The Giver Free Essays

The Giver †Summary The Giver This book is about a kid names Jonas. Jonas lives in a modern culture where there is no torment, dread, war, and scorn. There is additionally no preference, since everybody looks and acts fundamentally the equivalent, there is next to no opposition. We will compose a custom article test on The Giver or then again any comparative subject just for you Request Now They have likewise disposed of decision. You need to apply for a mate. You can't simply picked who you need and wed them, the network does it for you. His father fills in as a Nurturer of new youngsters, and his mother works at the Department of Justice. He additionally has a younger sibling named Lilly†¦. [tags: articles inquire about papers]559 words (1. 6 pages)$9. 95 [preview] The Giver †The Giver: Book Report The story begins as Jonas, a twelve-year-old kid, who is hanging tight for his life task. At the point when he is given his task, he is picked to be the Receiver of Memory. As the Receiver he needs to get each memory from everywhere throughout the world from the old Receiver he calls The Giver. The Giver: The Giver is the man who is the old Receiver. He is additionally the person who gives Jonas the recollections. In the network were Jonas lives is everything is controlled, even people’s memory. The Giver is the one in particular who isn't controlled†¦. [tags: articles explore papers]480 words (1. 4 pages)$9. 95 [preview] The Giver †Book Report †The Giver The Giver by Louis Lowry was distributed in 1993. I didn't pick this book it was prescribed to me I characterize this book as an inward experience. As in Jonas experiences an enthusiastic transformation (maybe) Jonas lives in a network where agony, impoliteness, and war are non-existent. All youngsters experiences a function in December consistently until they arrive at twelve years old, so, all in all they get their Assignments, the employments they will proceed as grown-ups. An advisory group of Elders cautiously observes every youngster so as to figure out which grown-up occupation best suits their abilities and interests†¦. labels: expositions look into papers]1057 words (3 pages)$19. 95 [preview] The Giver †The book The Giver by Louis Lowry is a fascinating book that everybody should set aside effort to peruse. This book takes you through a network of individuals where everything must be great. The story line is based around a kid named Jonas. Everybody in the network is doled out a vocation when they turn twelve and its Jonas go to step up and land his position. This book is fascinating on the grounds that everything must be great, Jonas lands the best position, and the experience Jonas needs to experience to spare another conceived youngster named Gabriel†¦. labels: papers explore papers]400 words (1. 1 pages)FREE Essays [view] The Giver †The Giver Essay Have you at any point wanted to start from the very beginning once more. Numerous individuals might want to have the chance to make a fresh start. In the book, The Giver, by Lois Lowry, Jonas is making a fresh start by making an end. Jonas is making an end by leaving the network. He leaves with Gabriel since he needs to encounter genuine things outside the network. He was harmed in the network since he was unable to share his emotions. He needed to have the option to share and experience his sentiments with other people†¦. labels: expos itions inquire about papers]383 words (1. 1 pages)FREE Essays [view] The Giver †He was a serene looking man, with an enormous round paunch and ruddy red cheeks. Jonas couldn’t help yet grin as he gazed at the delicate looking figure. The man looked down at the freezing pair. He saw Jonas’ trembling blue lips and the minuscule shaking heap of cover that was Gabriel. The man quickly welcomed Jonas into his home and shouted for his significant other to get covers and hot cocoa. Jonas sat modestly packaged in covers as the entirety of the outsiders around him murmured to one another about him and Gabe†¦. labels: expositions look into papers]806 words (2. 3 pages)FREE Essays [view] Lois Lowry’s The Giver †Lois Lowry’s The Giver There is a ton of discussion on why the book â€Å"The Giver† was named â€Å"The Giver†. A wide range of perspectives are communicated in the piece which gives a wide range of purposes behind the name. The book was entitled The Giver since this individual is the person who transmits recollections to the Receiver-in-preparing so the recollections can be given to the generations†¦. [tags: Louis Lowry Giver]970 words (2. 8 pages)FREE Essays [view] What is a Ring-provider? †What is a Ring-supplier. Those who’ve been requested the meaning of a ring-provider have replied with a puzzled outward appearance, â€Å"Does it have anything to do with the film Lord of the Rings? † Or others may essentially feel that the word â€Å"ring-giver† fundamentally implies an individual who gives out rings. This word can be viewed as an unclear term since it would seem like it has one ramifications, yet truth be told, it really has a more profound significance. During the Anglo-Saxon period, the word â€Å"ring-giver† is additionally named as a kenning, which is an all-encompassing metaphor†¦. [tags: Definition Ring Giver Essays]587 words (1. 7 pages)FREE Essays [view] The Giver by Lois Lowry †The supplier is composed from the perspective of Jonas, an eleven-year-old kid living in a cutting edge society that has wiped out all agony, dread, war, and disdain. There is no partiality, since everybody looks and acts essentially the equivalent, and there is almost no opposition. Everybody is unfailingly amenable. The general public has additionally disposed of decision: at age twelve each individual from the network is relegated a vocation dependent on their capacities and interests. Residents can apply for and be doled out good mates, and each couple is alloted precisely two youngsters each†¦. [tags: Lois Lowry Giver]1105 words (3. pages)$19. 95 [preview] The Giver by Lois Lowry †In numerous works of writing, a character impacts another character. Lois Lowry exhibited this idea in The Giver. At the point when one of the primary characters in the novel gave a positive impact to another character. In this work, the individuals lived in a ne twork that was intended to be almost perfect. No individual could see shading, feel neither contempt nor love; nobody had a decision in either occupation or training. In this novel, youngsters were doled out to a family when they were youthful and were raised by two parents†¦. [tags: Lois Lowry Giver] The most effective method to refer to The Giver, Essay models The Giver Free Essays Making an Acrostic Poem In this exercise, you will make an amazing acrostic sonnet. You will utilize your Intel-based MacBook, or iMac, (or other Macintosh PC running OSX 10. 5 or higher), and the preloaded programming to finish the undertaking. We will compose a custom paper test on The Giver or on the other hand any comparative subject just for you Request Now Pictures are given to help you en route, and there is an example sonnet on the last page of this exercise. Attempt to follow the means in the movement as intently as possible, yet once you have a vibe for the manner in which the product works, don't hesitate to expand so as to customize your sonnet and further build up your PC abilities. Here is a rundown of the devices you’ll use: HardwareSoftware ComputerMS Office-Word iSight CameraDashboard Widget-Dictionary/Thesaurus PrinterPhotoBooth, iPhoto (discretionary) Procedure: Setting Up the Document 1. Open MS Word application. Search for the symbol in the Dock. In the event that you can’t discover it there, open a New Finder Window, at that point click on Applications, at that point scoll down to MicroSoft Office 2004 or Office X, at that point open (or grow) that organizer to show the symbol. Double tap on it to open the application. 2. Pull down the File menu to New Blank Document, or, in the Project Gallery, click Word Document, at that point click Done. . Type the title of the sonnet (name of the individual, creature, thing) on the primary line of the page, in a perfect world with every single capital letter. 4. Press the arrival key a few times to leave some space between the title and the primary line of the sonnet. 5. Presently type a similar word vertically, down the left half of the page, again in all captial letters, squeezing the arrival key after each letter, with the goal that each letter is on its own line. Don’t stress over the appearance being fairly dull now. The principal task is to get the structure down. 6. Spare your archive. A few understudies may comment that they â€Å"†¦have not completed yet†¦Ã¢â‚¬  This is a decent chance to advise ourselves that we ought to be sparing our work at an early stage all the while, and afterward over and again as the report develops. Pull down the File menu to Save†¦ A ‘sheet’ will show up at the highest point of your window. The one appeared here shows that the report will be spared as: HENRY. doc on the Desktop. (You may choose to have your understudies spare their work with an increasingly explicit name, and in another area. ) Click Save. Utilizing the Dashboard Widget †Dictionary/Thesaurus 7. Snap on the Dashboard symbol in the Dock. 8. The word reference gadget may as of now be available on your work area, however on the off chance that it isn't, click on the in addition to sign (in the hover in the lower left corner of the screen), and different gadgets that are accessible will show up. 9. Snap on the word reference gadget (it likewise incorporates the thesaurus). The gadget will show up. You can drag it anyplace you like. Snap on the Thesaurus button at the highest point of the gadget, at that point type in a word you need to discover equivalents for. Let’s state, for instance, that you need to discover a word that implies ‘friendly’, however you don’t have a â€Å"F† in your name. Type the word amicable in, and afterward search for a word that begins with the letter you need. 0. When you have discovered the word, click on the Word symbol in the Dock to come back to your acrostic sonnet. Type your assertion on the line that creatures with its first letter. Rehash this procedure until you have filled in all the lines of your sonnet. Make sure to keep on sa

