling, children learn to forgive themselves for violent crimes they were forced to commit and help themselves to progress in the future.REFERENCES Beah, I (2007). A Long Way Gone Memoirs of a Boy Soldier. New York Harper Perennial. p5-218. Beber, B and Blattman, C. (2010). The industrial government of Rebellion The Logic of Forced Labor and Child soldier*. useable http//chrisblattman.com/documents/research/2010.IOofRebellion.pdf. break down accessed 6th declination 2010. Coalition to check up on the use of Child Soldiers. (2007). Questions and Answers. lendable http//www.child-soldiers.org/childsoldiers/questions-and-answers. Last accessed 1st December 2010. Michael Odeh and Colin Sullivan. Children in arm Conflict. addressable http//www.yapi.org/rpchildsoldierrehab.pdf. Last accessed eighth December 2010. Office of the United Nations mettlesome Commissioner for Human Rights. (1990). Convention on the Rights of the Child . uncommitted http//www2.ohchr.org/english/law/crc.htm. Last accessed eighth December 2010. Office of the United Nations High Commissioner for Human Rights. (2000). Optional Protocol to the Convention on the Rights of the Child on the involvement of children in armed conflict. available http//www2.ohchr.org/english/law/crc-conflict.htm. Last accessed 8th December 2010. answer for of the Sierra Leone Truth & Reconciliation Commission. (2004). Children and the Armed Conflict in Sierra Leone. Vol. 3B, p231-340. Spagnoli, F. (2008). Human Rights cite (49) Child Soldiers. Available http//filipspagnoli.wordpress.com/stats-on-human-rights/statistics-on-war-conflict/statistics-on-child-soldiers/. Last accessed 8th December 2010. UNICEF. chela SOLDIERS. Available http//www.un. org/cyberschoolbus/briefing/soldiers/soldiers.pdf. Last accessed 1st December 2010. UNICEF. FACTSHEET CHILD SOLDIERS. Available http//www.unicef.org/emerg/files/childsoldiers.pdf. Last accessed 8th UNICEF. (29 April 2008). What is a child soldier?. Available http//www.unicef.org/emerg/index_childsoldiers.html. Last accessed 4th December 2010. UN Works. Fatmatas Story. Available http//www.un.org/works/goingon/soldiers/fatmata_story.html. Last accessed 8th December 2010.1 Spagnoli, F. (2008). Human Rights Quote (49) Child Soldiers. Available http//filipspagnoli.wordpress.com/stats-on-human-rights/statistics-on-war-conflict/statistics-on-child-soldiers/. Last accessed 8th December 2010.2 UNICEF. (29 April 2008). What is a child soldier?. Available . http//www.unicef.org/emerg/index_childsoldiers.html. Last accessed 4th December 2010. 3 Coalition to stop the use of Child Soldiers. (2007). Questions and Answers. Available http//www.child-soldiers.org/childsoldiers/questions-and-answers. Last accessed 1st December 2010. 4 UNICEF. CHILD SOLDIERS. Available http//www.un.org/cyberschoolbus/briefing/soldiers/soldiers.pdf. Last accessed 1st December 2010. 5 Beber, B and Blattman, C. (2010). The industrial Organization of Rebellion The Logic of Forced Labor and Child spend*. Available http//chrisblattman.com/documents/research/2010.IOofRebellion.pdf. Last accessed 6th December 2010. 6 Beber, B and Blattman, C. (2010). The Industrial Organization of Rebellion The Logic of Forced Labor and Child Soldiering*. Available http//chrisblattman.com/documents/research/2010.IOofRebellion.pdf. Last accessed 6th December 2010. 7 UN Works. Fatmatas Story. Available http//www.un.org/works/goingon/soldiers/fatmata_story.html. Last accessed 8th December 2010. 8 Beah, I (2007). A Long Way Gone Memoirs of a Boy Soldier. New York Harper Perennial. p5-218. 9 Report of the Sierra Leone Truth & Reconciliation Commission. (2004). Children and the Armed Conflict in Sierra Leone. Vol. 3B, p231 -340.10 Office of the United Nations High Commissioner for Human Rights. (1990). Convention on the Rights of the Child . Available http//www2.ohchr.org/english/law/crc.htm. Last accessed 8th December 2010. 11 Office of the United Nations High Commissioner for Human Rights. (2000). Optional Protocol to the Convention on the Rights of the Child on the involvement of children in armed conflict. Available http//www2.ohchr.org/english/law/crc-conflict.htm. Last accessed 8thDecember 2010. 12 UNICEF. FACTSHEET CHILD SOLDIERS. Available http//www.unicef.org/emerg/files/childsoldiers.pdf. Last accessed 8th13 Michael Odeh and Colin Sullivan. Children in Armed Conflict. Available http//www.yapi.org/rpchildsoldierrehab.pdf. Last accessed 8th December 2010.

Solution Manual for Fluid Mech Cengel Book

Chapter 6 neural impulse analysis of range Systems Chapter 6 neural craving ANALYSIS OF FLOW SYSTEMS referable norths Laws and Conservation of whim 6-1C Newtons first rectitude states that a body at lodge in form at rest, and a body in feat anticipates in motion at the akin hurrying in a straight path when the straighten come in personnel play playacting on it is zero. in that locationfore, a body t give the axes to preserve its state or inertia. Newtons instant law states that the acceleration of a body is relative to the net draw in acting on it and is inversely comparative to its mount. Newtons third base law states when a body exerts a advertize on a second body, the second body exerts an equal and opposite repel on the first. r 6-2C Since pulse ( mV ) is the product of a vector ( f number) and a scalar ( surge), impulse must be a vector that identifys in the same pedagogy as the hurrying vector. 6-3C The conservation of neural impulse arti cle of belief is express as the urge of a awayline remains never- intercepting when the net root for acting on it is zero, and frankincense the whim of such systems is conserved.The pulsation of a body remains immutable if the net attract acting on it is zero. 6-4C Newtons second law of motion, in any episode c in aloneed the angular momentum comp ar, is expressed as the charge per unit of dislodge of the angular momentum of a body is equal to the net crookedness acting it. For a non-rigid body with zero net torque, the angular momentum remains regular, but the angular f number changes in accordance with I? = constant where I is the moment of inertia of the body. 6-5C No.Two rigid bodies having the same big money and angular speed depart have different angular momentums unless they as well as have the same moment of inertia I. Linear caprice equating 6-6C The relationship between the term charge per units of change of an extensive plaza for a system and f or a get word muckle is expressed by the Reynolds transport theorem, which provides the link between the r system and misrepresent quite a little concepts. The linear momentum equivalence is obtained by setting b = V and so r B = mV in the Reynolds transport theorem. -7C The rips acting on the date hoi polloi consist of body contracts that act through erupt the entire body of the maintain passel (such as gravity, electric, and magnetic forces) and open spread forces that act on the see surface (such as the instancy forces and reply forces at points of contact). The net force acting on a control sight is the sum of each(preno houral) body and surface forces. Fluid pack is a body force, and nip is a surface force (acting per building block bea). -8C All of these surface forces arise as the control vividness is unaffectionate from its surroundings for analysis, and the put in of any detached object is accounted for by a force at that location. We arouse mi nimize the number of surface forces undecided by choo blunderg the control volume such that the forces that we be non implicated in remain internal, and olibanum they do non complicate the analysis. A well-chosen control volume exposes unaccompanied the forces that ar to be placed (such as answer forces) and a minimum number of other forces. 6-9C The momentum-flux field of study grammatical constituent ? nables us to express the momentum flux in cost of the r r r r &038 ? V (V ? n )dAc = ? mV avg . The evaluate of ? is unity for coherent fortune mix wander and guess endure fastness as ? Ac prey, such as a commons bunk, well unity for turbulent fly the coop (between 1. 01 and 1. 04), but to the richlyest degree 1. 