Public Relations Techniques and Cases Essay Example | Topics and Well Written Essays - 1500 words

Advertising Techniques and Cases - Essay Example A contextual analysis is a favored system when ‘how’ or ‘why questions are being presented when the scientist has little command over occasions. The attention is consistently on contemporary wonders inside some true setting (Center et al., 2008). The scientist is empowered to investigate on genuine occasions that can't be controlled in the lab setting (Yin, 1994).The contextual analysis should utilize various proof sources to expand legitimacy (Jaques, 2008). The contextual investigation beneath featured the correspondence exercises in the main period of Phare and took an inside and out glance at the model correspondence program created in November 1997. The model was created by Brussels-based open undertakings consultancy to be utilized by the EU designation to the 10 EU part nations. The model can apply to numerous other financial and political circumstances and social factors of a nation. It accentuates on one-on â€one correspondence as opposed to including the broad communications. In the principal long stretches of activity from 1989-1994, the Phare program gave skill to the part nations from a wide scope of associations running from non-business, open and even private. It went about as a multiplier by animating ventures and reacting to needs that can't be met by different associations. Phare additionally went about as an amazing impetus for opening assets from different benefactors contemplates, ensure plans, and credit lines. It offers need to the improvement of the private division, rebuilding of state venture and condition assurance.

Alligators and Crocodiles Essay Essay Example

Gators and Crocodiles Essay Example Gators and Crocodiles Essay Gators and Crocodiles Essay Relatively few individuals can recognize a crocodile and a gator. Gators and crocodiles are comparative yet unique from various perspectives. In this paper I will talk the gator and crocodile likenesses and contrasts. In the event that you see a gator or a crocodile would you be able to express the distinction? The manners in which you can express the distinction in a gator and a crocodile is the neb. centripetal depressions. salt secretory organs on lingua. jaws and dentition. Other than in this paper I will paint you a picture of how the reptilians look and reveal to you the distinction in the reptile’s size and home ground. Crocs are semi-amphibian meat eating reptilians with four legs and a tremendous tail. Col. 2010 ) . The reptilian tail is a large portion of its length and it induces the crocodile through the H2O. It is other than utilized as an arm and shops fat for the gator which he will use for nutriment for the winter. They are merciless ( poikilothermic ) energize creatures which do non do their ain natural structure heat yet gain their warmth by getting a charge out of in the Sun. ( Col. 2010 ) . The Chinese crocodile can turn between 6 pess long and American gators are 13 pess long however can go up to 19 pess. Crocodiles have enormous. wide natural structures with short legs and long. strong tail. The crocodile has thick. rugged covering with hard. plate-formed graduated tables. ( Hayden ) . They are relentless quicken creatures that shading is either dim green or earthy colored. The crocodile have ears which are cuts on the caput that the vast majority of us do non see and let them to hold great hearing. The crocodile caput is long and pointed with the eyes and foremost nariss situated on the highest point of the caput. Crocodile can run from 7-15 pess long yet neer end turning and can populate up to 75 mature ages. Alligator’s upper jaw is more extensive than the lower jaw and its lower dentition are to a great extent concealed when oral pit is shut and fit into attachments in the upper jaw yet makes the fourth tooth on every side of its lower jaw fit of rage into an attachment in the upper jaw. Turner ) . Gators have a wide U-molded short neb. Crocodiles have non-utilitarian salt secretory organs and centripetal holes that are simply close to the jaws. ( Col. 2010 ) Crocodiles upper jaws is about a similar size as the lower jaw which makes its lower dentition appear outside the upper jaw when oral cavity is shut. ( Turner ) The crocodile upper dentition appear outside the lower jaw however nebs are thin. angular and long. Crocodile salt secretory organs on the lingua discharge additional salt and the centripetal cavities are over the majority of the natural structure. Gators are simply local to the United States and China however prefer to eat fish. polo-necks. grouped warm blooded animals. flying creatures and different reptilians. The croc lives just in new Waterss like pools. fens. wetlands. streams. lakes. what's more, swamps. ( Lutz. 2012 ) . When ashore the croc is delayed to travel however can travel sensibly quickly in short separations. The crocodiles are typically solitary energize creatures yet littler 1s can be found in huge Numberss close to one another. ( Lutz. 2012 ) Crocodiles live along the beach of Florida. . Focal America. what's more, portions of South America. The crocodile may populate in saline or salt-water that is warm and calm, for example, Rhizophora ruin overwhelms that are generally found against the shorelines. ( Turner ) . Crocodile other than may populate where the stream meets the ocean known as estuaries. The crocodile eat fish and other enliven creatures that they find in or close to the H2O. counting polo-necks. snakes. little well evolved creatures. also, winged creatures. The reptilian does the vast majority of its chasing at dim which makes him nighttime. Crocodiles are other than shy. isolated. what's more, only from time to time observed by individuals however are still extremely forceful. ( Hayden ) Since gators and crocodile are the two reptilians they are regularly simple mixed up. I trust by perusing this you would now be able to express the distinction between a gator and a crocodile. Gators and crocodile physical visual viewpoint are actually similarly however in the event that you take a gander at the reptilians you could simple show out what is unique. The things that are distinctive about them are the neb. salt secretory organs on lingua. centripetal pits. jaws. also, dentitions. Recall crocodiles are extremely forceful so do non close to them since they will assault. Since you have a superior visual of a crocodile and gator. if you somehow managed to come into contact with one of the reptilians would you be able to express the distinction between the two.

Cha-Ching! How to Budget in College

Cha-Ching! How to Budget in College Ever since I began writing blogs, I’ve learned about various topics like how to manage classes, how to stay involved while still being a full-time student, etc. Something that came to my mind that could be useful for many of us is a quick discussion on budgeting. We’ve all heard that college students are broke, and while it is true that we have tuition and books to pay for during our four years, I’ve come up with a few tips that I have implemented in my life to help me save a few extra bucks at the end of the day! Check your bank account. Checking your bank account is the most important thing to do. Sometimes it can be difficult to check it daily given our busy schedules. Set aside a few minutes every day to keep tabs on your account activity. This will ensure there are no discrepancies and youre aware of how much you have and are spending. Set financial goals. This past semester, my goal was to save enough money to be able to buy graduation gifts for my close friends and family at the end of the semester. No matter how big or small, it is nice to have a goal to work toward so that you don’t lose track of what you’re saving for. From: Kiplingers Financial Planning Create a budget. I prefer creating a weekly budget of how much I allocate for food, social activities, and miscellaneous costs throughout the week and over the weekend. Create an excel sheet or some sort of organized document that can list out your budgeted money for the week/month. Many programs have templates for budgeting that are completely free to use! These are just a few basic tips I think every student should follow to help with budgeting money. I have been following these few steps the past two semesters and I have seen my savings grow in my bank account. Being mindful of where and when you spend your money is a tough but important thing to do. This is especially vital as we will soon enter the real world where we will deal with more money. But before that happens, it’s important to take responsibility for our earnings and put them to good use! Kripa Class of 2020 I'm majoring in Psychology, minoring in Spanish, and pursuing a pre-dental track. It seems like I’m all over the place, but that’s what I like about college! I get to choose to study what I’m interested in, and I’m happy to be doing just that at Illinois.

Cerebral Palsy, The Most Common Physical Disability Of...