Analysis of Letter to the American people Essay Example | Topics and Well Written Essays - 750 words

Examination of Letter to the American individuals - Essay Example to break down in strict free for all that prompts him to submit: â€Å"(Q2) As for the second inquiry that we (container Laden) need to reply: What are we calling you to, and what do we need from you? (1) The principal thing that we are calling you to is Islam. (Letter). Along these lines container Laden is simply a strict sales rep and in view of this doesn't have the validity to represent the Islamic world with respect to different issues. Initially, the charges he levels against US backing of Israel appear to be empty considering certain real factors. He denounces us, saying, â€Å"As for the principal question: Why are we battling and contradicting you? The appropriate response is basic: (1) Because you assaulted us and keep on assaulting us... You assaulted us in Palestine.† (Letter) Obviously by this he implies through our help of Israel, Palestinians have endured. Or on the other hand isn't that right? Numerous pundits call attention to that al Qaeda has been prominently missing from any endeavors to help the Palestinians in any capacity other than vocal help for self destruction aircraft, the fulfillment of which is reflected in his announcement... Think not about the individuals who are executed in the method of Allah as dead. Nay, they are buzzing with their Lord, and they are being accommodated. They cheer in what Allah has offered to them from His abundance and celebrate for the individuals who have not yet gone along with them, however are abandoned (not yet martyred) that on them no dread will come, nor will they lament. They cheer in an effortlessness and an abundance from Allah, and that Allah won't squander the compensation of the devotees. [Quran 3:169-171] (Letter) He endeavors to demonstrate a point, and it’s a strict one having nothing to do with the Palestinians making sure about their own stateâ€a position sent by numerous American representatives throughout the years and just as of late given as an expressed objective of the Obama organization. This objective, as it shows up right now, comes over the complaints of the new Israeli administration. â€Å"...you assaulted us in Palestine,† is an unmistakable exertion to associate the Palestinians with

How to Recognize Verbal Abuse and Bullying

How to Recognize Verbal Abuse and Bullying Relationships Violence and Abuse Print How to Recognize Verbal Abuse and Bullying By Sherri Gordon facebook twitter Sherri Gordon is a published author and a bullying prevention expert. Learn about our editorial policy Sherri Gordon Reviewed by Reviewed by Amy Morin, LCSW on November 29, 2019 facebook twitter instagram Amy Morin, LCSW, is a psychotherapist, author of the bestselling book 13 Things Mentally Strong People Dont Do, and a highly sought-after speaker. Learn about our Wellness Board Amy Morin, LCSW Updated on January 19, 2020 PeopleImages / Getty Images More in Relationships Violence and Abuse Spouses & Partners LGBTQ Most people assume that if they were being verbally abused they would know about it. After all, verbal abuse often involves yelling, put-downs, name-calling, and belittling behaviors. But there is so much more to verbal abuse than people realize. In fact, some people are verbally abused on a regular basis without even recognizing that it’s happening. When someone is being verbally abused, the person attacking them may use a combination of both overt forms of abuse like engaging in name-calling and making threats but also more insidious methods like gaslighting or constantly correcting, interrupting, putting down, and demeaning them. Even prolonged silent treatment is a form of verbal abuse. When this happens, the person is attempting to control and punish the victim by refusing to talk to the other person. For some people, especially those who either experience verbal abuse in the home or  experienced it as a child, it can often be overlooked because the verbal assaults feel like a normal way to communicate. But they are anything but normal and can have lasting consequences. Defining Verbal Abuse and Bullying Because verbal abuse isn’t as clear-cut as other forms of abuse and  bullying, like physical bullying and sexual bullying, it can be hard to identify. But that doesn’t make it any less real. Typically, verbal abuse involves some sort of verbal interaction that causes a person emotional harm. For instance, when someone is being downright critical, acting out in anger, and using words to try to control another person, this is verbal abuse. This, in turn, leaves a victim questioning who they are. In fact, it is not uncommon for a victim of verbal abuse to feel inadequate, stupid, and worthless. After all, they are being defined by a verbally abusive person. If verbal abuse occurs in a dating relationship, it can be particularly confusing because the partner is likely not abusive all the time. As a result, when the abuser is loving and gentle the victim can forget all the about the negative behavior. Ultimately, the victim ends up ignoring the pattern of verbal abuse or makes excuses for the behavior saying things like the abuser is just stressed out or going through a tough time right now. The Effects of Verbal Abuse and Bullying Just like any other form of abuse or bullying, verbal abuse has a lasting impact on victims. Consequently, they can experience a host of issues, including everything from anxiety and depression to even PTSD in severe cases. A number of studies have shown that children who are verbally abused, either at home or by their peers at school, are at a greater risk for depression and anxiety as adults.?? Verbal abuse also can cause the victim to believe very negative things about themselves, which in turn impacts their self-esteem. It also can impact every element of their life, including their academic performance, their other relationships, and their success at work later in life.  In fact, when verbal abuse is particularly severe it can impact whether or not people can see themselves as being successful in any area of life.   Recognizing Verbal Abuse in Your Life When it comes to physical bullying, cyberbullying, and sexual assault, victims do not question whether or not they have been abused. These types of abuse are obvious. But when it comes to verbal abuse, victims often question whether or not what they are experiencing is truly abusive. They also wonder whether or not it is a big deal. Here are some signs that a family member, friend, peer, or dating partner is verbally abusive. They call you names. Anytime someone engages in name-calling this is a form of verbal abuse.  Even if the names are said in a neutral voice, this is not acceptable treatment of another person. They use words to shame you. Examples include critical, sarcastic, or mocking words that are meant to put you down. These may be comments about the way you dress, talk, or your intelligence. Basically, shaming is any comment that makes you feel inferior or ashamed of who you are.   They make  jokes at your expense. Typically, verbally abusive people will make you the butt of their jokes. This can be done in private or in person. But if you dont find it funny, then it is not harmless fun. Whats more, verbally abusive people usually select jokes that attack an area where you feel vulnerable or weak. They humiliate you in public. When you are insulted in public by a peer, a friend, a family member, or a dating partner, this can be particularly painful. The goal of the abuser is to control you by making you feel bad about who you are. They criticize you. Whether done in public or in private, criticism can be painful particularly if the person doing the criticizing is simply being mean and has no intention of being constructive.   They yell, scream, or swear at you. Any time someone yells or curses at you, this is a display of power and the goal is to control and intimidate you into submission. As a result, it is abusive and should not be tolerated or excused.   They make  threats.  No threat should ever  be taken lightly. When people make threats they are trying to control and manipulate you. Remember, there is no better way to control someone than to make them fearful in some way. A Word From Verywell Although the effects of verbal abuse can be significant, there is still hope for victims. In fact, once a person becomes able to recognize verbal abuse in their lives, they can start making informed decisions about which friendships and dating relationships are healthy and which are toxic, fake, or abusive. They also can learn to stand up to verbal bullying. Remember, verbal abuse doesnt have to leave a lasting impact. With intervention, victims  can overcome and cope with the bullying they have experienced.   How to Identify and Cope With Emotional Abuse