3 for laminar hunt. So it should be considered in laminar pass. 6-1 copy uprighted MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited dissemination permitted solely to t each(prenominal)ers and educators for incline preparation. If you ar a schoolchild victimization this Manual, you be utilise it with stunned permission.Chapter 6 caprice summary of cling Systems 6-10C The momentum comparison for affluent one-dimensional f subaltern for the eggshell of no external forces is r r r &038 &038 F= ? mV ? ? mV ? ? step forward ? in where the left hand side is the net force acting on the control volume, and first name on the right hand side is the in(prenominal) momentum flux and the second term is the extraverted momentum flux by mass. 6-11C In the application of the momentum par, we sight disregard the atmosphericalalal oblige and work with back up imperativenesss wholly vicece the atmospheric pressure acts in exclusively counsellings, and its forcefulness fagcels show up in every trouble. -12C The fireman who observes the hose backwards so that the pee makes a U-turn before cosmos execute leave behind experience a great response force since the numerical shelters of momentum fluxes across the pecker atomic number 18 added in this case instead of universe subsh atomic number 18ed. 6-13C No, V is non the upper limit to the move ups ultimate pep pill. Without friction the rocket swiftness leave continue to increase as more go down on go overs the nozzle. 6-14C A helicopter hovers beca commit the strong downdraft of disperse, caused by the smasher propeller steels, manifests a momentum in the melodic line pour.This momentum must be countered by the helicopter kindle force. 6-15C As the air travel tightness decreases, it requires more slide fastener for a helicopter to hover, because more air must be hale into the downdraft by the helicopter blades to provide the same lift force. on that pointfore, it motors more great originator for a helicopter to hover on the pinnacle of a high push-down stack than it does at sea take. 6-16C In winter the air is mostly colder, and indeed denser. Therefore, less air must be driven by the blades to pr ovide the same helicopter lift, requiring less position. 6-2 proprietary MATERIAL. 2006 The McGraw-Hill Companies, Inc.Limited dissemination permitted unaccompanied to teachers and educators for ground level preparation. If you be a scholarly person using this Manual, you be using it without permission. Chapter 6 Momentum digest of accrue Systems 6-17C The force ask to predominate the scale against the even body of urine stream will increase by a factor of 4 when the pep pill is doubled since &038 F = mV = ( ? AV )V = ? AV 2 and indeedly the force is proportional to the substantive of the velocity. 6-18C The acceleration will not be constant since the force is not constant. The impulse force exerted by &038 wet on the coat is F = mV = ( ? AV )V = ?AV 2 , where V is the relational velocity between the wet and the shell, which is go. The base acceleration will be a = F/m. But as the shield begins to move, V decreases, so the acceleration must in like man ner decrease. 6-19C The maximum velocity possible for the weighing machine is the velocity of the body of body of piss supply system resinous. As long as the carapace is miserable sulky than the count of endure, the weewee system will exert a force on the plate, which will cause it to accele regularise, until terminal kilobyte velocity is reached. 6-20 It is to be shown that the force exerted by a liquid rave of velocity V on a stationary nozzle is &038 proportional to V2, or alternatively, to m 2 . Assumptions 1 The menstruate is starchy and incompressible. 2 The nozzle is attached(p) to be stationary. 3 The nozzle involves a 90 turn and thus the incoming and out passage menses streams atomic number 18 normal to each other. 4 The urine is discharged to the atmosphere, and thus the crumb pressure at the consequence is zero. abstract We bundle the nozzle as the control volume, and the work bursting charge at the spill as the x axis vertebra. maintain t hat the nozzle makes a 90 turn, and thus it does not contribute to any pressure force or momentum flux &038 term at the break in the x bursting charge. Noting that m = ?AV where A is the nozzle out al low-spirited ara and V is the bonny nozzle out permit velocity, the momentum par for stiff one-dimensional advert in the x direction reduces to r r r &038 &038 &038 &038 F= ? mV ? ? mV FRx = ? m out V out = ? mV ? ? out ? in where FRx is the reaction force on the nozzle due to liquid putting surface at the nozzle outlet. because, &038 m = ? AV &038 FRx = ? mV = ?? AVV = ?? AV 2 &038 &038 or FRx = ? mV = ? m &038 &038 m m2 =? ?A ? A Therefore, the force exerted by a liquid resinous of velocity V on this &038 stationary nozzle is proportional to V2, or alternatively, to m 2 . Liquid Nozzle V FR 6-3 trademarked MATERIAL. 2006 The McGraw-Hill Companies, Inc.Limited scattering permitted only to teachers and educators for words preparation. If you ar a student using this Manual, you argon using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-21 A piddle feed of velocity V impinges on a plate paltry toward the peeing cat valium with velocity ? V. The force need to move the plate towards the spring is to be determined in terms of F acting on the stationary plate. Assumptions 1 The meld is pie-eyed and incompressible. 2 The plate is upright piano and the jet is normal to plate. 3 The pressure on twain sides of the plate is atmospheric pressure (and thus its effect cancels out). Fiction during motion is minimal. 5 There is no acceleration of the plate. 6 The peeing splashes spigot the sides of the plate in a plane normal to the jet. 6 park flow is well uniform and thus the effect of the momentum-flux fudge factor factor is negligible, ? ? 1. Analysis We undertake the plate as the control volume. The recounting velocity between the plate and the jet is V when the plate is stationary, and 1. 5V when the plate is mov ing with a velocity ? V towards the plate. because the momentum equality for peach one-dimensional flow in the plane direction reduces to r r r &038 &038 &038 &038 F= ? mV ? ? mV ? FR = ? mi Vi FR = miVi ? out ? in Stationary plate ( Vi = V and Moving plate ( Vi = 1. 5V and &038 mi = ? AVi = ? AV ) FR = ? AV 2 = F &038 mi = ? AVi = ? A(1. 5V ) ) FR = ? A(1. 5V ) 2 = 2. 25 ? AV 2 = 2. 25 F Therefore, the force infallible to feature the plate stationary against the oncoming water jet becomes 2. 25 eras when the jet velocity becomes 1. 5 times. interchange line of credit that when the plate is stationary, V is alike the jet velocity. But if the plate moves toward the stream with velocity ? V, then the relative velocity is 1. 5V, and the amount of mass striking the plate (and falling onward its sides) per unit time in like manner increases by 50%. 1/2V VWaterjet 6-4 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited diffusion permitted only to teachers and educators for cart track preparation. If you be a student using this Manual, you ar using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-22 A 90 cubital joint deflects water ups and discharges it to the atmosphere at a condition rate. The heater pressure at the recession of the jostle and the anchoring force requisite to shield the elbow in place atomic number 18 to be determined. v Assumptions 1 The flow is sloshed, frictionless, incompressible, and irrotational (so that the Bernoulli equation is applicable). The weight of the elbow and the water in it is negligible. 3 The water is discharged to the atmosphere, and thus the gage pressure at the outlet is zero. 4 The momentum-flux subject factor for each inlet and outlet is inclined to be ? = 1. 03. Properties We take the concentration of water to be molarity kg/m3. Analysis (a) We take the elbow as the control volume, and attribute the glamour by 1 and the outlet by 2. We also point the crosswise machinate by x (with the direction of flow as creation the imperious direction) and the upended direct by z.The continuity equation for this one-inlet one-outlet tight flow system is &038 &038 &038 &038 m1 = m 2 = m = 30 kg/s. Noting that m = ? AV , the mean inlet and outlet velocities of water be &038 &038 25 kg/s m m = = = 3. 