According to Lancet Neurology, Cerebral Palsy is â€Å"the most common physical disability of childhood†¦ and a clinical diagnosis encompassing a heterogeneous group of neurodevelopmental disorders that cause impairments of movement and posture†¦Ã¢â‚¬  (Moreno-De-Luca, Ledbetter, 2012). It is no wonder then, that Crotched Mountain strives to provide the best of services for individuals living with cerebral palsy. Some of these services include special school programming specific to an individual’s needs as well as thorough rehabilitation interventions and treatment through the hospital and residential living. These unique and purposeful services are what help residents and clients of Crotched Mountain take steps forward in their treatment or recovery. Crotched Mountain Rehab hopes that in offering so many specific programs and adapted services they are able to enhance the quality of lives both in and outside of their doors. Exact etiological factors of Cerebral Pal sy (CP) are not specifically known. Researchers have been doing much to decipher the causes of a child diagnosis of CP. What is believed up to this point is that there are several keys to the classification of cerebral palsy which in turn, lead o a greater understanding of what may have caused it. These classifications are made based off of the following; the severity (which is determined using the Gross Motor Function Classification System), the motor type determined (spastic, ataxic, or dyskinetic) and the topographicalShow MoreRelatedA Critical Review Of A Journal Paper1958 Words   |  8 PagesA Critical Review of a Journal Paper Introduction Cerebral palsy is a group of disorders that permanently affects an individual’s ability to move such as body movement, muscle control and contraction, this can be caused by a combination of abnormal development or damage to parts of the brain that control movement, balance and posture. 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Children with congenital brain malformations, a family history of epilepsy, or neonatal seizures are atRead MoreUnderstand the Context of Supporting Individuals with Learning Disabilities4094 Words   |  17 PagesLEARNING DISABILITIES OUTCOME 1 1. There are various pieces of legislation in place to promote equality and reduce discrimination. These include: * The Disability Discrimination Act 2005 * The Special Educational Needs and Disability Act 2001 * The Race Relations (Amendment) Act 2000 * Convention on the Rights of the Child (UN, 1989) * The Human Rights Act 1998 * The Sex Discrimination Act 1975 (as amended) * Employment Equality Regulations 2003 2. The Disability DiscriminationRead MoreNU 545 Unit 2 Essay10921 Words   |  44 Pagesand behavior, maintaining balance and posture? - Ch. 15 p. 454 Box 15-3 - Brainstem- midbrain, medulla oblongata, and pons Reticular Formation-Collection of nuclei within brainstem that maintains wakefulness and works in conjunction with the cerebral cortex and together they are known as the reticular activating system. P. 454 - 3 parts of the brain: forebrain, midbrain, hindbrain - Expression of affect (emotional and behavioral states) is mediated by extensive connections with the limbicRead MoreThe Effects Of Autism On Children With Autism3085 Words   |  13 PagesHFASD) appear to be particularly at risk for behavior and emotional problems, especially depression and anxiety† (Rosin 2014). Autism is defined by three key areas, and is known by specific disorders such as pervasive developmental disorders (PDD), childhood disintegrative disorder (CDD), and pervasive developmental disorder not otherwise specified (PDD-NOS). Among PPD’s include Asperger’s syndrome and Rett’s disorder. â€Å"About 1 in 68 children have been identified with autism spectrum disorder.† (DataRead MoreEssay on Life With Spina Bifida2829 Words   |  12 PagesBACKGROUND: Having a chronic physical disability affects many aspects of a person’s life beyond his or her general health (Eiser 1997). Myelomeningocele, the most severe form of spina bifida (SB), is commonly associated with hydrocephalus, Chiari II malformation, diminished or absent sensation or motor function in the lower limbs, and impaired bowel and bladder control (S.L. Kinsman 2007). Many people with SB rely on some form of assistive technology for mobility, such as wheelchairs, crutchesRead More The Impact and History of Learning Disorders on Children Essay5477 Words   |  22 Pagesout concisely the fundamental role that education would play in postwar America: â€Å"Today, education is perhaps the most important function of state and local governments. Compulsory school attendance laws and the great expenditures for education both demonstrate our recognition of the importance of education to our democratic society. It is required in the performance of our most basic public responsibilities, even service in the armed forces. It is the very foundation of good citizenship. TodayRead MoreThe Theory Of Counseling And Therapy Theories6153 Words   |  25 PagesSummary * Influences of Theories--How counseling theories influence your understanding of how to work with consumers with disabilities. The theories we learned provided a broad-based understanding of numerous factors related to the evolution of counseling and therapy theories and practices, along with new counseling and therapy skills. The important premise that underscores one of the central challenges of counseling and psychotherapy is that we are all in the same world, but each of us makes different

Incidents During The Life Of A Slave Girl By Harriet Jacobs

Incidents in the Life of a Slave Girl Incidents in the Life of a Slave Girl by Harriet Jacobs is an Autobiography from the point of view of a southern slave. She has named herself Linda Brent in the book to keep her identity anonymous. The book takes place in between 1820-1840 in which slavery was still legal and common throughout the United States south. The book begins in an unnamed town in the south in which the protagonist was raised in as a slave. Harriet Jacobs wrote the book to shine light on how slaves were treated in the south. She shows how even thought they were not always treated poorly they were never treated as equals.The purpose of the book is to show the horrors and tribulations a slave would have to go through on a daily basis. Not only does she point out the life of a slave but also the life of a women during a time in which even a white women were not treated as equals. Harriet Jacobs writes this book to anyone who is not a slave. In particular she writes to men and women in the north in hopes that t hey can help free them from the injustices that slaves and women face everyday. Harriet Jacobs chose to write to the north because she knows that only the north can stop slavery because the south is completely engulfed in the practice of slavery. Harriet Jacobs attempts to inform the north by writing a slave narrative about her own life. She does this by using the pen name of Linda Brent. The narrative begins in an unnamed town in the American South. She isShow MoreRelated Incidents In The Life Of A Slave Girl Essay1671 Words   |  7 PagesHarriet Jacobs wanted to tell her story, but knew she lacked the skills to write the story herself. She had learned to read while young and enslaved, but, at the time of her escape to the North in 1842, she was not a proficient writer. She worked at it, though, in part by writing letters that were published by the New York Tribune, and with the help of her friend, Amy Post. 