Allowing Plastic Surgery on Teenagers - 561 Words

Should Teenagers be able to get plastic surgery? In this day in age children know more than ever that plastic surgery has become a varied option , so most of them feel like it’s not a big deal to ask their parents, but most of them don’t know the risks and the dangers of plastic surgery.The dangers of plastic surgery are very high, the area that has been worked on could become permanently numb and could possibly ruin a persons life. Infections are also symptoms that could be caused by plastic surgery if it is not performed properly, infections are bad in many different ways because they can lead to death and other serious problems. In the year of of 2007 87,000 teenagers got cosmetic plastic surgery but almost half of the surgeries were to get new noses, which is a very disturbing thing to hear because there are children with more serious reasons to get plastic surgery not being seen about their problem. In 2008 there were 160,283 kids and teens under the age of 18 years old that had gone to the doctor to talk about g etting plastic surgery but in 2007 the number was 205,119; before this everything was different and more simpler, the numbers were down to 145,094 in the year of 2006. â€Å"Lifes hard enough without adding a physical burden. But at the same time, does that teach them problems have a surgical solution?† comments Hema Sundaram, who is a dermatologist and cosmetic laser surgeon in Washington D.C. Dr. Sundarams question is full of different debatable things like ‘IsShow MoreRelatedAnalysis Of The Article Teens Under The Knife By Kaitlyn Ali And Tiffany Lam1351 Words   |  6 PagesIn the article entitled Teens Under the Knife written by Kaitlyn Ali and Tiffany Lam readers are informed on the possible risks that are exposed to teens who have cosmetic surgery. Ali and Lam state, There are many risks in plastic surgery, such as permanent numbness, infections, blood clots, and even death (par. 9). The developing bodies of teens are still changing which could lead to alteri ng the effects or future displacement of the surgical procedure. The article states, Because teens Read MoreTeenagers Should Never Have Cosmetic Surgery Essay1555 Words   |  7 PagesTeenagers Should Never Have Cosmetic Surgery In 2012, over 236,000 teenagers from the ages of 13-19 years old, went under the syringe to have a cosmetic procedure done (Gilbert, Web). Teenagers should never be able to have cosmetic surgeries because of the harmful effects the procedures have. Teenage minds and bodies are not fully developed until they are in their early twenties. Therefore, doctors are unable to fully comprehend the risks these procedures will have on the teenagers, since theirRead MoreSociety s Outlook On Plastic Surgery963 Words   |  4 Pageson plastic surgery has changed throughout the years; it has become something so common that it is no longer looked down upon on. According to the American Society of Plastic Surgeons â€Å"15.6 million cosmetic procedures, including both minimally-invasive and surgical, were performed in the United States in 2014, an increase of 3 percent since 2013.† and the rates continue to expand as the years go by. There are so many more surgical procedures that can be done compared to when plastic surgeries beganRead MoreSocial Media On Teen Plastic Surgery1177 Words   |  5 PagesIntroduction a. Understanding plastic surgery. b. Knowing the reason why people would most likely operate plastic surgery. c. Knowing whether plastic surgery is a way to promote beauty or destroy it. II) The Main Conflict a. Knowing how plastic surgery destroys beauty rather than promote it. b. Many people go overboard with surgery to look MORE beautiful. c. Lack of self-confidence guides people into fakeness. III) Plastic surgery in a developing teenager a. The influence of socialRead MoreLove Yourself, There’s No One Better1294 Words   |  6 Pagesin life, only winners. Minorities began to push for equally in the work place and women were tired of being inferior to men. Everyone wanted to feel confident in themselves and what they were doing. So what is the healthy balance for self-esteem? Teenagers today struggle with the answer to this question, much due to the mixed messages sent by mass and social medias. These popular outlets of entertainment have brainwashed children today causing a lot of young adults to worry about their body image,Read MorePlastic Surgery: Why Is so Popular? Essay1307 Words   |  6 PagesPlastic surgery is medical process through which people can make their physical aspect look better. There are two major kinds of plastic surgeries: cosmetic and reconstructive. People are and have always concern about their body image and the perspective that other could have about it. Therefore, people are alway s looking for the solution, which most of the time end up being the plastic surgery. Where these procedures originated? Moreover, how do we get to the actual point of plastic surgery? ClearlyRead MoreShould Teens Get Forced Into Getting Plastic Surgery?1656 Words   |  7 Pagesmother looks different from her, due to the fact she has gotten a lot of plastic surgery done to herself. Whose little girl wants to grow up and look beautiful, just like her mother, but doesn’t understand the risk of plastic surgery. When the little girl grows into a teen, she thinks she is finally ready to get her first cosmetic surgery done, a nose job. Her mother is all for it, since she has had plenty of cosmetic surgeries before, but is this perfectly team getting this for herself, where to makeRead MoreAre Girls Get Exposure?897 Words   |  4 Pagesup to look like children. They strutted across the runway in baby doll lingerie as they dragged stuffed animals behind them (APA 12). Music is ov erflowing with songs that sexualize and degrade women (APA 6). Research has shown that children and teenagers on average listen to more than 2 hours of music a day (Parker-Pope). The message that young people are receiving from both female and male artists reinforce that sexualization of females is normal and accepted. For example, coming in at number 3Read MoreMedias Influence of Plastic Surgery581 Words   |  2 Pagescontinues to evolve, plastic surgery is becoming increasingly more acceptable. Since I am a journalism and film and video major, I always try to connect things back to how the media play a role in the issue. I believe that the media has an effect on people in a numerous of ways. It is very persuasive, and it sends messages to people without being completely obvious all of the time. So why not the same with cosmetic surgery? A lot of teenagers are starting to see cosmetic surgery as an option to alterRead MorePlastic Surgery Speech1220 Words   |  5 Pagesout hear t transplant its fascinating how one can come to a persons life for just a day and make them perceive the world in a whole new way. In the field of facial plastic surgery one does not only help those who want to enhance their appearance but also those who unfortunately undergo a trauma. First off one must know if plastic surgery is right for them. The surgeon most discuss with the patient thoroughly his/her desires and expectations to know if they have the right mindset to submit to such

Similarities Between The Spanish American And Atlantic...