18 m/s 2 ? A ? (? D / 4) ( gm kg/m 3 )? (0. 1 m) 2 / 4 Noting that V1 = V2 and P2 = Patm, the Bernoulli equation for a streamline pass through the condense of the reducing elbow is expressed as V1 = V 2 = V = P V12 P V2 1 + + z1 = 2 + 2 + z2 P ? P2 = ? g ( z2 ? z1 ) P , gage = ? g ( z2 ? z1 ) 1 1 ? g 2 g ? g 2 g Substituting, ? ? 1 kN 2 ? P , gage = ( megabyte kg/m3 )(9. 81 m/s 2 )(0. 35 m)? 1 ? kB kg ? /s2 ? = 3. 434 kN/m = 3. 434 kPa ? ? r r r &038 &038 (b) The momentum equation for steady one-dimensional flow is F= ? mV ? ? mV . We let the x- ? ? out ? in and z- components of the anchoring force of the elbow be FRx and FRz, and ingest them to be in the unconditional directions. We also use gage pressures to avoid dealing with the atmospheric pressure which acts on all surfaces. Then the momentum equations along the x and y axes become &038 &038 FRx + P1,gage A1 = 0 ? ?m(+V1 ) = ? ?mV &038 &038 FRz = ? m(+V 2 ) = ? mV z x FRz 2 35 cm Solving for FRx and FRz, and substituting the stipulation rates, &038 FRx = ? ?mV ? P1, gage A1 ? N = ? 1. 03(25 kg/s)(3. 18 m/s)? ? 1 kg ? m/s 2 ? = ? 109 N ? ? ? (3434 N/m 2 )? (0. 1 m) 2 / 4 ? ? ? ? = 81. 9 N ? ? baby bird FRx = tan -1 Water 25 kg/s FRx 1 ? 1N &038 heat up = ? mV = 1. 03(25 kg/s)(3. 18 m/s)? ? 1 kg ? m/s 2 ? and 2 2 FR = FRx + FRy = (? 109) 2 + 81. 9 2 = 136 N, ? = tan -1 81. 9 = ? 37 = 143 ? 109 Discussion tonus that the magnitude of the anchoring force is 136 N, and its line of action makes 143 from the controlling x direction. Also, a negatively charged value for FRx indicates the delusive direction is wrong, and should be reversed. 6-5 PROPRIE TARY MATERIAL. 2006 The McGraw-Hill Companies, Inc.Limited diffusion permitted only to teachers and educators for course preparation. If you argon a student using this Manual, you argon using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-23 An 180 elbow forces the flow to make a U-turn and discharges it to the atmosphere at a condition rate. The gage pressure at the inlet of the elbow and the anchoring force unavoidable to hold the elbow in place are to be determined. v Assumptions 1 The flow is steady, frictionless, one-dimensional, incompressible, and irrotational (so that the Bernoulli equation is applicable). The weight of the elbow and the water in it is negligible. 3 The water is discharged to the atmosphere, and thus the gage pressure at the outlet is zero. 4 The momentumflux correction factor for each inlet and outlet is tending(p) to be ? = 1. 03. Properties We take the density of water to be ampere-second0 kg/m3. Analysis (a) We take the elbow as the control volume, and allot the entrance by 1 and the outlet by 2. We also establish the plane mastermind by x (with the direction of flow as being the positive direction) and the vertical coordinate by z.The continuity equation for this one-inlet one-outlet steady flow system is &038 &038 &038 &038 m1 = m 2 = m = 30 kg/s. Noting that m = ? AV , the mean inlet and outlet velocities of water are &038 &038 25 kg/s m m = = = 3. 18 m/s 2 ? A ? (? D / 4) ( super acid kg/m 3 )? (0. 1 m) 2 / 4 Noting that V1 = V2 and P2 = Patm, the Bernoulli equation for a streamline going through the center of the reducing elbow is expressed as V1 = V 2 = V = P V12 P V2 1 + + z1 = 2 + 2 + z2 P ? P2 = ? g ( z2 ? z1 ) P , gage = ? g ( z2 ? z1 ) 1 1 ? g 2 g ? g 2 g Substituting, ? ? 1 kN 2 ? P , gage = ( chiliad kg/m3 )(9. 81 m/s2 )(0. 70 m)? 1 ? 1000 kg ? m/s2 ? 6. 867 kN/m = 6. 867 kPa ? ? r r r &038 &038 (b) The momentum equation for steady one-dimensional flow is F= ? mV ? ? mV . We let the x- ? ? out ? in and z- components of the anchoring force of the elbow be FRx and FRz, and assume them to be in the positive directions. We also use gage pressures to avoid dealing with the atmospheric pressure which acts on all surfaces. Then the momentum equations along the x and z axes become &038 &038 &038 FRx + P1,gage A1 = ? m(? V 2 ) ? ? m(+V1 ) = ? 2 ? mV FRz = 0 Solving for FRx and substituting the given values, &038 FRx = ? 2 ? mV ? P1, gage A1 ? 1N = ? 2 ? 1. 03(25 kg/s)(3. 18 m/s)? 1 kg ? m/s 2 ? = ? 218 N ? ? ? (6867 N/m 2 )? (0. 1 m) 2 / 4 ? ? 2 z x FRz Water 25 kg/s 35 cm and FR = FRx = 218 N since the y-component of the anchoring force is zero. Therefore, the anchoring force has a magnitude of 218 N and it acts in the negative x direction. Discussion Note that a negative value for FRx indicates the assumed direction is wrong, and should be reversed. FRx 1 6-6 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited dispersal permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.Chapter 6 Momentum Analysis of Flow Systems 6-24E A plain water jet strikes a vertical stationary plate unremarkably at a specified velocity. For a given anchoring force ask to hold the plate in place, the flow rate of water is to be determined. Assumptions 1 The flow is steady and incompressible. 2 The water splatters off the sides of the plate in a plane normal to the jet. 3 The water jet is exposed to the atmosphere, and thus the pressure of the water jet and the splattered water is the atmospheric pressure which is disregarded since it acts on the entire control surface. The vertical forces and momentum fluxes are not considered since they have no effect on the flat reaction force. 5 jet plane flow is nearly uniform and thus the effect of the momentum-flux correction factor is negligible, ? ? 1. Properties We take the density of water to be 62. 4 lbm/ft3. Analysis W e take the plate as the control volume such that it contains the entire plate and cuts through the water jet and the support bar normally, and the direction of flow as the positive direction of x axis. The momentum equation for steady one-dimensional flow in the x (flow) direction reduces in this case o r r r &038 &038 &038 &038 F= ? mV ? ? mV ? FRx = ? mV1 FR = mV1 ? ? out ? in We note that the reaction force acts in the opposite direction to flow, and we should not forget the negative &038 sign for forces and velocities in the negative x-direction. Solving for m and substituting the given values, &038 m= FRx 350 lbf = V1 30 ft/s ? 32. 2 lbm ? ft/s 2 ? ? 1 lbf ? ? ? = 376 lbm/s ? ? Then the volume flow rate becomes V&038 = &038 m ? = 376 lbm/s 62. 4 lbm/ft 3 = 6. 02 ft 3 /s Therefore, the volume flow rate of water under stated assumptions must be 6. 02 ft3/s.Discussion In reality, whatsoever water will be scattered back, and this will add to the reaction force of water. The flow rate in that case will be less. m 1 FRx = 350 lbf Waterjet 6-7 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-25 A reducing elbow deflects water upwards and discharges it to the atmosphere at a specified rate.The anchoring force take to hold the elbow in place is to be determined. v Assumptions 1 The flow is steady, frictionless, one-dimensional, incompressible, and irrotational (so that the Bernoulli equation is applicable). 2 The weight of the elbow and the water in it is considered. 3 The water is discharged to the atmosphere, and thus the gage pressure at the outlet is zero. 4 The momentumflux correction factor for each inlet and outlet is given to be ? = 1. 03. Properties We take the density of water to be 1000 kg/m3. Analysis The weight of the elbow and th e water in it is W = mg = (50 kg)(9. 1 m/s 2 ) = 490. 5 N = 0. 4905 kN We take the elbow as the control volume, and designate the entrance by 1 and the outlet by 2. We also designate the horizontal coordinate by x (with the direction of flow as being the positive direction) and the vertical coordinate by z. The continuity equation for this one-inlet one-outlet steady flow system is &038 &038 &038 &038 m1 = m 2 = m = 30 kg/s. Noting that m = ? AV , the inlet and outlet velocities of water are &038 30 kg/s m V1 = = = 2. 0 m/s ? A1 (1000 kg/m 3 )(0. 0150 m 2 ) &038 30 kg/s m V2 = = = 12 m/s ? A2 (1000 kg/m 3 )(0. 025 m 2 ) Taking the center of the inlet cross section as the name and address level (z1 = 0) and noting that P2 = Patm, the Bernoulli equation for a streamline going through the center of the reducing elbow is expressed as ? V 2 ? V12 ? ? V22 ? V12 ? P V12 P V2 1 ? ? ? + + z1 = 2 + 2 + z2 P ? P2 = ? g ? 2 1 1 ? 