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I think that this narrative writing is an important text to help us understand the different perspectives of slavery in America. There are some slave owners that are kind and humane, and some slave owners that are cruel and abusive. Additionally, reading from a female slave’s perspectives teaches us that life on the plantations and life in theRead More Incidents in the Life of a Slave Girl by Harriet Jacobs Essay1711 Words   |  7 PagesIncidents in the Life of a Slave Girl by Harriet Jacobs Harriet Jacobs in Incidents in the Life of a Slave Girl uses clear detail and straightforward language, except when talking about her sexual history, to fully describe what it is like to be a slave. Jacobs says that Northerners only think of slavery as perpetual bondage; they dont know the depth of degradation there is to that word. She believes that no one could truly understand how slavery really is unless they have gone through it.Read MoreJacobs Douglass: An Insight Into The Experience of The American Slave1019 Words   |  5 PagesThe slave narratives of the ante-bellum time period have come across numerous types of themes. Much of the work concentrates on the underlining ideas beneath the stories. In the narratives, fugitives and ex-slaves appealed to the humanity they shared with their readers during these times, men being lynched and marked all over and women being the subject of grueling rapes. The slave narrative of Frederick Douglas and Harriet Jacobs: Incidents in the Life of a Slave Girl themes come from the existenceRead MoreEssay about Harriet Jacobs Incidents In The Life Of A Slave Girl1355 Words   |  6 PagesHarriet Jacobs Incidents In The Life Of A Slave Girl The feminist movement sought to gain rights for women. Many feminist during the early nineteenth century fought for the abolition of slavery around the world. The slave narrative became a powerful feminist tool in the nineteenth century. Black and white women are fictionalized and objectified in the slave narrative. White women are idealized as pure, angelic, and chaste while black woman are idealized as exotic and contained an uncontrollableRead MoreIncidents In The Life A Slave Girl Summary1630 Words   |  7 Pages Harriet Jacobs writes, â€Å"No pen can give an adequate description of all [the] pervading corruption of slavery.† In the book, Incidents in the Life a Slave Girl, Harriet Jacobs recount her time as a slave before escaping the cruelties of slavery to freedom. This quote from the book outlines the intelligence Harriet Jacobs has about the torment in slavery. In the beginning of the book the preface and the editor’s introduction to the book outline Harriet Jacobs story. Both the preface and the author’sRead MoreIncidents Throughout The Life Of A Slave Girl By Harriet Jacobs1505 Words   |  7 PagesIncidents in the life of a slave girl’ written by Harriet Jacobs and published by L.Maria Child (in 1831), is an autobiography by the author herself which documents Jacobs life as a slave and therefore The book starts when Jacobs is born as a slave in a city of North Carolina and then continues through her escape, her status as a runaway fugitive in the North, and finally her path to freedom when one of her northern white friends buys her in the year 1852. Incidents in the Life of a Slave GirlRead MoreThe Life of A Slave Girl by Harriet A. Jacobs Essay1272 Words   |  6 PagesA slave narrative is to tell a slaves story and what they have been through. Six thousand former slaves from North America told about their lives during the 18th and 19th centuries. About 150 narratives were published as separate books or articles most slaves were born in the last years of the slave regime or during the Civil War. Some Slaves told about their experiences on plantations, in cities, and on small farms. Slave narratives are one of the only ways that people today know about the wayRead MoreHarriet Jacobs s Story : The True Meaning Of A Slave s Quest For Freedom1682 Words   |  7 PagesHarriet Jacobs’s story informs the reader of her experiences and transformative tribulations she had to undergo from childhood to adulthood. No one in today’s society could come close to comprehending the amount of heartache, torment, anguish, and co mplete misery women had to suffer and endure during slavery. However, we can all learn from Jacobs’s heartbreaking story to understand the true meaning of a slave’s quest for freedom and the inalienable bond a mother has for her children. Life was tough

Steam Jet Refrigeration Cycle Free Essays

string(61) " ow rates gives the mass \? ow rate of the compressed vapor\." Chemical Engineering and Processing 41 (2002) 551– 561 www. elsevier. com/locate/cep Evaluation of steam jet ejectors Hisham El-Dessouky *, Hisham Ettouney, Imad Alatiqi, Ghada Al-Nuwaibit Department of Chemical Engineering, College of Engineering and Petroleum, Kuwait Uni6ersity, P. We will write a custom essay sample on Steam Jet Refrigeration Cycle or any similar topic only for you Order Now O. Box 5969, Safat 13060, Kuwait Received 4 April 2001; received in revised form 26 September 2001; accepted 27 September 2001 Abstract Steam jet ejectors are an essential part in refrigeration and air conditioning, desalination, petroleum re? ning, petrochemical and chemical industries. The ejectors form an integral part of distillation columns, condensers and other heat exchange processes. In this study, semi-empirical models are developed for design and rating of steam jet ejectors. The model gives the entrainment ratio as a function of the expansion ratio and the pressures of the entrained vapor, motive steam and compressed vapor. Also, correlations are developed for the motive steam pressure at the nozzle exit as a function of the evaporator and condenser pressures and the area ratios as a function of the entrainment ratio and the stream pressures. This allows for full design of the ejector, where de? ing the ejector load and the pressures of the motive steam, evaporator and condenser gives the entrainment ratio, the motive steam pressure at the nozzle outlet and the cross section areas of the diffuser and the nozzle. The developed correlations are based on large database that includes manufacturer design data and experimental data. The model includes correlatio ns for the choked ? ow with compression ratios above 1. 8. In addition, a correlation is provided for the non-choked ? ow with compression ratios below 1. 8. The values of the coef? cient of determination (R 2) are 0. 85 and 0. 78 for the choked and non-choked ? w correlations, respectively. As for the correlations for the motive steam pressure at the nozzle outlet and the area ratios, all have R 2 values above 0. 99.  © 2002 Elsevier Science B. V. All rights reserved. Keywords: Steam jet ejectors; Choked ? ow; Heat pumps; Thermal vapor compression 1. Introduction Currently, most of the conventional cooling and refrigeration systems are based on mechanical vapor compression (MVC). These cycles are powered by a high quality form of energy, electrical energy. The inef? cient use of the energy required to operate such a process can be generated by the combustion of fossil uels and thus contributes to an increase in greenhouse gases and the generation of air pollutants, such as NOx, S Ox, particulates and ozone. These pollutants have adverse effects on human health and the environment. In addition, MVC refrigeration and cooling cycles use unfriendly chloro-? oro-carbon compounds (CFCs), which, upon release, contributes to the destruction of the protective ozone layer in the upper atmosphere. * Corresponding author. Tel. : + 965-4811188Ãâ€"5613; fax: + 9654839498. E -mail address: eldessouky@kuc01. kuniv. edu. kw (H. El-Dessouky). Environmental considerations and the need for ef? cient se of available energy call for the development of processes based on the use of low grade heat. These processes adopt entrainment and compression of low pressure vapor to higher pressures suitable for different systems. The compression process takes place in absorption, adsorption, chemical or jet ejector vapor compression cycles. Jet ejectors have the simplest con? guration among various vapor compression cycles. In contrast to other processes, ejectors are formed of a single uni t connected to tubing of motive, entrained and mixture streams. Also, ejectors do not include valves, rotors or other moving parts and are available ommercially in various sizes and for different applications. Jet ejectors have lower capital and maintenance cost than the other con? gurations. On the other hand, the main drawbacks of jet ejectors include the following: ? Ejectors are designed to operate at a single optimum point. Deviation from this optimum results in dramatic deterioration of the ejector performance. 