This period of time is made up by the American, French, Haitian, and Spanish American Revolutions. If broken down, the revolutions have very few things in common and the list of differences seem to go on forever. However, the similarities are what tie all of the revolutions together. Their similar political vocabulary and a large democratic nature are a couple of examples that make them alike. If looking at the picture as a whole, the revolutions can be compared because they all had one goal to meet. Some of the revolutions are considered victories, while others did not benefit the citizens at all. In addition to that, the Revolutions took place to prove to not only others, but to themselves that they are more than what they believe- if†¦show more content†¦Lastly, the Spanish American Revolutions, which took place in the Spanish and Portuguese colonies of mainland Latin American. The Spanish American colonists saw the change that took place after the three previous revolut ions and realized that they were in the same position. The natives of the Latin American colonies, creoles, become insulted by how the government of their country had become. They, too, also had a monarchy system that tried to tax the colonists. However, the Spanish colonist did not create their own revolution; they were invaded by Napoleon. Ultimately, the outcome was good because the king was overthrown and the states gained their independence. All of the people who were directly impacted by these revolutions were pleased because they gained their independence from a higher power. Though, the people who were not directly affected, they did not get benefitted in the long run. Throughout the revolution, the main point was to overthrow a higher power. As a result, all four revolutions gained their independence and were directly impacted by the results; however, the people who were not impacted directly (the people of higher power) suffered in the long run. First, the American Revolution made Britain suffer due to the debt that they were in. British parliament had decided that they could rely on the New England colonies to pay their debt from the war with France. Their plan backfired and ended up makingShow MoreRelatedAtlantic History : Concept And Contours854 Words   |  4 PagesThe study of the Atlantic as an interwoven community is a relatively new theory. Historians are beginning to see Atlantic History as â€Å"a sudden and harsh encounter between two old worlds that transformed both and integrated them into a single New World† , and not just separate entities with detached pasts. Atlantic History: Concept and Contours by Bernard Bailyn lays t he framework for what Atlantic History is and how it should be studied. Bailyn states that the reasoning behind writing the book isRead MoreThe Role Of Gold Of Global Commerce Between 1450 And 17501887 Words   |  8 Pages1. Describe the role of silver in global commerce between 1450 and 1750. Provide specific examples from the assigned readings. [Week 10] During 1450 and 1750, silver fueled global commerce as it was the â€Å"first direct and sustained link between the Americas and Asia† and initiated trade connections across the Pacific. As a key commodity, silver enriched economies and was used for purchase of African slaves, spices, and Asian goods. Economic investment in silver provided opportunities for women, increasedRead MoreCCOT And CC Essay1549 Words   |  7 Pages600 bce, 600 bce – 600 ce Africa Compare and contrast life in foraging societies with life in agricultural societies after the Agricultural Revolution Identify two key changes in early African history that resulted in a new period in the history of the region The Middle East Analyze the political changes in the Middle East from the Agricultural Revolution to 600 c.e. Compare and contrast the basic features of TWO of the following religious systems prior to 600 c.e. Polytheism Judaism ChristianityRead MoreCompare and Contrast the Early Colonial Empires of Portugal, Spain, and England in Terms of Motives, Economic Foundations, and Relations with Africans and Native Americans. What Factors Explain the Similarities and Di1220 Words   |  5 Pagesâ€Å"Compare and contrast the early colonial empires of Portugal, Spain, and England in terms of motives, economic foundations, and relations with Africans and Native Americans. What factors explain the similarities and differences in the two ventures?† Darwin proclaimed that when push comes to shove, only the robust characters would survive. Outfitted with an effective military, a divine hostility against competing faiths and diseases unknown to even the carriers, three powerful and greedy nationsRead MoreThe Migration Of European Settlers1635 Words   |  7 Pagesworthy of deeper analysis. The conquest of North America by Europeans and American settlers from the 16th to 19th centuries had a profound effect on the indigenous political landscape by defining a new relationship dynamic between natives and settlers, by upsetting existing native political, economic and military structures, and by establishing a paradigm where the indigenous peoples felt they had to resist the European and American incursions. The engaging and brilliant works of Andres Rensendez andRead MoreComparative Practice 2009 Racial Ideologies in the Americas C31787 Words   |  8 Pages2009 Comparative Essay from the World History AP For the period from 1500 to 1830, compare North American racial ideologies and their effects on society with Latin American/Caribbean racial ideologies and their effects on society. Do Now: â€Å"With the exception of some early viceroys, few members of Spain’s nobility came to the New World. 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Admission Essay Medical Free Essays

Why are you interested in entering this major or field? I am interested for this field because I find it noble and very fascinating. Without the Radiologic Technician, nobody understands the use of x-rays and how it works. This profession would give me the ability to understand more on x-rays and other related and important topics. We will write a custom essay sample on Admission Essay Medical or any similar topic only for you Order Now 2. What are your goals after you graduate from Harcum? After I graduate from Harcum, I will immediately practice my profession as Radiologic Technician and serve people who need my service. At the same time, I will educate myself more or have an advance studies which is related to Radiology to update myself about newfangled technology and be a better Radiologic Technician. 3. How can Harcum assist you in attaining your goals? I consider Harcum as a good match for my learning because it is a college that has so much to offer. I strongly believe that the professors and facilities here are well-equipped which are able to assist and cater the needs of the students. One thing that attracts me most in this college is the way the professors teach their students. This is the college too which has close cooperation with the community which serves to the functioning of modern education. We all know that the community needs the school as a positive force for social and economic betterment. There are many problems in the community, such as those relating to health, economic, and social problems, that can be solved by educative process. This college is one agency in the community equipped to lead in the solution of problems. I believe that Harcum College can be useful in promoting and improving community life and conditions and which will enable less fortunate people to live richer, fuller, and better everyday lives, as well as on the development of techniques of their studies. I also believe that this college enhanced my skills, abilities, and attitudes to be more learned and extend it to the community. The university does not only educate the students academically but it is concerned too with the interaction of human individuals and their environment. In addition, the university is concerned with producing growth or changes in human knowledge, skills, abilities, attitudes, feelings, morals, and habits of every type. How to cite Admission Essay Medical, Essays

Perception Of Death Essays - Anglo-Welsh Literature,

Perception Of Death Trying to understand a poem when first reading it is very difficult. One must read the poem several times to understand the author's point. It is important to concentrate on grammatical structures and rhyme schemes. This essay will compare the work of Dylan Thomas' "Do not go gentle into that good night" to the work of Andrew Hudgins' "Elegy for My Father, Who Is Not Dead." Both works concentrate on their fathers, as they become closer to death. The authors of the respective poems have different views behind the word "death." Within the poem "Do not go gentle into that good night", Thomas speaks on how one should value life. He feels as though life is something special and should not be taken for granted. Moreover, he believes that one should keep their head up and believe that there will be a brighter day tomorrow. The refrains: "Rage, rage against the dying of the light" and "Do not go gentle into that good night" symbolize the thought. On the other hand, Hudgins views death as something that is very special, a stepping stone in life. He feels that death is a continuation of life, instead of the end of life. Lines 3-5 of "Elegy for My Father, Who Is Not Dead" says, "In the sureness of his faith, he talks about the world beyond this world as though his reservations have been made" supports the theory. In addition, the tones of the poems are comparable. Each poem reveals a lonely and sorrowful tone. In "Elegy for My Father, Who Is Not Dead", line 14 says, He's ready. I am not. I can't just say good-bye as cheerfully as if he were embarking on a trip..." reveals that the passing of his father is something that he is not ready to handle. He knows that the passing of his father's will bring sadness, loneliness, and a sense of emptiness to his hearts. Likewise, Thomas would feel the same way is his father was to pass away. Finally, the poems have contrasting themes; Thomas feels death as a horrible experience, while Hudgins sees death as a joyous experience. For example, the poem "Elegy for My Father, Who Is Not Dead" views death as a cruise to a place that is promised to be joyous. Also, it indicates that the son would eventually repeat the journey of death the father took. On the other hand, line 4 of "Do not go gentle into that good night says, "Though wise men at their end know dark is right..". Thomas sees death as something dreary and dark. The author does not see death as a mark in life, but rather the end of life in all aspects; mentally, physically, and spiritually. Thomas believes that death is like being blind, and not knowing what is going on. In conclusion, both poems express different views of death. Thomas feels that death as something that is dreary, while Hudgins views death as a joyous occasion that is just a stepping stone of life. Each poem reveals that the sons are not ready for their father's death. The authors feel that their fathers should try everything to avoid death. Also, the authors not that their life's would not be the same without their fathers beside them. Death is a word that can be interpreted in many different ways.