2 g + z2 ? z1 ? P , gage = ? g ? 2 g + z2 ? ?g 2 g ? g 2 g ? ? ? ? Substituting, ? (12 m/s) 2 ? (2 m/s) 2 ?? ? 1 kN ? = 73. 9 kN/m 2 = 73. 9 kPa P , gage = (1000 kg/m3 )(9. 81 m/s 2 )? + 0. 4 ?? 1 2 ? ?? 1000 kg ? m/s 2 ? 2(9. 81 m/s ) ? ? ?? The momentum equation for steady one-dimensional flow is &038 &038 ? F = ? mV ? ? ? mV . We let the x- and out in r r r z- components of the anchoring force of the elbow be FRx and FRz, and assume them to be in the positive directions. We also use gage pressures to avoid dealing with the atmospheric pressure which acts on all surfaces. Then the momentum equations along the x and z axes become &038 &038 &038 FRx + P1,gage A1 = ? mV 2 cos ? ? ? mV1 and FRz ? W = ? mV 2 sin ? 2 25 cm2 Solving for FRx and FRz, and substituting the given values, &038 FRx = ? m(V 2 cos ? ? V1 ) ? P1, gage A1 ? 1 kN = 1. 03(30 kg/s)(12cos45 2) m/s? ? 1000 kg ? m/s 2 ? ? (73. 9 kN/m 2 )(0. 0150 m 2 ) = ? 0. 908 kN ? ? ? Water 30 kg/s 45 FRz FRx 150 m2 W 1 ? ? 1 kN ? &038 FRz = ? mV 2 sin ? + W = 1. 03(30 kg/s)(12sin45 m/s)? ? 10 00 kg ? m/s 2 ? + 0. 4905 kN = 0. 753 kN ? ? 0. 753 2 2 2 2 -1 FRz FR = FRx + FRz = (? 0. 908) + (0. 753) = 1. 18 kN, ? = tan = tan -1 = ? 39. 7 FRx ? 0. 908 Discussion Note that the magnitude of the anchoring force is 1. 18 kN, and its line of action makes 39. 7 from +x direction. Negative value for FRx indicates the assumed direction is wrong. 6-8 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation.If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-26 A reducing elbow deflects water upwards and discharges it to the atmosphere at a specified rate. The anchoring force needed to hold the elbow in place is to be determined. v Assumptions 1 The flow is steady, frictionless, one-dimensional, incompressible, and irrotational (so that the Bernoulli equation is applicable). 2 The weight of the elbow and the water in it is consi dered. 3 The water is discharged to the atmosphere, and thus the gage pressure at the outlet is zero. The momentumflux correction factor for each inlet and outlet is given to be ? = 1. 03. Properties We take the density of water to be 1000 kg/m3. Analysis The weight of the elbow and the water in it is W = mg = (50 kg)(9. 81 m/s 2 ) = 490. 5 N = 0. 4905 kN We take the elbow as the control volume, and designate the entrance by 1 and the outlet by 2. We also designate the horizontal coordinate by x (with the direction of flow as being the positive direction) and the vertical coordinate by z. The continuity equation for this one-inlet one-outlet steady flow system is &038 &038 &038 &038 m1 = m 2 = m = 30 kg/s. Noting that m = ?AV , the inlet and outlet velocities of water are &038 30 kg/s m = = 2. 0 m/s V1 = ? A1 (1000 kg/m 3 )(0. 0150 m 2 ) &038 30 kg/s m V2 = = = 12 m/s ? A2 (1000 kg/m 3 )(0. 0025 m 2 ) Taking the center of the inlet cross section as the annexe level (z1 = 0) and not ing that P2 = Patm, the Bernoulli equation for a streamline going through the center of the reducing elbow is expressed as ? V 2 ? V12 ? ? V22 ? V12 ? P V12 P V2 1 ? ? ? + + z1 = 2 + 2 + z2 P ? P2 = ? g ? 2 1 1 ? 2 g + z2 ? z1 ? P , gage = ? g ? 2 g + z2 ? ?g 2 g ? g 2 g ? ? ? ? or, P , gage = (1000 kg/m3 )(9. 81 m/s2 )? 1 ? ? ? (12 m/s)2 ? (2 m/s)2 2(9. 81 m/s ) ?? ? 1 kN ? = 73. 9 kN/m 2 = 73. 9 kPa + 0. 4 ?? ?? 1000 kg ? m/s 2 ? ? ?? The momentum equation for steady one-dimensional flow is &038 &038 ? F = ? ?mV ? ? ? mV . We let the xout in r r r and y- components of the anchoring force of the elbow be FRx and FRz, and assume them to be in the positive directions. We also use gage pressures to avoid dealing with the atmospheric pressure which acts on all surfaces. Then the momentum equations along the x and z axes become &038 &038 FRx + P1,gage A1 = ? mV 2 cos ? ? ? mV1 and &038 FRy ? W = ? mV 2 sin ? Solving for FRx and FRz, and substituting the given values, &038 FRx = ? m(V 2 cos ? V1 ) ? P1, gage A1 ? 1 kN = 1. 03(30 kg/s)(12cos110 2) m/s? ? 1000 kg ? m/s 2 ? FRz ? ? ? (73. 9 kN/m 2 )(0. 0150 m 2 ) = ? 1. 297 kN ? ? ? ? 1 kN ? + 0. 4905 kN = 0. 8389 kN &038 = ? mV 2 sin ? + W = 1. 03(30 kg/s)(12sin110 m/s)? 2 ? ? 1000 kg ? m/s ? ? 2 25 cm2 110 2 2 FR = FRx + FRz = (? 1. 297) 2 + 0. 8389 2 = 1. 54 kN and FRz 0. 8389 = tan -1 = ? 32. 9 FRx ? 1. 297 Discussion Note that the magnitude of the anchoring force is 1. 54 kN, and its line of action makes 32. 9 from +x direction. Negative value for FRx indicates assumed direction is wrong, and should be reversed. ? = tan -1 FRz FRx Water 1 30 kg/s 50 m2 W 6-9 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-27 Water deepen by a nozzle strikes the back surface of a baby carriage moving horizont ally at a constant velocity. The braking force and the baron wasted by the s outstrip are to be determined. . Assumptions 1 The flow is steady and incompressible. 2 The water splatters off the sides of the plate in all directions in the plane of the back surface. The water jet is exposed to the atmosphere, and thus the pressure of the water jet and the splattered water is the atmospheric pressure which is disregarded since it acts on all surfaces. 4 Fiction during motion is negligible. 5 There is no acceleration of the drag in. 7 The motions of the water jet and the perambulator are horizontal. 6 Jet flow is nearly uniform and thus the effect of the momentum-flux correction factor is negligible, ? ? 1. Analysis We take the cart as the control volume, and the direction of flow as the positive direction of x axis. The relative velocity between the cart and the jet is V r = V jet ?Vcart = 15 ? 10 = 10 m/s 15 m/s 5 m/s Therefore, we can assume the cart to be stationary and the jet t o move Waterjet with a velocity of 10 m/s. The momentum equation for steady onedimensional flow in the x (flow) direction reduces in this case to r r r &038 &038 &038 &038 F= ? mV ? ? mV FRx = ? mi Vi Fbrake = ? mV r FRx ? ? out ? in We note that the brake force acts in the opposite direction to flow, and we should not forget the negative sign for forces and velocities in the negative x-direction. Substituting the given values, ? 1N &038 Fbrake = ? mV r = ? (25 kg/s)(+10 m/s)? ? 1 kg ? m/s 2 ? ? ? = ? 250 N ? ?The negative sign indicates that the braking force acts in the opposite direction to motion, as expected. Noting that work is force times distance and the distance traveled by the cart per unit time is the cart velocity, the precedent wasted by the brakes is 1 kW ? ? &038 W = FbrakeV cart = (250 N)(5 m/s)? ? = 1. 25 kW ? 1000 N ? m/s ? Discussion Note that the function wasted is equivalent to the maximum power that can be generated as the cart velocity is maintained consta nt. 6-10 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation.If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-28 Water accelerate by a nozzle strikes the back surface of a cart moving horizontally. The acceleration of the cart if the brakes fail is to be determined. Analysis The braking force was determined in previous problem to be 250 N. When the brakes fail, this force will propel the cart forward, and the accelerating will be a= F 250 N ? 1 kg ? m/s 2 ? = m cart 300 kg ? 1N ? ? ? = 0. 833 m/s 2 ? ? Discussion This is the acceleration at the moment the brakes fail.The acceleration will decrease as the relative velocity between the water jet and the cart (and thus the force) decreases. 5 m/s 15 m/s 300 kg Waterjet FRx 6-11 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-29E A water jet hits a stationary partition, such that half of the flow is diverted upward at 45, and the other half is directed down.The force mandatory to hold the splitter in place is to be determined. vEES Assumptions 1 The flow is steady and incompressible. 2 The water jet is exposed to the atmosphere, and thus the pressure of the water jet before and after(prenominal) the split is the atmospheric pressure which is disregarded since it acts on all surfaces. 3 The gravitational personal effects are disregarded. 4 Jet flow is nearly uniform and thus the effect of the momentum-flux correction factor is negligible, ? ? 1. Properties We take the density of water to be 62. 