0255-2701/02/$ – see front matter  © 2002 Elsevier Science B. V. All rights reserved. PII: S 0 2 5 5 – 2 7 0 1 ( 0 1 ) 0 0 1 7 6 – 3 552 ? H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 Ejectors have very low thermal ef? iency. Applications of jet ejectors include refrigeration, air conditioning, removal of non-condensable gases, transport of solids and gas recovery. The function of the jet ejector differs considerably in these processes. For example, in refrigeration and air conditioning cycles, the ejector compresses the entrained vapor to higher pressure, which allows for condensation at a higher temperature. Also, the ejector entrainment process sustains the low pressure on the evaporator side, which allows evaporation at low temperature. As a result, the cold evaporator ? uid can be used for refrigeration and cooling functions. As for the removal of non-condensable gases in heat transfer units, the ejector entrainment process prevents their accumulation within condensers or evaporators. The presence of non-condensable gases in heat exchange units reduces the heat transfer ef? ciency and increases the condensation temperature because of their low thermal conductivity. Also, the presence of these gases enhances corrosion reactions. However, the ejector cycle for cooling and refrigeration has lower ef? ciency than the MVC units, but their merits are manifested upon the use of low grade energy that has limited effect on the environment and lower ooling and heating unit cost. Although the construction and operation principles of jet ejectors are well known, the following sections provide a brief summary of the major features of ejectors. This is necessary in order to follow the discussion and analysis that follow. The conventional steam jet ejector has three main parts: (1) the nozzle; (2) the suction chamber; a nd (3) the diffuser (Fig. 1). The nozzle and the diffuser have the geometry of converging/diverging venturi. The diameters and lengths of various parts forming the nozzle, the diffuser and the suction chamber, together with the stream ? ow rate and properties, de? e the ejector capacity and performance. The ejector capacity is de? ned in terms of the ? ow rates of the motive steam and the entrained vapor. The sum of the motive and entrained vapor mass ? ow rates gives the mass ? ow rate of the compressed vapor. You read "Steam Jet Refrigeration Cycle" in category "Essay examples" As for the ejector performance, it is de? ned in terms of entrainment, expansion and compression ratios. The entrainment ratio (w ) is the ? ow rate of the entrained vapor Fig. 1. Variation in stream pressure and velocity as a function of location along the ejector. H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 divided by the flow rate of the motive steam. As for the expansion ratio (Er), it is de? ned as the ratio of the motive steam pressure to the entrained vapor pressure. The compression ratio (Cr) gives the pressure ratio of the compressed vapor to the entrained vapor. Variations in the stream velocity and pressure as a function of location inside the ejector, which are shown in Fig. 1, are explained below: ? The motive steam enters the ejector at point (p ) with a subsonic velocity. ? As the stream ? ows in the converging part of the ejector, its pressure is reduced and its velocity increases. The stream reaches sonic velocity at the nozzle throat, where its Mach number is equal to one. The increase in the cross section area in the diverging part of the nozzle results in a decrease of the shock wave pressure and an increase in its velocity to supersonic conditions. ? At the nozzle outlet plane, point (2), the motive steam pressure becomes lower than the entrained vapor pressure and its velocity ranges between 900 and 1200 m/s. ? The entrained vapor at point (e ) enters the ejector, where its velocity increases and its pressure decreases to that of point (3). ? The motive steam and entrained vapor streams may mix within the suction chamber and the converging section of the diffuser or it may ? ow as two separate treams as it enters the constant cross section area of the diffuser, where mixing occurs. ? In either case, the mixture goes through a shock inside the constant cross section area of the diffuser. The shock is associated with an increase in the mixture pressure and reduction of the mixture velocity to subsonic conditions, point (4). The shock occurs because of the back pressure resistance of the condenser. ? As the subsonic mixture emerges from the constant cross section area of the diffuser, further pressure increase occurs in the diverging section of the diffuser, where part of the kinetic energy of the mixture is converted into pressure. The pressure of the emerging ? uid is slightly higher than the condenser pressure, point (c ). Summary for a number of literature studies on ejector design and performance evaluation is shown in Table 1. The following outlines the main ? ndings of these studies: ? Optimum ejector operation occurs at the critical condition. The condenser pressure controls the location of the shock wave, where an increase in the condenser pressure above the critical point results in a rapid decline of the ejector entrainment ratio, since the shock wave moves towards the nozzle exit. Operating at pressures below the critical points has negligible effect on the ejector entrainment ratio. 553 ? At the critical condition, the ejector entrainment ratio increases at lower pressure for the boiler and condenser. Also, higher temperature for the evaporator increases the entrainment ratio. ? Use of a variable position nozzle can maintain the optimum conditions for ejector operation. As a result, the ejector can be maintained at critical conditions even if the operating conditions are varied. ? Multi-ejector system increases the operating range and improves the overall system ef? ciency. Ejector modeling is essential for better understanding of the compression process, system design and performance evaluation. Models include empirical correlations, such as those by Ludwig [1], Power [2] and El-Dessouky and Ettouney [3]. Such models are limited to the range over which it was developed, which limits their use in investigating the performance of new ejector ? uids, designs or operating conditions. Semi-empirical models give more ? exibility in ejector design and performance evaluation [4,5]. Other ejector models are based on fundamental balance equations [6]. This study is motivated by the need for a simple mpirical model that can be used to design and evaluate the performance of steam jet ejectors. The model is based on a large database extracted from several ejector manufacturers and a number of experimental literature studies. As will be discussed later, the model is simple to use and it eliminates the need for iterative procedures. 