How to Write an Analytical Essay on Environmental Economics

How to Write an Analytical Essay on Environmental Economics When you sit down to write your analytical essay on environmental economics, you should make sure you have all of the right components. When writing an essay on any topic you should make sure that you have the following components: Introduction Body with Evidence for Each Argument Conclusion References or Bibliography Some analytical essays on environmental economics will differ slightly in terms of style but the majority of essays you are tasked with writing are all formatted like this. Remember: All analytical essays on environmental economics require thorough research to support your thesis. All analytical essays on environmental economics require an introduction that offers the reader adequate background information in order to understand your argument. All analytical essays on environmental economics require proper citations in accordance with the format style assigned to you by your teacher or by your TA. The analytical essay is an important piece of writing which requires you to review all of the related literature to your topic. Your purpose in doing so is to analyze what literature exists to date related to your topic or your theme and determine where are any gaps or if one author makes a more valid claim substantiated by evidence than another. It is an opportunity as a student to expose yourself to the work that professionals in your field have completed and to review it critically. It is also a chance for you to learn valuable research and note-taking skills. Once you know what you should be looking for when you begin researching and reading. Facts and theories which provide an answer to your question are perfect, while opinions given without fact are not. If the opinion is whether a specific answer or solution is viable or not, and it comes from an expert in the field, is perfectly fine though. As you write your notes, it is important that you avoid writing too much. So often students run into issues with plagiarism, or simply lack adequate unique ideas in their work because they write too much down in their notes. When it comes time to produce a paper, the essay becomes a patchwork of ideas borrowed from other writers and not an expression of unique thinking. Therefore, your time spent researching should be a collective effort to understand the sources and to integrate the sources into personal knowledge and thinking. It should not be a time to merely copy entire paragraphs and weave together an essay from the remarks of others alone. Note cards should record ideas which are relevant to a topic and they should summarize information more often than quoting it. Remember these tips while taking notes: Only write exact words copied from a text if the ideas are surprisingly expressed or the phrasing is memorable; these can be used as actual quotes in the final essay. Compress ideas using your words. Paraphrasing something word for word is wasteful of your time. Instead, take the most important ideas and use them as a heading or label and then fill in some sub-points below. Avoid underlining and highlighting as your only source of note taking. This is a good resource and method of studying to be sure, but when researching for a paper it would behoove you to write your own words in a sticky note or in the margin. We hope this guide will prove useful to you. Please be sure to check our 20 topics and 1 sample essay on environmental economics along with 10 facts to ground the foundation of your paper. CustomWritings is committed to provide students with high-quality custom analytical essays written from scratch by experienced writers. Contact our service right now!

How to Make Your Book Review More Critical with an Outline

How to Make Your Book Review More Critical with an Outline How to Make Your Book Review More Critical with an Outline? Setting out to write a critical book review is a daunting task. Something about the word ‘critical’ seems to conjure up scary visions of having to wade through huge tomes of literary theory that threaten to swallow your limited analyzing abilities as a student. A review at the end of the day is supposed to be critical where you share your opinion on a specific topic and it tells the makers or readers your honest opinion on it. There are many reviewers out there, criticizing all kinds of books including fiction and essays, but not all these reviewers or their opinions are valued. At times, it is only because they’re lacking a proper outline and hence are not able to write their thoughts properly. Why Have an Outline for a Critical Book Review? Like any other assignment set by a systematically produced curriculum, a critical book review is also easy. You simply apply a systematic approach and break it into parts. You jot down the essential elements you need to include. Working according to an outline is a great way to accomplish your goals. An outline serves as a systematic tool that will keep you on track. You can always refer to your outline to make sure you are not missing anything. Moreover, we mention some tips on actual critical book review writing, so it’s two birds with one shot. This guide will tell you how to prepare an outline in four easy steps which correspond to the recommended sections. Introduction (1-2 Paragraphs, Half a Page) Like any good piece of writing, start with an introduction. The specific form is up to you, choose a quotation that you liked, a particularly powerful scene in the book, even a personal anecdote which ties into the broader opinion you hold of the book. The goal is to capture the reader’s attention and keep them hooked. Include an overview of the book where you summarize the plot and also present an expression of your overall judgment. Summary (1 Page or about 23 Lines of Typed Text) A summary is a brief discussion of the major themes, concepts, and ideas presented in the book. It is recommended that you write this entirely in your own words. Present a condensed picture of the book. If your summary contains spoilers, make sure you warn your readers about it. Critical Evaluation (3 Pages) The third is an in-depth section which includes the reviewer’s reactions to the thoughts of the author. Most students often find it challenging to be critical, probably because they are under the impression that in order to critique something you have to possess expert-level knowledge. This is an unfortunate opinion that must be dispelled from your mind. Conclusion (1-2 Paragraphs, Half a Page) A short section which shows the overall impression and evaluation arrived at by the reviewer. It can be written in first person if desired and should include: Things which you learned from the book; Whether you would recommend the book to other people. A critique is simply a collection of responses, reactions and thoughts to what you are reading. No one expects you to produce an expert-level critique if you are only a learner. The best way to make this easy is to write down your thoughts and impressions while you are reading the book. Jot down any questions or aspects you like and at the end of your read you will have a significant set of notes that will make the critique a breeze. Here are the aspects that you need to include: Your overall opinion and the reasons behind it. How did the book make you feel? Was the writing able to hold your interest? What was the author trying to communicate? How well- or not- did the author present his or her points, ideas and assumptions? Did you detect any underlying philosophy in the book? Is the author’s view objective? How does the book fit into the context of the course? How useful are the footnotes, index, bibliography etc.? Is the book a useful contribution to the field in general? What are the strengths/weaknesses of the book? Do you have unanswered questions from what book? What would you like to add or remove from the book to make it better? You need to mention these questions in your outline to know what to focus on in your writing. Then, while creating the actual book review, formulate these sections as a properly structured essay that includes topic sentences and logical transitions. These outline guidelines are extremely important because the moment you detail them, you’ll have a clear structure in your head. We hope that they will make your book review as critical as possible (in a good way).