4 lbm/ft3. Analysis The mass flow rate of water jet is &038 &038 m = ? V = (62. lbm/ft 3 )(100 ft 3 /s) = 6240 lbm/s We take the splitting section of water jet, including the splitter as the control volume, and designate the entrance by 1 and the outlet of either arm by 2 (both arms have the same velocity and mass flow rate). We also designate the horizontal coordinate by x with the direction of flow as being the positive direction and the vertical coordinate by z. r r r &038 &038 The momentum equation for steady one-dimensional flow is F= ? mV ? ? mV . We let ? ? out ? in the x- and y- components of the anchoring force of the splitter be FRx and FRz, and assume them to be in the &038 &038 positive directions.Noting that V2 = V1 = V and m 2 = 1 m , the momentum equations along the x and z 2 axes become &038 &038 &038 FRx = 2( 1 m)V 2 cos ? ? mV1 = mV (cos ? ? 1) 2 &038 &038 FRz = 1 m(+V 2 sin ? ) + 1 m(? V 2 sin ? ) ? 0 = 0 2 2 Substituting the given values, 1 lbf ? ? FRx = (6240 lbm/s)(20 ft/s)(cos45 1)? ? = ? 1 one hundred thirty-five lbf 32. 2 lbm ? ft/s 2 ? ? FRz = 0 The negative value for FRx indicates the assume d direction is wrong, and should be reversed. Therefore, a force of 1135 lbf must be utilize to the splitter in the opposite direction to flow to hold it in place. No holding force is necessary in the vertical direction.This can also be concluded from the symmetry. Discussion In reality, the gravitational effects will cause the upper stream to slow down and the lower stream to speed up after the split. But for short distances, these effects are indeed negligible. 20 ft/s 100 ft/s FRz 45 45 FRx 6-12 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-30E Problem 6-29E is reconsidered.The effect of splitter run on the force exerted on the splitter as the half splitter angle varies from 0 to 180 in increments of 10 is to be investi entred. g=32. 2 ft/s2 rho=62. 4 lbm/ft3 V_dot=100 ft3/s V=20 ft/s m_dot=rho*V_dot F_R=-m_dot*V*(cos(theta)-1)/g lbf ?, 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 one hundred sixty 170 180 8000 7000 6000 5000 &038 m , lbm/s 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 FR, lbf 0 59 234 519 907 1384 1938 2550 3203 3876 4549 5201 5814 6367 6845 7232 7518 7693 7752 FR, lbf 000 3000 2000 1000 0 0 20 40 60 80 100 120 140 160 180 ?, 6-13 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-31 A horizontal water jet impinges normally upon a vertical plate which is held on a frictionless track and is initially stationary. The initial acceleration of the plate, the time it takes to reach a certain velocity, and the velocity at a given time are to be determin ed.Assumptions 1 The flow is steady and incompressible. 2 The water always splatters in the plane of the retreating plate. 3 The water jet is exposed to the atmosphere, and thus the pressure of the water jet and the splattered water is the atmospheric pressure which is disregarded since it acts on all surfaces. 4 The tract is nearly frictionless, and thus fiction during motion is negligible. 5 The motions of the water jet and the cart are horizontal. 6 The velocity of the jet relative to the plate remains constant, Vr = Vjet = V. 7 Jet flow is nearly uniform and thus the effect of the momentum-flux correction factor is egligible, ? ? 1. Properties We take the density of water to be 1000 kg/m3. Analysis (a) We take the vertical plate on the frictionless track as the control volume, and the direction of flow as the positive direction of x axis. The mass flow rate of water in the jet is &038 m = ? VA = (1000 kg/m 3 )(18 m/s)? (0. 05 m) 2 / 4 = 35. 34 kg/s The momentum equation for stea dy one-dimensional flow in the x (flow) direction reduces in this case to r r r &038 &038 &038 &038 F= ? mV ? ? mV FRx = ? mi Vi FRx = ? mV ? ? out ? in where FRx is the reaction force required to hold the plate in place.When the plate is released, an equal and opposite impulse force acts on the plate, which is determined to ? 1N &038 Fplate = ? FRx = mV = (35. 34 kg/s)(18 m/s)? ? 1 kg ? m/s 2 ? ? ? = 636 N ? ? Then the initial acceleration of the plate becomes a= Fplate m plate = 636 N ? 1 kg ? m/s 2 ? 1000 kg ? 1 N ? ? ? = 0. 636 m/s 2 ? ? 18 m/s 1000 kg Waterjet Frictionless track This acceleration will remain constant during motion since the force acting on the plate remains constant. (b) Noting that a = dV/dt = ? V/? t since the acceleration a is constant, the time it takes for the plate to reach a velocity of 9 m/s is ? t = ? V plate a = (9 ? ) m/s 0. 636 m/s 2 FRx = 14. 2 s (c) Noting that a = dV/dt and thus dV = adt and that the acceleration a is constant, the plate veloci ty in 20 s becomes V plate = V0, plate + a? t = 0 + (0. 636 m/s 2 )(20 s) = 12. 7 m/s Discussion The assumption that the relative velocity between the water jet and the plate remains constant is valid only for the initial moments of motion when the plate velocity is low unless the water jet is moving with the plate at the same velocity as the plate. 6-14 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation.If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-32 A 90 reducer elbow deflects water downwards into a smaller diameter pipe. The resultant force exerted on the reducer by water is to be determined. Assumptions 1 The flow is steady, frictionless, one-dimensional, incompressible, and irrotational (so that the Bernoulli equation is applicable). 2 The weight of the elbow and the water in it is disregarded since the gravi tational effects are negligible. 3 The momentum-flux correction factor for each inlet and outlet is given to be ? 1. 04. Properties We take the density of water to be 1000 kg/m3. Analysis We take the elbow as the control volume, and designate the entrance by 1 and the outlet by 2. We also designate the horizontal coordinate by x (with the direction of flow as being the positive direction) and the vertical coordinate by z. The continuity equation for this one-inlet one-outlet steady flow system is &038 &038 &038 &038 m1 = m 2 = m = 353. 4 kg/s. Noting that m = ? AV , the mass flow rate of water and its outlet velocity are 2 &038 m = ? V1 A1 = ? V1 (? D1 / 4) = (1000 kg/m 3 )(5 m/s)? (0. 3 m) 2 / 4 = 353. 4 kg/s &038 &038 353. kg/s m m = = = 20 m/s 2 ? A2 ?? D 2 / 4 (1000 kg/m 3 )? (0. 15 m) 2 / 4 The Bernoulli equation for a streamline going through the center of the reducing elbow is expressed as V2 = P V12 P V2 1 + + z1 = 2 + 2 + z2 ? g 2 g ? g 2 g ? V 2 ? V22 ? ? P2 = P + ? g ? 1 1 ? 2 g + z1 ? z2 ? ? ? Substituting, the gage pressure at the outlet becomes ? (5 m/s)2 ? (20 m/s)2 ?? ?? 1 kPa ? 1 kN ? P2 = (300 kPa) + (1000 kg/m 3 )(9. 81 m/s 2 )? + 0. 5 ?? = 117. 4 kPa 2 ? ?? 1000 kg ? m/s 2 ?? 1 kN/m 2 ? 2(9. 81 m/s ) ? ?? ? ?? The momentum equation for steady one-dimensional flow is &038 &038 ? F = ? ?mV ? ? ? mV . We let the xout in r r and z- components of the anchoring force of the elbow be FRx and FRz, and assume them to be in the positive directions. Then the momentum equations along the x and z axes become &038 FRx + P1,gage A1 = 0 ? ? mV1 &038 FRz ? P2,gage A2 = ? m(? V 2 ) ? 0 Note that we should not forget the negative sign for forces and velocities in the negative x or z direction. Solving for FRx and FRz, and substituting the given values, ? 1 kN &038 FRx = ? ?mV1 ? P1, gage A1 = ? 1. 04(353. 4 kg/s)(5 m/s)? ? 1000 kg ? m/s 2 ? ? ? (0. 3 m) 2 ? ? (300 kN/m 2 ) = ? 23. 0 kN ? 4 ? ? ? (0. 15 m) 2 ? + (117. 4 kN/m 2 ) = ? 5. 28 kN ? ? FRz ? 1 kN &0 38 FRz = ? ? mV 2 + P2, gage A1 = ? 1. 04(353. 4 kg/s)(20 m/s)? ? 1000 kg ? m/s 2 ? and 2 2 FR = FRx + FRz = (? 23. 0) 2 + (? 5. 28) 2 = 23. 6 kN FRx 30 cm Water 5 m/s ? = tan -1 FRz ? 5. 28 = tan -1 = 12. 9 FRx ? 23. 0 Discussion The magnitude of the anchoring force is 23. 6 kN, and its line of action makes 12. 9 from +x direction. Negative values for FRx and FRy indicate that the assumed directions are wrong, and should be reversed. 15 cm 6-15 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation.If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-33 A cheat on turbine with a given traverse diameter and efficiency is subjected to steady abstracts. The power generated and the horizontal force on the supporting mast of the turbine are to be determined. vEES Assumptions 1 The wind flow is steady and incompressible. 