2. Mathematical model The review by Sun and Eames [7] outlined the developments in mathematical modeling and design of jet ejectors. The review shows that there are two basic approaches for ejector analysis. These include mixing of the motive steam and entrained vapor, either at constant ressure or at constant area. Design models of stream mixing at constant pressure are more common in literature because the performance o f the ejectors designed by this method is more superior to the constant area method and it compares favorably against experimental data. The basis for modeling the constant pressure design procedure was initially developed by Keenan [6]. Subsequently, several investigators have used the model for design and performance evaluation of various types of jet ejectors. This involved a number of modi? cations in the model, especially losses within the ejector and mixing of the primary and secondary streams. In this section, the constant pressure ejector model is developed. The developed model is based on a number of literature studies [8 – 11]. The constant pressure model is based on the following assumptions: H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 554 Table 1 Summary of literature studies on ejector design and performance Reference Fluid Boiler, evaporator and condenser temperature ( °C) Conclusion [19] R-113 60–100; 5–18; 40–50 Basis for refrigerant selection for solar system, system performance increased with increasing boiler and evaporator temperatures and decreasing condenser temperature. 20] R-113; R-114; R-142b; R-718 80–95; 5–13; 25–45 Comparison of ejector and refrigerant performance. Dry, wet and isentropic ?uids. Wet ? uid damage ejectors due phase change during isentropic expansion. R-113 (dry) has the best performance and R142b (wet) has the poorest performance. [21,22] R-11 4 86; ? 8; 30 Increase in ejector performance using mechanical compression booster. [8] Water 120–140; 5–10; 30–65 Choking of the entrained ? uid in the mixing chamber affects system performance. Maximum COP is obtained at the critical ? ow condition. [13] Water 120–140; 5–10; 30–60 Effect of varying the nozzle position to meet operating condition. Increase in COP and cooling capacity by 100%. [23] R-113 70–100; 6–25; 42–50 Entrainment ratio is highly affected by the condenser temperature especially at low evaporator temperature. [24] R-11 82. 2–182. 2; 10; 43. 3 Entrainment ratio is proportional to boiler temperature. [25,26] R-114 90; 4; 30 Combined solar generator and ejector air conditioner. More ef? cient system requires multi-ejector and cold energy storage (cold storage in either phase changing materials, cold water or ice). [27] R-134A 15; 30 Modeling the effect of motive nozzle on system performance, in which the ejector is used to recover part of the work that would be lost in the expansion valve using high-pressure motive liquid. [28] Water 100–165; 10; 30–45 Combined solar collector, refrigeration and seawater desalination system. Performance depends on steam pressure, cooling water temperature and suction pr essure. [4] Water [29] Water – Model of multistage steam ejector refrigeration system using annular ejector in which the primary ? uid enters the second stage at annular nozzle on the sidewall. This will increase static pressure for low-pressure stream and mixture and reduce the velocity of the motive stream and reduce jet mixing losses shock wave formation losses. [24] R11; R113; R114 93. 3; 10; 43. 3 Measure and calculate ejector entrainment ratio as a function of boiler, condenser and evaporator temperatures. Entrainment ratio decreases for off design operation and increases for the two stage ejectors. [30] R113; R114; R142b 120–140; 65–80 Effect of throat area, location of main nozzle and length of the constant area section on backpressure, entrainment ratio and compression ratio. Developed a new ejector theory in which the entrained ? uid is choked, the plant scale results agree with this theory. Steam jet refrigeration should be designed for the most often prevailing conditions rather than the most severe to achieve greater overall ef? ciency. [5] Mathematical model use empirical parameters that depend solely on geometry. The parameters are obtained experimentally for various types of ejectors. [31] R134a 5; ? 12, ? 18; 40 Combined ejector and mechanical compressor for operation of domestic refrigerator-freezer increases entrainment ratio from 7 to 12. 4%. The optimum throat diameter depends on the freezer emperature [9] R11; HR-123 80; 5; 30 Performance of HR-123 is similar to R-11 in ejector refrigeration. Optimum performance is achieved by the use of variable geometry ejector when operation conditions change. H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 1. The motive steam expands isentropically in the nozzle. Al so, the mixture of the motive steam and the entrained vapor compresses isentropically in the diffuser. 2. The motive steam and the entrained vapor are saturated and their velocities are negligible. 3. Velocity of the compressed mixture leaving the ejector is insigni? cant. 4. Constant isentropic expansion exponent and the ideal gas behavior. 5. The mixing of motive steam and the entrained vapor takes place in the suction chamber. 6. The ? ow is adiabatic. 7. Friction losses are de? ned in terms of the isentropic ef? ciencies in the nozzle, diffuser and mixing chamber. 8. The motive steam and the entrained vapor have the same molecular weight and speci? c heat ratio. 9. The ejector ? ow is one-dimensional and at steady state conditions. The model equations include the following: ? Overall material balance (2) Expansion ratio ? ‘ 2pn k? 1   Pp P2 n (k ? 1/k) ?1 Pe P2 n (k ? 1/k) ?1 (6) M*2 + wM*2 Te/Tp p e ‘ M 2(k + 1) M 2(k ? 1) + 2 (8) Eq. (8) is used to calculate M*2, M*2, M4 e p Mach number of the mixed ? ow after the shock wave 2 M2+ 4 (k ? 1) M5 = (9) 2k 2 M ? 1 (k ? 1) 4 Pressure increase across the shock wave at point 4 (10) In Eq. (10) the constant pressure assumption implies that the pressure between points 2 and 4 remains constant. Therefore, the following equality constraint applies P2 = P3 = P4. Pressure lift in the diffuser  n Pc p (k ? 1) 2 =d M5+1 P5 2 ? (5) ? (k/k ? 1) (11) where pd is the diffuser ef? ciency. The area of the nozzle throat A1 = where M is the Mach number, P is the pressure and is the isentropic expansion coef? cient. In the above equation, pn is the nozzle ef? ciency and is de? ned as the ratio between the actual enthalpy change and the enthalpy change undergone during an isentropic process. Isentropic expansion of the entrained ? uid in the suction chamber is expressed in terms of the Mach number of the entrained ? uid at the nozzle e xit plane   P5 1 + kM 2 4 = P4 1 + kM 2 5 (4) Isentropic expansion of the primary ? uid in the nozzle is expressed in terms of the Mach number of the primary ? uid at the nozzle outlet plane Mp2 = ? ? (3) Er = Pp/Pe ? ? 2 k? 1 (7) (1 + w )(1 + wTe/Tp) here w is the entrainment ratio and M * is the ratio between the local ? uid velocity to the velocity of sound at critical conditions. The relationship between M and M * at any point in the ejector is given by this equation M* = Compression ratio Cr = Pc/Pe ? ? ‘ The mixing process is modeled by one-dimensional continuity, momentum and energy equations. These equations are combined to de? ne the critical Mach number of the mixture at point 5 in terms of the critical Mach number for the primary and entrained ?uids at point 2 M* = 4 where m is the mass ? ow rate and the subscripts c, e and p, de? ne the compressed vapor mixture, the ntrained vapor and the motive steam or primary stream. Entrainment ratio w = me/mp ? ? (1) mp + m e = mc ? Me2 = 555 mp Pp ‘ RTp k + 1 kpn 2 (k + 1)/(k ? 1) (12) The area ratio of the nozzle throat and diffuser constant area        A1 Pc 1 = A3 Pp (1 + w )(1 + w (Te/Tp)) P2 1/k P (k ? 1)/k 1/2 1? 2 Pc Pc 2 1/(k ? 