Report Research Paper Example | Topics and Well Written Essays - 500 words

Report - Research Paper Example For this reason, one should start with writing a draft, which helps one to identify the mistakes – both stylistic and grammatical, the flow as well as check for any information omitted (Bowden, 2004). One should follow an outline to ensure all information that is supposed to be in the report is included. Moreover, one should find out, for instance asking from the supervisor what is expected and if there is a standard format to be followed. If there are any sample reports available, it is advisable to go through them and if applicable utilize them as a model for the report to be written. Another way to write a concise and complete report is to take time to choose what information will be put into the report i.e. how brief or detailed it should be. When compiling and writing the report, the researcher ought to keep in mind the nature of the audience. The report should start with a clear, brief proclamation of the research aspirations and later, an explanation of the research pla n. A summary of major findings should come next. The report should end with a presentation of the recommendations and conclusions and any available exhibits appended. Finally, it is important to note that, report writing, like any skill, improves with practice. The use of computers can significantly facilitate report compiling and writing (Mooi & Sarstedt, 2011). The market research issue covered in the call center report is determine how long the customers have to wait to access customer service of various companies through a phone call (Collier, 2009). The major market research issues and outcomes are well outlined - how long different companies take to answer the call, whether it is an automated message or a person and overall quality of the customer service. The language used is objective, factual and user-friendly comparing and rating the companies depending on the findings. The research design and processes are adequately reported and the

EMs education program for a community based on EMS related issues Essay

EMs education program for a community based on EMS related issues within the community - Essay Example Such areas are majorly faced by the EMS problem of disease outbreak. These areas are constantly faced with malaria outbreak thus high mortality rate of both children and adults. Accessing health facilities is a problem to such people because of the following reasons. Poverty level, poor transport, poor communication. Unless health facilities and governments come up with long lasting strategies to avert the situation, then the nationals in such areas continue to suffer more and more. The community education program that can be employed to avert the above situation of malaria epidemic is first to develop, collect and disseminate the necessary information on the importance of good health to individuals and the importance of living in clean environment. In this case, professionals trained in the field of medicine should be given the first priority to undertake the exercise. The training programs should also be made affordable and accessible so as to achieve the entire goal. There are some established communities agencies which I can well involve myself in and provide the program. These agencies are either private or public but with a common goal of providing quick response to any medical care in a certain community. These agencies include NHTSA. This agency has been leading for the past forty years in the provision of a system approach to emergency medical services in various communities. Volunteers and other trained medical personnel have teamed up in the past to provide much assistance to these communities. NEMSIS (National Emergency Medical Services Information System) is another cooperative agency in the same ( Brenna, pg. 60). Research shows that there few developed programs designed to provide emergency medical services. This is due to some challenges faced such as lack of adequate trained personnel to conduct such services, slow response to cases of emergency in rural

My Choices and Commitments Essay -- Personal Narrative Essay Example

In pondering what my life will be like when I am finished with college, I have to consider the rapid life-changing events and choices that I am facing now at the age of 17. In a short span of time I have had to make a decision about my future career and, based on that decision, choose where I would go to college. I realize that I am in a crucial part of my life now, and that the commitments I make today will drastically affect my status ten years from now. It's a known fact that the majority of teenagers' decisions are inadvertently made based on the order of their priorities. Priorities at age 17 are not the same as those that one will have at age 27 or older. Since no one has written instructions for perfect living, bad decisions and irresponsible errors are prominent. My past four years in high school have helped me learn from my mistakes and have also given me time to prioritize. Time management has allowed me to participate in school athletics and other extra curricular activities and still remain at the top of my class. Now that I am at the point where graduation is simply weeks away, I am beginning to feel pressure about the major decisions I have made and will make in the next few months of my life. Since I am already set as far as college plans, (I will be attending the University of North Carolina at Chapel Hill), the major worries are yet to come. In the next four years of my life I will encounter a variety of diverse people, lifestyles, beliefs and cultures. Though not all of these experiences will be negative, I realize how important it is that I go to college with my standards, priorities, and morals secure. I know that how I choose to live, learn and succeed will directly impact the quality of the rest of ... ...h both my peers and the school administration and staff. This reputation came about because of choices I made years ago. My church youth group has been a wonderful way to learn about community service. Seeing others who are disadvantaged, ill or needy has taught me the importance of caring for others and to be thankful for my own good health and stable family situation. Through committing myself to these various activities, I have been able to help people, as well as help myself. I have learned the importance of teamwork, gained leadership skills, and learned how to humble myself to serve others. These interactions introduced opportunities that have helped prepare me for greater things. Ten years from now, I will be able to say that the hard work was worth it, the determination paid off, and that my priorities took me to the status that I aspired to achieve.