2 The efficiency of the turbine-generator is independent of wind speed. 3 The frictional effects are negligible, and thus none of the incoming energising energy is converted to thermic energy. Wind flow is uniform and thus the momentum-flux correction factor is nearly unity, ? ? 1. Properties The density of air is given to be 1. 25 kg/m3. Analysis (a) The power potential of the wind is its energising energy, &038 which is V2/2 per unit mass, and mV 2 / 2 for a given mass flow rate ? 1 m/s ? V1 = (25 km/h)? ? = 6. 94 m/s ? 3. 6 km/h ? &038 m = ? 1V1 A1 = ? 1V1 Wind V1 1 2 D V2 ?D 2 4 2 = (1. 25 kg/m 3 )(6. 94 m/s) ? (90 m) 2 4 2 = 55,200 kg/s V (6. 94 m/s) &038 &038 &038 W max = mke1 = m 1 = (55,200 kg/s) 2 2 ? 1 kN ? ? 1000 kg ? m/s 2 ? ?? 1 kW ? ?? ?? 1 kN ? m/s ? = 1330 kW ? ? FR Then the actual power produced becomes &038 Wact = ? wind turbineW max = (0. 32)(1330 kW) = 426 kW (b) The frictional effects are assumed to be negligible, and thus the portion of incoming energizing energy not converted to electric power leaves the wind turbine as outgoing kinetic energy. Therefore, V2 V2 &038 &038 &038 &038 mke 2 = mke1 (1 ? ? wind turbine ) m 2 = m 1 (1 ? ? wind turbine ) 2 2 or V 2 = V1 1 ? ? wind turbine = (6. 94 m/s) 1 0. 32 = 5. 72 m/s We read the control volume roughly the wind turbine such that the wind is normal to the control surface at the inlet and the outlet, and the entire control surface is at the atmospheric pressure.The momentum r r r &038 &038 equation for steady one-dimensional flow is F= ? mV ? ? mV . Writing it along the x-direction ? ? out ? in (without forgetting the negative sign for forces and velocities in the negative x-direction) and assuming the flow velocity through the turbine to be equal to the wind velocity give ? 1 kN &038 &038 &038 FR = mV 2 ? mV1 = m(V 2 ? V1 ) = (55,200 kg/s)(5. 72 6. 94 m/s)? ? 1000 kg ? m/s 2 ? ? ? = ? 67. 3 kN ? ? The negative sign indicates that the reaction force acts in the negative x direction, as expec ted.Discussion This force acts on top of the tower where the wind turbine is installed, and the fold moment it generates at the diffuse of the tower is obtained by multiplying this force by the tower height. 6-16 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-34E A horizontal water jet strikes a curved plate, which deflects the water back to its original direction.The force required to hold the plate against the water stream is to be determined. Assumptions 1 The flow is steady and incompressible. 2 The water jet is exposed to the atmosphere, and thus the pressure of the water jet and the splattered water is the atmospheric pressure, which is disregarded since it acts on all surfaces. 3 Friction between the plate and the surface it is on is negligible (or the fri ction force can be included in the required force to hold the plate). 4 There is no splashing of water or the deformation of the jet, and the reversed jet leaves horizontally at the same velocity and flow rate. Jet flow is nearly uniform and thus the momentum-flux correction factor is nearly unity, ? ? 1. Properties We take the density of water to be 62. 4 lbm/ft3. Analysis We take the plate together with the curved water jet as the control volume, and designate the jet inlet by 1 and the outlet by 2. We also designate the horizontal coordinate by x (with the direction of incoming flow as being the positive direction). The continuity equation for this one-inlet one-outlet steady &038 &038 &038 flow system is m1 = m 2 = m where &038 m = ? VA = ? V ? D 2 / 4 = (62. 4 lbm/ft 3 )(140 ft/s)? (3 / 12 ft) 2 / 4 = 428. lbm/s r r r &038 &038 The momentum equation for steady one-dimensional flow is F= ? mV ? ? mV . Letting the ? ? out ? in reaction force to hold the plate be FRx and assuming it to be in the positive direction, the momentum equation along the x axis becomes &038 &038 &038 FRx = m(? V 2 ) ? m(+V1 ) = ? 2mV Substituting, 1 lbf ? ? FRx = ? 2(428. 8 lbm/s)(140 ft/s)? ? = ? 3729 lbf 2 ? 32. 2 lbm ? ft/s ? Therefore, a force of 3729 lbm must be applied on the plate in the negative x direction to hold it in place. Discussion Note that a negative value for FRx indicates the assumed direction is wrong (as expected), and should be reversed.Also, there is no need for an analysis in the vertical direction since the fluid streams are horizontal. 2 140 ft/s Waterjet FRx 1 140 ft/s 3 in 6-17 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-35E A horizontal water jet strikes a stage set plate, which deflects the water by 135 from its original direction. The force required to hold the plate against the water stream is to be determined.Assumptions 1 The flow is steady and incompressible. 2 The water jet is exposed to the atmosphere, and thus the pressure of the water jet and the splattered water is the atmospheric pressure, which is disregarded since it acts on all surfaces. 3 Frictional and gravitational effects are negligible. 4 There is no splattering of water or the deformation of the jet, and the reversed jet leaves horizontally at the same velocity and flow rate. 5 Jet flow is nearly uniform and thus the momentum-flux correction factor is nearly unity, ? ? 1. Properties We take the density of water to be 62. 4 lbm/ft3.Analysis We take the plate together with the curved water jet as the control volume, and designate the jet inlet by 1 and the outlet by 2. We also designate the horizontal coordinate by x (with the direction of incoming flow as being the positive direction), and the vertical coordinate by z. The continuity equati on for &038 &038 &038 this one-inlet one-outlet steady flow system is m1 = m 2 = m where &038 m = ? VA = ? V ? D 2 / 4 = (62. 4 lbm/ft 3 )(140 ft/s)? (3 / 12 ft) 2 / 4 = 428. 8 lbm/s r r r &038 &038 The momentum equation for steady one-dimensional flow is F= ? mV ? ? mV . We let the x- ? ? out ? in nd z- components of the anchoring force of the plate be FRx and FRz, and assume them to be in the positive directions. Then the momentum equations along the x and y axes become &038 &038 &038 FRx = m(? V 2 ) cos 45 ? m(+V1 ) = ? mV (1 + cos 45) &038 (+V 2 ) sin 45 = mV sin 45 &038 FRz = m Substituting the given values, 1 lbf ? ? FRx = ? 2(428. 8 lbm/s)(140 ft/s)(1 + cos45)? 2 ? ? 32. 2 lbm ? ft/s ? = ? 6365 lbf 1 lbf ? ? FRz = (428. 8 lbm/s)(140 ft/s)sin45? = 1318 lbf 2 ? ? 32. 2 lbm ? ft/s ? 2 140 ft/s Waterjet 135 FRz FRx 3 in 1 and 2 2 FR = FRx + FRz = (? 6365) 2 + 1318 2 = 6500 lbf , ? = tan -1 FRy FRx = tan -1 1318 = ? 1. 7 = 168. 3 ? 6365 Discussion Note that the magnitude of the an choring force is 6500 lbf, and its line of action makes 168. 3 from the positive x direction. Also, a negative value for FRx indicates the assumed direction is wrong, and should be reversed. 6-18 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-36 Firemen are holding a nozzle at the end of a hose while trying to extinguish a fire.The fair(a) water outlet velocity and the resistance force required of the firemen to hold the nozzle are to be determined. Assumptions 1 The flow is steady and incompressible. 2 The water jet is exposed to the atmosphere, and thus the pressure of the water jet is the atmospheric pressure, which is disregarded since it acts on all surfaces. 3 Gravitational effects and vertical forces are disregarded since the horizontal resistance force is to be determined. 5 Jet flow is nearly uniform and thus the momentum-flux correction factor can be taken to be unity, ? ? 1. Properties We take the density of water to be 1000 kg/m3.Analysis (a) We take the nozzle and the horizontal portion of the hose as the system such that water enters the control volume vertically and outlets horizontally (this way the pressure force and the momentum flux at the inlet are in the vertical direction, with no contribution to the force balance in the horizontal direction), and designate the entrance by 1 and the outlet by 2. We also designate the horizontal coordinate by x (with the direction of flow as being the positive direction). The average outlet velocity and the mass flow rate of water are determined from V= V&038 A = V&038 ? D / 4 2 = 5 m 3 /min ? (0. 06 m) 2 / 4 1768 m/min = 29. 