1) 2 1/2 1? k+1 k+1 1/2 (13) H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 556 ? The area ratio of the nozzle throat and the nozzle outlet A2 = A1 ‘  1 2 (k ? 1) 2 1+ M p2 2 M p2 (k + 1 2  ? (k + 1)/(k ? 1) (14) ? 3. Solution procedure ? Two solution procedures for the above model are shown in Fig. 2. Either procedure requires iterative calculations. The ? rst procedure is used for system design, where the system pressures and the entrainment ratio is de? ned. Iterations are made to determine the pressure of the motive steam at the nozzle outlet (P2) that gives the same back pressure (Pc). The iteration sequence for this procedure is shown in Fig. 2(a) and it includes the following steps: ? De? ne the design parameters, which include the entrainment ratio (w ), the ? ow rate of the compressed ? ? ? ? vapor (mc) and the pressures of the entrained vapor, ompressed vapor and motive steam (Pe, Pp, Pc). De? ne the ef? ciencies of the nozzle and diffuser (pn, pd). Calculate the saturation temperatures for the compressed vapor, entrained vapor and motive steam, which include Tc, Tp, Te, using the saturation temperature correlation given in the appendix. As for the universal gas constant and the speci? c heat ratio for steam , their values are taken as 0. 462 and 1. 3. The ? ow rates of the entrained vapor (me) and motive steam (mp) are calculated from Eqs. (1) and (2). A value for the pressure at point 2 (P2) is estimated and Eqs. (5) – (11) are solved sequentially to obtain the ressure of the compressed vapor (Pc). The calculated pressure of the compressed vapor is compared to the design value. A new value for P2 is estimated and the previous step is repeated until the desired value for the pressure of the compressed vapor is reached. Fig. 2. Solution algorithms of the mathematical model. (a) Design procedure to calculate area ratios. (b) Performance evaluation to calculate w. H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 ? The ejector cross section areas (A1, A2, A3) and the area ratios (A1/A3 and A2/A1) are calculated from Eqs. (12) – (14). The second solution procedure is used for performance evaluation, where the cross section areas and the entrainment and motive steam pressures are de? ned. Iterations are made to determine the entrainment ratio that de? nes the ejector capacity. The iteration sequence for this procedure is shown in Fig. 2(b) and it includes the following steps: ? De? ne the performance parameters, which include the cross section areas (A1, A2, A3), the pressures of the entrained vapor (Pe) and the pressure of the primary stream (Pp). ? De? ne the ef? ciencies of the nozzle and diffuser (pn, pd). ? Calculate the saturation temperatures of the primary nd entrained streams, Tp and Te, using the saturation temperature correlation given in the appendix. ? As for the universal gas constant and the speci? c heat ratio for steam, their values are taken as 0. 462 and 1. 3. ? Calculate the ? ow rate of the motive steam and the properties at the nozzle outlet, which include mp, P2, Me2, Mp2. These are obtained by solving Eqs. (5), (6), (12) and (14). ? An estimate is made for the entrainment ratio, w. ? This value is used to calculate other system parameters de? ned in Eqs. (7) – (11), which includes M*2, e M*2, M*, M4, M5, P5, Pc. p 4 ? A new estimate for w is obtained from Eq. 13). ? The error in w is determined and a new iteration is made if necessary. ? The ? ow rates of the compressed and entrained vapor are calculated from Eqs. (1) and (2). 4. Semi-empirical model Development of the semi-empirical model is thought to provide a simple method for designing or rating of steam jet ejectors. As shown above, solution of the mathematical model requires an iterative procedure. Also, it is necessary to de? ne values of pn and pd. The values of these ef? ciencies widely differ from one study to another, as shown in Table 2. The semi-empirical model for the steam jet ejector is developed over a wide ange of operating conditions. This is achieved by using three sets of design data acquir ed from major ejector manufacturers, which includes Croll Reynolds, Graham and Schutte – Koerting. Also, several sets of experimental data are extracted from the literature and are used in the development of the empirical model. The semiempirical model includes a number of correlations to calculate the entrainment ratio (w ), the pressure at the nozzle outlet (P2) and the area ratios in the ejector 557 Table 2 Examples of ejector ef? ciencies used in literature studies Reference [27] [32] [33] [31] [10] [24] [8] [34] pn pd 0. 9 0. 5 0. 7–1 0. 8–1 0. 85–0. 98 0. 85 0. 75 0. 75 0. 8 0. 85 0. 7–1 0. 8–1 0. 65–0. 85 0. 85 0. 9 pm 0. 8 0. 95 (A2/A1) and (A1/A3). The correlation for the entrainment ratio is developed as a function of the expansion ratio and the pressures of the motive steam, the entrained vapor and the compressed vapor. The correlation for the pressure at the nozzle outlet is developed as a function of the evaporator and co ndenser pressures. The correlations for the ejector area ratios are de? ned in terms of the system pressures and the entrainment ratio. Table 3 shows a summary of the ranges of the experimental and the design data. The table also includes the ranges for the data reported by Power [12]. A summary of the experimental data, which is used to develop the semi-empirical model is shown in Table 4. The data includes measurements by the following investigators: ? Eames et al. [8] obtained the data for a compression ratio of 3 – 6, expansion ratio 160 – 415 and entrainment ratio of 0. 17 – 0. 58. The measurements are obtained for an area ratio of 90 for the diffuser and the nozzle throat. ? Munday and Bagster [4] obtained the data for a compression ratio of 1. 8 – 2, expansion ratio of 356 – 522 and entrainment ratio of 0. 57 – 0. 905. The measurements are obtained for an area ratio of 200 for the diffuser and the nozzle throat. ? Aphornratana and Eames [13] obtained the data for a compression ratio of 4. 6 – 5. 3, expansion ratio of 309. 4 and entrainment ratio of 0. 11 – 0. 22. The measurements are obtained for an area ratio of 81 for the diffuser and the nozzle throat. ? Bagster and Bresnahan [14] obtained the data for a compression ratio of 2. 4 – 3. 4, expansion ratio of 165 – 426 and entrainment ratio of 0. 268 – 0. 42. The measurements are obtained for an area ratio of 145 for the diffuser and the nozzle throat. ? Sun [15] obtained the data for a compression ratio of . 06 – 3. 86, expansion ratio of 116 – 220 and entrainment ratio of 0. 28 – 0. 59. The measurements are obtained for an area ratio of 81 for the diffuser and the nozzle throat. ? Chen and Sun [16] obtained the data for a compression ratio of 1. 77 – 2. 76, expansion ratio of 1. 7 â⠂¬â€œ 2. 9 and entrainment ratio of 0. 37 – 0. 62. The measure- H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 558 ments are obtained for an area ratio of 79. 21 for the diffuser and the nozzle throat. ? Arnold et al. [17] obtained the data for a compression ratio of 2. 47 – 3. 86, expansion ratio of 29. 7 – 46. , and entrainment ratio of 0. 27 – 0. 5. ? Everitt and Riffat [18] obtained the data for a compression ratio of 1. 37 – 2. 3, expansion ratio of 22. 6 – 56. 9 and entrainment ratio of 0. 57. The correlation for the entrainment ratio of choked ?ow or compression ratios above 1. 8 is given by W = aErbP cP d ec (e + fP g ) p (h + iP jc) (15) Similarly, the correlation for the entrainment ratio of un-choked ? ow with compression ratios below 1. 8 is given by W = aErbP cP d ec (e + f ln(Pp)) (g + h ln(Pc)) (16) vapor compression applications. As shown in Fig. 3, the ? tting result is very satisfact ory for entrainment ratios between 0. 2 and 1. This is because the major part of the data is found between entrainment ratios clustered over a range of 0. 