Solution Manual for Fluid Mech Cengel Book

Chapter 6 Momentum Analysis of Flow Systems Chapter 6 MOMENTUM ANALYSIS OF FLOW SYSTEMS Newton’s Laws and Conservation of Momentum 6-1C Newton’s first law states that â€Å"a body at rest remains at rest, and a body in motion remains in motion at the same velocity in a straight path when the net force acting on it is zero. † Therefore, a body tends to preserve its state or inertia. Newton’s second law states that â€Å"the acceleration of a body is proportional to the net force acting on it and is inversely proportional to its mass. Newton’s third law states â€Å"when a body exerts a force on a second body, the second body exerts an equal and opposite force on the first. † r 6-2C Since momentum ( mV ) is the product of a vector (velocity) and a scalar (mass), momentum must be a vector that points in the same direction as the velocity vector. 6-3C The conservation of momentum principle is expressed as â€Å"the momentum of a system remains constant when the net force acting on it is zero, and thus the momentum of such systems is conserved†.The momentum of a body remains constant if the net force acting on it is zero. 6-4C Newton’s second law of motion, also called the angular momentum equation, is expressed as â€Å"the rate of change of the angular momentum of a body is equal to the net torque acting it. † For a non-rigid body with zero net torque, the angular momentum remains constant, but the angular velocity 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 mass and angular speed will have different angular momentums unless they also have the same moment of inertia I. Linear Momentum Equation 6-6C The relationship between the time rates of change of an extensive property for a system and for a control volume is expressed by the Reynolds transport theorem, which provides the link between the r system and control volume concepts. The linear momentum equation is obtained by setting b = V and thus r B = mV in the Reynolds transport theorem. -7C The forces acting on the control volume consist of body forces that act throughout the entire body of the control volume (such as gravity, electric, and magnetic forces) and surface forces that act on the control surface (such as the pressure forces and reaction forces at points of contact). The net force acting on a control volume is the sum of all body and surface forces. Fluid weight is a body force, and pressure is a surface force (acting per unit area). -8C All of these surface forces arise as the control volume is isolated from its surroundings for analysis, and the effect of any detached object is accounted for by a force at that location. We can minimize the number of surface forces exposed by choosing the control volume such that the forces that we are not interested in remain internal, and thus they do not complicate the analysis. A well-chosen cont rol volume exposes only the forces that are to be determined (such as reaction forces) and a minimum number of other forces. 6-9C The momentum-flux correction factor ? nables us to express the momentum flux in terms of the r r r r & ? V (V ? n )dAc = ? mV avg . The value of ? is unity for uniform mass flow rate and mean flow velocity as ? Ac flow, such as a jet flow, nearly unity for turbulent flow (between 1. 01 and 1. 04), but about 1. 3 for laminar flow. So it should be considered in laminar flow. 6-1 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 6-10C The momentum equation for steady one-dimensional flow for the case of no external forces is r r r & & F= ? mV ? ? mV ? ? out ? in where the left hand side is the net force acting on the control volume, and first term on the right hand side is the incoming momentum flux and the second term is the outgoing momentum flux by mass. 6-11C In the application of the momentum equation, we can disregard the atmospheric pressure and work with gage pressures only since the atmospheric pressure acts in all directions, and its effect cancels out in every direction. -12C The fireman who holds the hose backwards so that the water makes a U-turn before being discharged will experience a greater reaction force since the numerical values of momentum fluxes across the nozzle are added in this case instead of being subtracted. 6-13C No, V is not the upper limit to the rocket’s ultimate velocity. Without friction the rocket velocity will continue to increase as more gas outlets the nozzle. 6-14C A helicopter hovers because the strong downdraft of air, caused by the overhead propeller blades, manifests a momentum in the air stream.This momentum must be countered by the helicopter lift force. 6-15C As the air density decreases, it requires more energy for a helicopter to hover, because more air must be forced into the downdraft by the helicopter blades to provide the same lift force. Therefore, it takes more power for a helicopter to hover on the top of a high mountain than it does at sea level. 6-16C In winter the air is generally colder, and thus denser. Therefore, less air must be driven by the blades to provide the same helicopter lift, requiring less power. 6-2 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 6-17C The force required to hold the plate against the horizontal water stream will increase by a factor of 4 when the velocity is doubled since & F = mV = ( ? AV )V = ? AV 2 and thus the force is proportional to the square of the velocity. 6-18C The accele ration will not be constant since the force is not constant. The impulse force exerted by & water on the plate is F = mV = ( ? AV )V = ?AV 2 , where V is the relative velocity between the water and the plate, which is moving. The plate acceleration will be a = F/m. But as the plate begins to move, V decreases, so the acceleration must also decrease. 6-19C The maximum velocity possible for the plate is the velocity of the water jet. As long as the plate is moving slower than the jet, the water will exert a force on the plate, which will cause it to accelerate, until terminal jet velocity is reached. 6-20 It is to be shown that the force exerted by a liquid jet of velocity V on a stationary nozzle is & proportional to V2, or alternatively, to m 2 . Assumptions 1 The flow is steady and incompressible. 2 The nozzle is given to be stationary. 3 The nozzle involves a 90 ° turn and thus the incoming and outgoing flow streams are normal to each other. 4 The water is discharged to the atmo sphere, and thus the gage pressure at the outlet is zero. Analysis We take the nozzle as the control volume, and the flow direction at the outlet as the x axis. Note that the nozzle makes a 90 ° turn, and thus it does not contribute to any pressure force or momentum flux & term at the inlet in the x direction. Noting that m = ?AV where A is the nozzle outlet area and V is the average nozzle outlet velocity, the momentum equation for steady one-dimensional flow in the x direction reduces to r r r & & & & F= ? mV ? ? mV > FRx = ? m out V out = ? mV ? ? out ? in where FRx is the reaction force on the nozzle due to liquid jet at the nozzle outlet. Then, & m = ? AV & > FRx = ? mV = AVV = AV 2 & & or FRx = ? mV = ? m & & m m2 =? ?A ? A Therefore, the force exerted by a liquid jet of velocity V on this & stationary nozzle is proportional to V2, or alternatively, to m 2 . Liquid Nozzle V FR 6-3 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 6-21 A water jet of velocity V impinges on a plate moving toward the water jet with velocity ? V. The force required to move the plate towards the jet is to be determined in terms of F acting on the stationary plate. Assumptions 1 The flow is steady and incompressible. 2 The plate is vertical and the jet is normal to plate. 3 The pressure on both sides of the plate is atmospheric pressure (and thus its effect cancels out). Fiction during motion is negligible. 5 There is no acceleration of the plate. 6 The water splashes off the sides of the plate in a plane normal to the jet. 6 Jet flow is nearly uniform and thus the effect of the momentum-flux correction factor is negligible, ? ? 1. Analysis We take the plate as the control volume. The relative velocity between the plate and the jet is V when the plate is st ationary, and 1. 5V when the plate is moving with a velocity ? V towards the plate. Then the momentum equation for steady one-dimensional flow in the horizontal direction reduces to r r r & & & & F= ? mV ? ? mV > ? FR = ? mi Vi > FR = miVi ? out ? in Stationary plate: ( Vi = V and Moving plate: ( Vi = 1. 5V and & mi = ? AVi = ? AV ) > FR = ? AV 2 = F & mi = ? AVi = ? A(1. 5V ) ) > FR = ? A(1. 5V ) 2 = 2. 25 ? AV 2 = 2. 25 F Therefore, the force required to hold the plate stationary against the oncoming water jet becomes 2. 25 times when the jet velocity becomes 1. 5 times. Discussion Note that when the plate is stationary, V is also 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 off its sides) per unit time also increases by 50%. 1/2V VWaterjet 6-4 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 6-22 A 90 ° elbow deflects water upwards and discharges it to the atmosphere at a specified rate. The gage pressure at the inlet of the elbow and the anchoring force needed to hold the elbow in place are to be determined. v Assumptions 1 The flow is steady, 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 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 (a) 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 & & & & m1 = m 2 = m = 30 kg/s. Noting that m = ? AV , the mean inlet and outlet velocities of water are & & 25 kg/s m m = = = 3. 18 m/s 2 ? A ? (? D / 4) (1000 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 = (1000 kg/m3 )(9. 81 m/s 2 )(0. 35 m)? 1 ? 1000 kg ? /s2 ? = 3. 434 kN/m = 3. 434 kPa ? ? r r r & & (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 y axes become & & FRx + P1,gage A1 = 0 ? ?m(+V1 ) = ? ?mV & & FRz = ? m(+V 2 ) = ? mV z x FRz 2 35 cm Solving for FRx and FRz, and substituting the given values, & 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 ? ? FRy FRx = tan -1 Water 25 kg/s FRx 1 ? 1N & FRy = ? 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 Note that the magnitude of the anchoring force is 136 N, and its line of action makes 143 ° from the positive x direction. Also, a negative value for FRx indicates the assumed direction is wrong, and should be reversed. 6-5 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc.Limited distribution permitted only to teachers and educators for course preparatio n. If you are a student using this Manual, you are 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 specified rate. The gage pressure at the inlet of the elbow and the anchoring force needed 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 given to be ? = 1. 03. Properties We take the density of water to be 1000 kg/m3. Analysis (a) 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 b eing the positive direction) and the vertical coordinate by z.The continuity equation for this one-inlet one-outlet steady flow system is & & & & m1 = m 2 = m = 30 kg/s. Noting that m = ? AV , the mean inlet and outlet velocities of water are & & 25 kg/s m m = = = 3. 18 m/s 2 ? A ? (? D / 4) (1000 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 = (1000 kg/m3 )(9. 81 m/s2 )(0. 70 m)? 1 ? 1000 kg ? m/s2 ? 6. 867 kN/m = 6. 867 kPa ? ? r r r & & (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 & & & FRx + P1,gage A1 = ? m(? V 2 ) ? ? m(+V1 ) = ? 2 ? mV FRz = 0 Solving for FRx and substituting the given values, & 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 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 6-24E A horizontal water j et strikes a vertical stationary plate normally at a specified velocity. For a given anchoring force needed 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 horizontal reaction force. 5 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 We 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 & & & & 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 & sign for forces and velocities in the negative x-direction. Solving for m and substituting the given values, & 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& = & 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, some 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 preparati on. 