5 m/s &038 m = ? V&038 = (1000 kg/m 3 )(5 m 3 /min) = 5000 kg/min = 83. 3 kg/s (b) The momentum equation for steady one-dimensional flow is &038 &038 ? F = ? ?mV ? ? ? mV . We let out in r r r horizontal force applied by the firemen to the nozzle to hold it be FRx, and assume it to be in the positive x direction. Then the momentum equation along the x direction gives ? ? 1N ? = 2457 N &038 &038 FRx = mVe ? 0 = mV = (83. 3 kg/s)(29. 5 m/s)? ? 1kg ? m/s 2 ? ? ? Therefore, the firemen must be able to resist a force of 2457 N to hold the nozzle in place. Discussion The force of 2457 N is equivalent to the weight of about(predicate) 250 kg.That is, holding the nozzle requires the strength of holding a weight of 250 kg, which cannot be done by a single person. This demonstrates why several firemen are used to hold a hose with a high flow rate. FRz FRx 5 m3/min 6-19 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-37 A horizontal je t of water with a given velocity strikes a flat plate that is moving in the same direction at a specified velocity.The force that the water stream exerts against the plate is to be determined. Assumptions 1 The flow is steady and incompressible. 2 The water splatters in all directions in the plane of the plate. 3 The water jet is exposed to the atmosphere, and thus the pressure of the water jet and the splattered water is the atmospheric pressure, which is disregarded since it acts on all surfaces. 4 The vertical forces and momentum fluxes are not considered since they have no effect on the horizontal force exerted on the plate. 5 The velocity of the plate, and the velocity of the water jet relative to the plate, are constant. Jet flow is nearly uniform and thus the momentum-flux correction factor can be taken to be unity, ? ? 1. Properties We take the density of water to be 1000 kg/m3. Analysis We take the plate as the control volume, and the flow direction as the positive directio n of x axis. The mass flow rate of water in the jet is &038 m = ? V jet A = ? V jet 10 m/s 30 m/s FRx 5 cm Waterjet ?D 4 2 = (1000 kg/m 3 )(30 m/s) ? (0. 05 m) 2 4 = 58. 9 kg/s The relative velocity between the plate and the jet is V r = V jet ? V plate = 30 ? 10 = 20 m/s Therefore, we can assume the plate to be stationary and the jet to move with a velocity of 20 m/s.The r r r &038 &038 F= ? mV ? ? mV . We let the horizontal momentum equation for steady one-dimensional flow is ? ? out ? in reaction force applied to the plate in the negative x direction to counteract the impulse of the water jet be FRx. Then the momentum equation along the x direction gives ? ? 1N ? &038 &038 ? FRx = 0 ? mVi FRx = mV r = (58. 9 kg/s)(20 m/s)? ? 1kg ? m/s 2 ? = 1178 N ? ? Therefore, the water jet applies a force of 1178 N on the plate in the direction of motion, and an equal and opposite force must be applied on the plate if its velocity is to remain constant.Discussion Note that we used the relativ e velocity in the determination of the mass flow rate of water in the momentum analysis since water will enter the control volume at this rate. (In the limiting case of the plate and the water jet moving at the same velocity, the mass flow rate of water relative to the plate will be zero since no water will be able to strike the plate). 6-20 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.Chapter 6 Momentum Analysis of Flow Systems 6-38 Problem 6-37 is reconsidered. The effect of the plate velocity on the force exerted on the plate as the plate velocity varies from 0 to 30 m/s in increments of 3 m/s is to be investi provided. rho=1000 kg/m3 D=0. 05 m V_jet=30 m/s Ac=pi*D2/4 V_r=V_jet-V_plate m_dot=rho*Ac*V_jet F_R=m_dot*V_r N Vplate, m/s 0 3 6 9 12 15 18 21 24 27 30 Vr, m/s 30 27 24 21 18 15 12 9 6 3 0 FR, N 176 7 1590 1414 1237 1060 883. 6 706. 9 530. 1 353. 4 176. 7 0 1800 1600 1400 1200 1000 FR, N 800 600 400 200 0 0 5 10 15 20 25 30 Vplate, m/s 6-21PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-39E A cull out moves air at sea level at a specified rate. The force required to hold the yellowish brown and the minimum power scuttlebutt signal required for the fan are to be determined. v Assumptions 1 The flow of air is steady and incompressible. 2 Standard atmospheric conditions exist so that the pressure at sea level is 1 atm. oxygenise leaves the fan at a uniform velocity at atmospheric pressure. 4 Air approaches the fan through a large area at atmospheric pressure with negligible velocity. 5 The frictional effects are negligible, and thus the entire mechanical pow er stimulation is converted to kinetic energy of air (no conversion to thermal energy through frictional effects). 6 Wind flow is nearly uniform and thus the momentum-flux correction factor can be taken to be unity, ? ? 1. Properties The gas constant of air is R = 0. 3704 psi? ft3/lbm? R. The standard atmospheric pressure at sea level is 1 atm = 14. 7 psi.Analysis (a) We take the control volume to be a horizontal hyperbolic cylinder spring by streamlines on the sides with air entering through the large cross section(prenominal) (section 1) and the fan located at the narrow cross section at the end (section 2), and let its centerline be the x axis. The density, mass flow rate, and discharge velocity of air are 14. 7 psi P ? = = = 0. 0749 lbm/ft 3 RT (0. 3704 psi ? ft 3 /lbm ? R)(530 R) &038 m = ? V&038 = (0. 0749 lbm/ft 3 )(2000 ft 3/min) = 149. 8 lbm/min = 2. 50 lbm/s V2 = V&038 A2 = V&038 2 ? D 2 / 4 = 2000 ft 3 /min ? (2 ft) 2 / 4 = 636. 6 ft/min = 10. ft/s &038 &038 ? F = ? ?mV ? ? ? mV . Letting the out in The momentum equation for steady one-dimensional flow is r r r reaction force to hold the fan be FRx and assuming it to be in the positive x (i. e. , the flow) direction, the momentum equation along the x axis becomes 1 lbf ? ? &038 &038 FRx = m(V 2 ) ? 0 = mV = (2. 50 lbm/s)(10. 6 ft/s)? ? = 0. 82 lbf 2 ? 32. 2 lbm ? ft/s ? Therefore, a force of 0. 82 lbf must be applied (through friction at the base, for example) to prevent the fan from moving in the horizontal direction under the influence of this force. (b) Noting that P1 = P2 = Patm and V1 ? , the energy equation for the selected control volume reduces to ?P V2 ? ?P V2 ? &038 &038 &038 &038 &038 m? 1 + 1 + gz1 ? + W pump, u = m? 2 + 2 + gz 2 ? + W turbine + E mech,loss ?? ? ? ? ? 2 2 ? ? ? ? Substituting, V &038 &038 Wfan, u = m 2 2 2 V2 (10. 6 ft/s) 2 ? 1 lbf 1W ?? ? &038 &038 Wfan,u = m 2 = (2. 50 lbm/s) ? ?? ? = 5. 91 W 2 2 2 ? 32. 2 lbm ? ft/s ?? 0. 73756 lbf ? ft/s ? Therefore, a useful mech anical power of 5. 91 W must be supplied to 2000 cfm air. This is the minimum required power input required for the fan. Discussion The actual power input to the fan will be larger than 5. 1 W because of the fan inefficiency in converting mechanical power to kinetic energy. Fan 1 2 24 in 6-22 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-40 A helicopter hovers at sea level while being loaded. The volumetric air flow rate and the required power input during discharge hover, and the rev and the required power input during loaded hover are to be determined. Assumptions 1 The flow of air is steady and incompressible. 2 Air leaves the blades at a uniform velocity at atmospheric pressure. 3 Air approaches the blades from the top through a large area at atmospheric pres sure with negligible velocity. 4 The frictional effects are negligible, and thus the entire mechanical power input is converted to kinetic energy of air (no conversion to thermal energy through frictional effects). 5 The change in air pressure with superlative is negligible because of the low density of air. 6 There is no acceleration of the helicopter, and thus the lift generated is equal to the full weight. Air flow is nearly uniform and thus the momentum-flux correction factor can be taken to be unity, ? ? 1. Properties The density of air is given to be 1. 18 kg/m3. Analysis (a) We take the control volume to be a vertical hyperbolic cylinder bounded by streamlines on the sides with air entering through the large cross-section (section 1) at the top and the fan located at the narrow cross-section at the bottom (section 2), and let its centerline be the z axis with upwards being the positive direction. r r r &038 &038 F= ? mV ? ? mV . Noting The momentum equation for steady one-d imensional flow is ? out ? in that the only force acting on the control volume is the total weight W and it acts in the negative z direction, the momentum equation along the z axis gives W &038 &038 ? W = m(? V 2 ) ? 