2 – 0. 8. Examining the experimental data ? t shows that the major part of the data ? t is well within the correlation predictions, except for a small number of points, where the predictions have large deviations. The correlations for the motive steam pressure at the nozzle outlet and the area ratios are obtained semi-empirically. In this regard, the design and experimental data for the entrainment ratio and system pressures are used to solve the mathematical model and to calculate the area ratios and motive steam pressure at the nozzle utlet. The results are obtained for ef? ciencies of 100% for the diffuser, nozzle and mixing and a value of 1. 3 for k. The results are then correlated as a function of the system variables. The following relations give the correlations for the choked ? ow: The constants in Eqs. (15) and (16) are given as follows P2 = 0. 13 P 0. 33P 0. 73 e c (17) A1/A3 = 0. 34 P 1. 09P ? 1. 12w ? 0. 16 c p Entrainment ratio Entrainment ratio correlation choked correlation non-choked ?ow (Eq. (15); Fig. 3) ? ow (Eq. (16), Fig. 4) ?1. 89? 10? 5 ?5. 32 5. 04 9. 05? 10? 2 22. 09 ?6. 13 0. 82 ?3. 37? 10? 5 ? ? 0. 79 a 0. 65 b ?1. 54 c 1. 72 d 6. 9v10? 2 e 22. 82 f 4. 21? 10? 4 g 1. 34 h 9. 32 j 1. 28? 10? 1 j 1. 14 R2 0. 85 A2/A1 = 1. 04 P ? 0. 83 c P 0. 86 p w (18) ? 0. 12 (19) The R 2 for each of the above correlations is above 0. 99. Similarly, the following relations give the correlations for the un-choked ? ow: P2 = 1. 02 P ? 0. 000762P 0. 99 e c (20) A1/A3 = 0. 32 P 1. 11P ? 1. 13w ? 0. 36 c p (21) A2/A1 = 1. 22 P ? 0. 81P 0. 81w ? 0. 0739 c p (22) 2 Fitting results against the design and experimental data are shown in Figs. 3 and 4, respectively. The results shown in Fig. 3 cover the most commonly used range for steam jet ejectors, especially in vacuum and The R values for the above three correlations are above 0. 99. The semi-empirical ejector design procedure involves sequential solution of Eqs. (1) – (14) together with Eq. (17) or Eq. (20) (depending on the ? ow type, choked or non-choked). This procedure is not iterative in contrast with the procedure given for the mathematical model in the previous section. As for the semi-empirical performance evaluation model, it involves non-iterative solution of Eqs. (1) – (14) together with Eq. (15) or Eq. (16) for choked or non-choked ? ow, respectively. It should be stressed that both solution procedures are indepen- Table 3 Range of design and experimental data used in model development Source Er Cr Pe (kPa) Pc (kPa) Pp (kPa) w Experimental Schutte–Koerting Croll–Rynolds Graham Power 1. 4–6. 19 1. 008–3. 73 1. 25–4. 24 1. 174–4. 04 1. 047–5. 018 1. 6–526. 1 1. 36–32. 45 4. 3–429. 4 4. 644–53. 7 2–1000 0. 872–121. 3 66. 85–2100. 8 3. 447–124. 1 27. 58–170. 27 2. 76–172. 37 2. 3–224. 1 790. 8–2859. 22 446. 06–1480. 27 790. 8–1480. 27 3. 72–510. 2 38. 6–1720 84. 09–2132. 27 6. 2–248. 2 34. 47–301. 27 344. 74–2757. 9 0. 11–1. 132 0. 1–4 0. 1818–2. 5 0. 18–3. 23 0. 2–4 H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 559 Table 4 Summary of literature experimental data for steam jet ejectors Ad/At Pp (kPa) Pe (kPa) Pc (kPa) Pp/Pe Pc/Pe w Reference 90 198. 7 232. 3 270. 3 313. 3 361. 6 1. 23 1. 23 1. 23 1. 23 1. 23 3. 8 4. 2 4. 7 5. 3 6 161. 8 189. 1 220. 1 255. 1 294. 4 3. 09 3. 42 3. 83 4. 31 4. 89 0. 59 0. 54 0. 47 0. 39 0. 31 [8] [8] [8] [8] [8] 90 198. 7 232. 3 270. 3 313. 3 361. 6 1. 04 1. 04 1. 04 1. 04 1. 04 3. 6 4. 1 4. 6 5. 1 5. 7 191. 6 223. 9 260. 7 302. 1 348. 7 3. 47 3. 95 4. 44 4. 91 5. 49 0. 5 0. 42 0. 36 0. 29 0. 23 [8] [8] [8] [8] [8] 90 198. 7 232. 3 270. 3 313. 3 361. 6 0. 87 0. 87 0. 87 0. 87 0. 87 3. 4 3. 7 4. 4 5. 1 5. 4 227. 7 266. 2 309. 8 59 414. 4 3. 89 4. 24 5. 04 5. 85 6. 19 0. 4 0. 34 0. 28 0. 25 0. 18 [8] [8] [8] [8] [8] 200 834 400 669 841 690 690 1. 59 1. 59 1. 71 1. 59 1. 94 1. 94 3. 2 3. 07 3. 67 3. 51 3. 38 3. 51 521. 7 250. 2 392. 3 526. 1 356 356 2. 0 1. 92 2. 15 2. 19 1. 74 1. 81 0. 58 1. 13 0. 58 0. 51 0. 86 0. 91 [4] [4] [4] [4] [4] [4] 81 270 270 270 270 270 0. 87 0. 8 7 0. 87 0. 87 0. 87 4. 1 4. 2 4. 4 4. 5 4. 7 309. 5 309. 5 309. 5 309. 5 309. 5 4. 7 4. 8 5. 04 5. 16 5. 39 0. 22 0. 19 0. 16 0. 14 0. 11 [13] [13] [13] [13] [13] 145 660 578 516 440 381 312 278 1. 55 1. 55 1. 58 1. 57 1. 59 1. 62 1. 68 5. 3 5. 3 5. 3 5. 03 4. 77 4. 23 4. 1 426. 5 373. 5 326. 280. 6 239. 9 192. 6 165. 1 3. 42 3. 42 3. 36 3. 21 3 2. 61 2. 44 0. 27 0. 31 0. 35 0. 38 0. 42 0. 46 0. 42 [14] [14] [14] [14] [14] [14] [14] 143. 4 169. 2 198. 7 232. 3 270. 3 1. 23 1. 23 1. 23 1. 23 1. 23 2. 53 2. 67 3. 15 4 4. 75 116. 8 137. 8 161. 8 189. 1 220. 1 2. 06 2. 17 2. 56 3. 26 3. 87 0. 59 0. 51 0. 43 0. 35 0. 29 [15] [15] [15] [15] [15] 29. 7 33. 5 37. 8 46. 5 2. 47 2. 78 3. 14 3. 86 0. 5 0. 4 0. 3 0. 27 [17] [17] [17] [17] 119. 9 151. 7 224. 1 195. 1 195. 1 186. 2 1. 7 2. 3 3. 9 1. 6 1. 9 2. 9 1. 8 2. 2 3. 3 1. 6 1. 9 2. 8 0. 62 0. 49 0. 34 0. 78 0. 64 0. 37 [16] [16] [16] [16] [16] [16] 2. 3 2. 3 2. 3 56. 9 38. 6 22. 6 . 3 1. 9 1. 4 0. 57 0. 56 0. 57 [18] [18] [18] 81 1720 1720 1720 1720 79. 21 116 153 270 198 198 198 57. 9 47. 4 38. 6 57. 7 51. 4 45. 5 37. 01 67. 6 67. 6 67. 6 121. 3 99. 9 67. 6 1. 02 1. 2 1. 7 143 143 143 143 560 H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 wide range of compression, expansion and entrainment ratios, especially those used in industrial applications. The developed correlations are simple and very useful for design and rating calculations, since it can be used to determine the entrainment ratio, which, upon speci? cation of the system load, can be used to determine the motive steam ? w rate and the cross section areas of the ejector. Acknowledgements Fig. 3. Fitting of the entrainment ratio for compression ratios higher than 1. 8. The authors would like to acknowledge funding support of the Kuwait University Research Administration, Project No. EC084 entitled ‘Multiple Effect Evaporation and Absorption/Adsorption Heat Pumps’. Appendix A. Nomenclature A COP Cr Er m M M* Fig. 4. Fitting of the entrainment ratio for compression ratios lower than 1. 8. dent of the nozzle and diffuser ef? ciencies, which varies over a wide range, as shown in Table 2. 5. Conclusions A semi-empirical model is developed for design and erformance evaluation of steam jet ejector. The model includes correlations for the entrainment ratio in choked and non-choked ? ow, the motive steam pressure at the nozzle outlet and the area ratios of the ejector. The correlations for the entrainment ratio are obtained by ? tting against a large set of design data and experimental measurements. In addition, the correlations for the motive steam pressure at the nozzle outlet and the area ratios are obtained semi-empirically by solving the mathematical model using the design and experimental data for the entrainment ratio and system pressures. The correlations cover a P DP R Rs T w cross section area (m2) coef? cient of performance, dimensionless compression ratio de? ned as pressure of compressed vapor to pressure of entrained vapor expansion ratio de? ned as pressure of compressed vapor to pressure of entrained vapor mass ? ow rate (kg/s) Mach number, ratio of ? uid velocity to speed of sound critical Mach number, ratio of ? uid velocity to speed of sound pressure (kPa) pressure drop (kPa) universal gas constant (kJ/kg  °C) load ratio, mass ? ow rate of motive steam to mass ? ow rate of entrained vapor temperature (K) ntrainment ratio, mass ? ow rate of entrained vapor to mass ? ow rate of motive steam Greek symbols k compressibility ratio p ejector ef? ciency Subscripts 1–7 locations inside the ejector b boiler c condenser d diffuser e evaporator or entrained vapor m mixing n nozzle p primary stream or motive steam t throat of the nozzle H. El -Dessouky et al. / Chemical Engineering and Processing 41 (2002) 551 – 561 Appendix B B. 1. Correlations of saturation pressure and temperature   The saturation temperature correlation is given by T = 42. 6776 ? 3892. 7 ? 273. 15 (ln(P /1000) ? 9. 48654) here P is in kPa and T is in  °C. The above correlation is valid for the calculated saturation temperature over a pressure range of 10 – 1750 kPa. The percentage errors for the calculated versus the steam table values are B 0. 1%. The correlation for the water vapor saturation pressure is given by  ln(P /Pc) = Tc ?1 T + 273. 15  8 ? % fi (0. 01(T + 273. 15 ? 338. 15))(i ? 1) i=1 where Tc = 647. 286 K and Pc = 22089 kPa and the values of fi are given in the following table f1 f2 f3 f4 ?7. 419242 0. 29721 ?0. 1155286 0. 008685635 f5 f6 f7 f8 0. 001094098 ?0. 00439993 0. 002520658 ?0. 000521868 How to cite Steam Jet Refrigeration Cycle, Essay examples