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 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 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 the 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 coordina te 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 & & & & m1 = m 2 = m = 30 kg/s. Noting that m = ? AV , the inlet and outlet velocities of water are & 30 kg/s m V1 = = = 2. 0 m/s ? A1 (1000 kg/m 3 )(0. 0150 m 2 ) & 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 reference 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 & & ? 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 & & & 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, & 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 ? & FRz = ? mV 2 sin ? + W = 1. 03(30 kg/s)(12sin45 ° m/s)? ? 1000 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 considered. 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 densi ty 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 & & & & m1 = m 2 = m = 30 kg/s. Noting that m = ?AV , the inlet and outlet velocities of water are & 30 kg/s m = = 2. 0 m/s V1 = ? A1 (1000 kg/m 3 )(0. 0150 m 2 ) & 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 reference 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 ? ? ? ? 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 & & ? 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 & & FRx + P1,gage A1 = ? mV 2 cos ? ? ? mV1 and & FRy ? W = ? mV 2 sin ? Solving for FRx and FRz, and substituting the given values, & 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 & = ? 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 accelerated by a nozzle strikes the back surface of a cart moving horizontally at a constant velocity. The braking force and the power wasted by the brakes are to be determined. . Assumptions 1 The flow is steady and incompressible. 2 The water splatters off the sides of the plate in all direction s 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 cart. 7 The motions of the water jet and the cart 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 to 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 & & & & 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 & 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 power wasted by the brakes is 1 kW ? ? & W = FbrakeV cart = (250 N)(5 m/s)? ? = 1. 25 kW ? 1000 N ? m/s ? Discussion Note that the power wasted is equivalent to the maximum power that can be generated as the cart velocity is maintained constant. 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 Fl ow Systems 6-28 Water accelerated 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 splitter, such that half of the flow is diverted up ward at 45 °, and the other half is directed down.The force required 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 the split is the atmospheric pressure which is disregarded since it acts on all surfaces. 3 The gravitational 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 & & 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 & & 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 & & positive directions.Noting that V2 = V1 = V and m 2 = 1 m , the momentum equations along the x and z 2 axes become & & & FRx = 2( 1 m)V 2 cos ? ? mV1 = mV (cos ? ? 1) 2 & & 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)? ? = ? 1135 lbf 32. 2 lbm ? ft/s 2 ? ? FRz = 0 The negative value for FRx indicates the assumed direction is wrong, and should be reversed. Therefore, a force of 1135 lbf must be applied 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 cau se 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 angle on the force exerted on the splitter as the half splitter angle varies from 0 to 180 ° in increments of 10 ° is to be investigated. g=32. 2 â€Å"ft/s2† rho=62. 4 â€Å"lbm/ft3† V_dot=100 â€Å"ft3/s† V=20 â€Å"ft/s† m_dot=rho*V_dot F_R=-m_dot*V*(cos(theta)-1)/g â€Å"lbf† ?,  ° 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 8000 7000 6000 5000 & m , lbm/s 6240 6240 6240 6240 6240 6240 6240 6240 6240 6240 624 0 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 determined.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 a tmospheric 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 & m = ? VA = (1000 kg/m 3 )(18 m/s)[? (0. 05 m) 2 / 4] = 35. 34 kg/s The momentum equation for steady one-dimensional flow in the x (flow) direction reduces in this case to r r r & & & & 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, a n equal and opposite impulse force acts on the plate, which is determined to ? 1N & 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 velocity 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 gravitational 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 & & & & m1 = m 2 = m = 353. 4 kg/s. Noting that m = ? AV , the mass flow rate of water and its outlet velocity are 2 & m = ? V1 A1 = ? V1 (? D1 / 4) = (1000 kg/m 3 )(5 m/s)[? (0. 3 m) 2 / 4] = 353. 4 kg/s & & 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 & & ? 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 & FRx + P1,gage A1 = 0 ? ? mV1 & 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 & 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 & 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 wind turbine with a given span diameter and efficiency is subjected to steady winds. 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 kinetic energy is converted to thermal 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 kinetic energy, & 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 ? & 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) & & & 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 & 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 kinetic energy not converted to electric power leaves the wind turbine as outgoing kinetic energy. Therefore, V2 V2 & & & & 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 choose the control volume around the wind turbine such that the wind is norm al 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 & & 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 & & & 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 expected.Discussion This force acts on top of the tower where the wind turbine is installed, and the bending moment it generates at the bottom 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 c ourse 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 friction 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 w ater 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 & & & flow system is m1 = m 2 = m where & 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 & & 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 & & & 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 nega tive 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 bent 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 effec ts 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 equation for & & & this one-inlet one-outlet steady flow system is m1 = m 2 = m where & 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 & & 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 assu me them to be in the positive directions. Then the momentum equations along the x and y axes become & & & FRx = m(? V 2 ) cos 45 ° ? m(+V1 ) = ? mV (1 + cos 45 °) & (+V 2 ) sin 45 ° = mV sin 45 ° & 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 anchoring 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 average 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 (thi s 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& A = V& ? D / 4 2 = 5 m 3 /min ? (0. 06 m) 2 / 4 1768 m/min = 29. 5 m/s & m = ? V& = (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 & & ? 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 & & 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 t he nozzle in place. Discussion The force of 2457 N is equivalent to the weight of about 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 jet 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 o f 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 direction of x axis. The mass flow rate of water in the jet is & 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 & & 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 ? & & ? 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 relative 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 Comp anies, 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 investigated. rho=1000 â€Å"kg/m3† D=0. 05 â€Å"m† V_jet=30 â€Å"m/s† Ac=pi*D^2/4 V_r=V_jet-V_plate m_dot=rho*Ac*V_jet F_R=m_dot*V_r â€Å"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 1767 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 ar e using it without permission. Chapter 6 Momentum Analysis of Flow Systems 6-39E A fan moves air at sea level at a specified rate. The force required to hold the fan and the minimum power input 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. Air 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 power input 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 bounded by streamlines on the sides with air entering through the large cross-section (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) & m = ? V& = (0. 0749 lbm/ft 3 )(2000 ft 3/min) = 149. 8 lbm/min = 2. 50 lbm/s V2 = V& A2 = V& 2 ? D 2 / 4 = 2000 ft 3 /min ? (2 ft) 2 / 4 = 636. 6 ft/min = 10. ft/s & & ? 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 ? ? & & 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 frict ion 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 ? & & & & & m? 1 + 1 + gz1 ? + W pump, u = m? 2 + 2 + gz 2 ? + W turbine + E mech,loss > ? ? ? ? 2 2 ? ? ? ? Substituting, V & & Wfan, u = m 2 2 2 V2 (10. 6 ft/s) 2 ? 1 lbf 1W ? & & 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 mechanical 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 unloaded hover, and the rpm 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 pressure 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 elevation 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. 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 & & 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 & & ? W = m(? V 2 ) ? 0 > W = mV 2 = ( ? AV 2 )V 2 = ? AV 22 > V2 = ? A 1 where A is the blade span 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 unloaded mode become V 2,unloaded = m unloaded 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&unloaded = AV 2,unloaded = (176. 7 m 2 )(21. m/s) = 3834 m 3 /s & munloaded = ? V&unloaded = (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 & & & & & & & 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 & ? ? & = (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 now 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 & mloaded = ? V&loaded = ? AV2, loaded = (1. 18 kg/m 3 )(176. 7 m 2 )(34. 3 m/s) = 7152 kg/s ? V2 ? (34. 3 m/s)2 & & = (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 & V 2 = kn > V 2,loaded V 2, unloaded = & n loaded & n unloaded > & n loaded = V 2,loaded V 2, unloaded & 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.  © 200 6 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 mountain where the air density considerably lower than that at sea level. The blade rotational velocity to hover at the higher altitude and the percent increase in the required power 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 locatio n 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 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 & & 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 & & ? 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 & n = kV 2 > & n mountain V 2, mountain = & n sea V 2,sea > & n mountain = V 2, mountain V 2,sea & 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 & & & & & & & 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 & & 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 & Wmountain fan,u 0. 5W 1. 5 / ? mountain A = & 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 both 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 sluice 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 shear 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&1 = V&2 = V& > A1V1 = A2V 2 = V& > V1 = V& A1 = V& wy1 and V2 = V& A2 = V& wy 2 (2) Substituting into Eq. (1), ? V& ? ? wy ? 2 ? ? V& ? 2 g ( y1 ? y 2 ) & ? ? ? ? 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& = 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 & & 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