0 W = mV 2 = ( ? AV 2 )V 2 = ? AV 22 V2 = ? A 1 where A is the blade duo area, 15 m A = ? D / 4 = ? (15 m) / 4 = 176. 7 m 2 2 2 Then the discharge velocity, volume flow rate, and the mass flow rate of air in the drop off mode become V 2,drop = m discharge g = ? A (10,000 kg)(9. 81 m/s 2 ) (1. 18 kg/m 3 )(176. 7 m 2 ) = 21. 7 m/s Sea level 2 V&038unloaded = AV 2,unloaded = (176. 7 m 2 )(21. m/s) = 3834 m 3 /s &038 munloaded = ? V&038unloaded = (1. 18 kg/m 3 )(3834 m 3/s) = 4524 kg/s Load 15,000 kg Noting that P1 = P2 = Patm, V1 ? 0, the elevation effects are negligible, and the frictional effects are disregarded, the energy equation for the selected control volume reduces to ? P V2 ? ?P V2 ? V2 &038 &038 &038 &038 &038 &038 &038 m? 1 + 1 + gz1 ? + W pump, u = m? 2 + 2 + gz 2 ? + W turbine + E mech,loss Wfan, u = m 2 ?? ? ? ? ? 2 2 2 ? ? ? ? Substituting, ? V2 ? ?? 1 kW ? (21. 7 m/s) 2 ? 1 kN &038 ? ? &038 = (4524 kg/s) W unloaded fan,u = ? m 2 ? ? = 1065 kW 2 ? 1 kN ? m/s ? 1000 kg ? m/s ? ? 2 ? 2 ? ? ?? ? ? nloaded (b) We at a time repeat the calculations for the loaded helicopter, whose mass is 10,000+15,000 = 25,000 kg V 2,loaded = m loaded g = ? A (25,000 kg)(9. 81 m/s 2 ) (1. 18 kg/m 3 )(176. 7 m 2 ) = 34. 3 m/s &038 mloaded = ? V&038loaded = ? AV2, loaded = (1. 18 kg/m 3 )(176. 7 m 2 )(34. 3 m/s) = 7152 kg/s ? V2 ? (34. 3 m/s)2 &038 &038 = (7152 kg/s) Wloaded fan,u = ? m 2 ? ? 2 ? 2 ? ?loaded ? ?? 1 kW ? 1 kN ? ? ? 1000 kg ? m/s 2 ?? 1 kN ? m/s ? = 4207 kW ? ? ?? 6-23 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation.If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems Noting that the average flow velocity is proportional to the overhead blade rotational velocity, the rpm of the loaded helicopter blades becomes &038 V 2 = kn V 2,loaded V 2, unloaded = &038 n loaded &038 n unloaded &038 n loaded = V 2,loaded V 2, unloaded &038 n unloaded = 34. 3 (400 rpm) = 632 rpm 21. 7 Discussion The actual power input to the helicopter blades will be considerably larger than the calculated power input because of the fan inefficiency in converting mechanical power to kinetic energy. -24 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-41 A helicopter hovers on top of a high hand where the air density considerably lower than that at sea level. The blade rotational velocity to hover at the higher altitude and the per centum increase in the required po wer input to hover at high altitude relative to that at sea level are to be determined. Assumptions 1 The flow of air is steady and incompressible. 2 The air leaves the blades at a uniform velocity at atmospheric pressure. 3 Air approaches the blades from the top through a large area at atmospheric pressure with negligible velocity. 4 The frictional effects are negligible, and thus the entire mechanical power input is converted to kinetic energy of air. 5 The change in air pressure with elevation while hovering at a given location is negligible because of the low density of air. 6 There is no acceleration of the helicopter, and thus the lift generated is equal to the total weight. Air flow is nearly uniform and thus the momentum-flux correction factor can be taken to be unity, ? ? 1. Properties The density of air is given to be 1. 18 kg/m3 at sea level, and 0. 79 kg/m3 on top of the mountain. Analysis (a) We take the control volume to be a vertical hyperbolic cylinder bounded by str eamlines on the sides with air entering through the large cross-section (section 1) at the top and the fan located at the narrow cross-section at the bottom (section 2), and let its centerline be the z axis with upwards being the positive direction. r r &038 &038 F= ? mV ? ? mV . Noting The momentum equation for steady one-dimensional flow is ? ? out ? in that the only force acting on the control volume is the total weight W and it acts in the negative z direction, the momentum equation along the z axis gives W &038 &038 ? W = m(? V 2 ) ? 0 W = mV 2 = ( ? AV 2 )V 2 = ? AV 22 V2 = ? A where A is the blade span area. Then for a given weight W, the ratio of discharge velocities becomes V 2,mountain V 2,sea = W / ? mountain A W / ? sea A = ? sea ? mountain = 1. 18 kg/m 3 0. 79 kg/m 3 = 1. 222Noting that the average flow velocity is proportional to the overhead blade rotational velocity, the rpm of the helicopter blades on top of the mountain becomes &038 n = kV 2 &038 n mountain V 2, mountain = &038 n sea V 2,sea &038 n mountain = V 2, mountain V 2,sea &038 nsea = 1. 222(400 rpm) = 489 rpm Noting that P1 = P2 = Patm, V1 ? 0, the elevation effect are negligible, and the frictional effects are disregarded, the energy equation for the selected control volume reduces to ? P V2 ? ?P V2 ? V2 &038 &038 &038 &038 &038 &038 &038 m? 1 + 1 + gz1 ? + W pump, u = m? 2 + 2 + gz 2 ? W turbine + E mech,loss Wfan, u = m 2 ?? ? ? ? ? 1 2 2 2 ? ? ? ? or V2 V2 V3 &038 &038 Wfan,u = m 2 = ? AV2 2 = ? A 2 = 2 2 2 1 2 ?A? ? ? W ? ? = ? ? ? A ? 3 1 2 ?A? ? ?W ? ? ? ? ? A ? 1 . 5 = W 1 . 5 2 ? A 15 m Then the ratio of the required power input on top of the mountain to that at sea level becomes &038 Wmountain fan,u 0. 5W 1. 5 / ? mountain A = &038 Wsea fan,u 0. 5W 1. 5 / ? sea A 2 ? mountain ?sea = 1. 18 kg/m3 = 1. 222 0. 79 kg/m3 Sea level Load 15,000 kg Therefore, the required power input will increase by 22. 2% on top of the mountain relative to the sea level.Discussion Note that b oth the rpm and the required power input to the helicopter are inversely proportional to the square root of air density. Therefore, more power is required at higher elevations for the helicopter to operate because air is less dense, and more air must be forced by the blades into the downdraft. 6-25 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.Chapter 6 Momentum Analysis of Flow Systems 6-42 The flow rate in a channel is controlled by a crimson gate by raising or lowering a vertical plate. A relation for the force acting on a sluice gate of width w for steady and uniform flow is to be developed. Assumptions 1 The flow is steady, incompressible, frictionless, and uniform (and thus the Bernoulli equation is applicable. ) 2 Wall crop forces at surfaces are negligible. 3 The channel is exposed to the atmosphere, and thus the pressure at free surfaces is the atmospheric pressure. 4 The flow is horizontal. Water flow is nearly uniform and thus the momentum-flux correction factor can be taken to be unity, ? ? 1. Analysis We take point 1 at the free surface of the upstream flow before the gate and point 2 at the free surface of the downstream flow after the gate. We also take the bottom surface of the channel as the reference level so that the elevations of points 1 and 2 are y1 and y2, respectively. The application of the Bernoulli equation between points 1 and 2 gives P1 V12 P V2 + + y1 = 2 + 2 + y 2 ? g 2 g ? g 2 g V 22 ? V12 = 2 g( y1 ? y 2 ) (1)The flow is assumed to be incompressible and thus the density is constant. Then the conservation of mass relation for this single stream steady flow device can be expressed as V&0381 = V&0382 = V&038 A1V1 = A2V 2 = V&038 V1 = V&038 A1 = V&038 wy1 and V2 = V&038 A2 = V&038 wy 2 (2) Substituting into Eq. (1), ? V&038 ? ? wy ? 2 ? ? V&038 ? 2 g ( y 1 ? y 2 ) &038 ? ? ?? ? ? wy ? = 2 g ( y1 ? y 2 ) V = w 1 / y 2 ? 1 / y 2 ? ? 1? 2 1 2 2 2 g ( y1 ? y 2 ) V&038 = wy 2 2 2 1 ? y 2 / y1 (3) Substituting Eq. (3) into Eqs. (2) gives the following relations for velocities, V1 = y2 y1 2 g ( y1 ? y 2 ) 1? y2 / 2 y1 and V2 = 2 g ( y1 ? y 2 ) 2 2 1 ? y 2 / y1 (4) We choose the control volume as the water body surrounded by the vertical cross-sections of the upstream and downstream flows, free surfaces of water, the inner surface of the sluice gate, and the bottom surface of r r r &038 &038 F= ? mV ? ? mV . The the channel. The momentum equation for steady one-dimensional flow is ? ? out ? in force acting on the sluice gate FRx is horizontal