History Of Jazz And Classical Music (1751 words) Essay Example For Students

History Of Jazz And Classical Music (1751 words) Essay History Of Jazz And Classical MusicHistory of Jazz and Classical MusicUpon entering a modern record store, one is confronted with a wide variety of choices in recorded music. These choices not only include a multitude of artists, but also a wide diversity of music categories. These categories run the gamut from easy listening dance music to more complex art music. On the complex side of the scale are the categories known as Jazz and Classical music. Some of the most accomplished musicians of our time have devoted themselves to a lifelong study of Jazz or Classical music, and a few exceptional musicians have actually mastered both. A comparison of classical and Jazz music will yield some interesting results and could also lead to an appreciation of the abilities needed to perform or compose these kinds of music. Lets begin with a look at the histories of the two. The music called classical, found in stores and performed regularly bysymphonies around the world, spans a length of time from 1600 up to the present. This time frame includes the Renaissance, Baroque, Classical, Romantic and Contemporary periods. The classical period of music actually spans a time from of 1750 to 1800; thus, the term Classical is a misnomer and could more correctly be changed to Western Art Music or European Art Music. European because most of the major composers up till the 20th century were European. Vivaldi was Italian, Bach was German, Mozart and Beethoven were Austrian; they are some of the more prominent composers. Not until the twentieth century with Gershwin and a few others do we find American composers writing this kind of art music. For the sake of convention, we can refer to Western Art Music as Classical music. Jazz is a distinctively American form of music, and its history occupies a much smaller span of time. Its origins are found in theearly 1900s as some dance band leaders in the southern U.S. began playing music that combined ragtime and blues. Early exponents of this dance music were Jelly Roll Martin (a blues player) and Scott Joplin (ragtime). The terms Jazz and Jazz Band first surfaced in the year 1900. Some say this occurred in New Orleans, although similar music was played at the same time in other places. The most prominent exponents of this early music, called Dixieland Jazz, included Louis Armstrong and Sidney Bechet. After World War I, Jazz music had evolved and was aided by the development of the recording industry. Thesmall dance band ensemble grew into the larger orchestra known as the Big Band. The music of the Big Bands became known as Swing. Two of the more famous Swing band leaders were Tommy Dorsey and Harry James. In the late 40s and through the 50s, a different kind of Jazz became popular. This music, played by a very small ensemble, was much moresophisticated and complex . Its rich harmonic changes and melodic counterpoint were not conducive to dance. It became known as Bop, with Charlie Parker and Dizzie Gillespie being the early proponents. In the last twenty years there has been a combination of Jazz with popular music of the US and Latin America. This modern Jazz music has been called Fusion. Present day exponents include Pat Metheny and Chic Corea. There has also been a return to the sound of Bop in the last ten years by such musicians as trumpeter Winton Marsalis and his brother Branford, a saxophonist. Lets focus on the instrumentation of the two kinds of music. In Classical music, both large orchestras and small ensembles are used. But generally, the greatest and most prominent compositions are for the larger symphony orchestra. The largest part of the orchestra is the string section consisting of violins, violas, cellos and string basses. These instruments were invented very early in medieval times but really matured into their present form during the late 18th century. The wind instruments, comprised of brass and woodwinds, took longer to mature. The brass section in particular did not posses the ability to play chromatically (in all keys) until the advent of valves which allowed the length of the instrument to be changed while playing. This occurred around the middle to late 19th century. Consequently, the brass instruments are less prominent in the music of Bach, Mozart and Beethoven along with their contemporaries. Late 19th and early 20th century composers make use of a very large orchestra with all the fully developed wind instruments. Some of the master orchestrator/composers of this time were: Wagner, Rimskey-Korsakov, Ravel and Stravinsky. Currently, composers also make use of the full orchestra but with the addition of increasingly larger percussion sections which add many unique and unheard of sounds than in earlier music. Body Ritual Among the Nacirema EssayIn Classical music, modern listeners are mostly unaware of the fact that many of the great composers of the past were not onlyexcellent performers but also great improvisers. Starting with J.S. Bach (1685-1750), the greatest composer of the Baroque era, he in fact made his living through his great skill as an improvisor. It was common for the Lutheran Church organist of his day be able to improvise on choral melodies and Bach was considered one of the greatest at this. There are written accounts of other composers improvisational abilities including Mozart (1756-1791), Beethoven (1770-1829), and Franz Liszt (1811-1886). Yet, as time went on, improvising gave way to the composers desire to exert complete control over his music. By the late 19th century, improvising was rare and not used at all in public performances of classical music. In summation, we can say that Jazz and Classical music represent two approaches to Art Music. The Classical composer or performer has a long and rich body of music in written form that he uses to learn from while the Jazz musician uses a body of recorded music to learn. Because of its small size, the modern Jazz ensemble allows loose interaction while the symphony orchestras large size and diversity of instruments provides many different sounds and wide dynamic range. In classical music the composer strives for control; he uses printed music to guide and direct the musicians through the conductor. In Jazz music, the songs are loosely composed, thus forming a basis for individual expression within an ensemble. When you go to hear asymphony, you hear an orchestra conducted by the conductor playing a composition. When you go to a Jazz club you hear a small jazz ensemble interacting and improvising a song. Both of these kinds of music provide rich expression and detail to the serious lis tener. They take different paths to reach their final form but give a person equal opportunities to appreciate the creative output of each. Music Essays