The Pyramids in Giza Essay Example | Topics and Well Written Essays - 1250 words

The Pyramids in Giza - Essay Example The flight to Cairo was extremely long, with delays and the usual combination of drama and comedy involved in international flights; the destination would be worth it, I told myself. The Captain had just notified us that we were leaving Saudi Arabia flying towards Egypt when I noticed from my wing side seat that the ground below us looked like a plethora of interesting shapes, mostly â€Å"stones† in the middle of a dessert. I later came to realize that these â€Å"stones† were actually buildings. Along the Nile delta, there is greenery, but I soon discovered that dust and sand was the order of the day. Believe it or not, twenty-eight hours after takeoff, we finally taxied down the runway at Cairo airport. It was a step back in time! It wasn’t a particularly hot evening; thankfully wisdom had decreed that we make the journey during the winter months when the sun was not so likely to bake us from the outside in. After traveling for more than one day, exhaustion ha d set in and the only thing I was truly interested in was a hot shower, something to eat, and a still place to lie down.  At the hotel, which, by the way, faced the Nile River, we secured our room and proceeded to unwind.

Case study,I will have to attach a copy of the case.the name of the Study

,I will have to attach a copy of the .the name of the file will be - Case Study Example A tort occurs as a result of a person’s duty to others which is created by one or more laws. A person who perpetrates a tort is referred to as a wrongdoer or a tortfeaser. A wrongdoing act of tort is referred to as a tortuous act (Stuhmcke 56). The principle goal of the law of tort is compensation of victims or their dependants. The generic pattern of tort comprises of an act or omission by the defendant which causes damage to the plaintiff. The damage has to be caused by the fault of the defendant, and the fault must be a form of harm acknowledged as attracting legal liability. The model of determining whether a tort occurred follows the act or omission leads to causation and faults a person’s protected interests, which results in personal damage and injury (Stuhmcke 60). By suing Dangerfield, continental and Sandman Corporation on basis of negligence, Hartman has to prove several things in a court of law. One, Hartman must prove that the three defendants owed her a du ty of care. This concept is grounded in the ruling of the Donologhue v Stevenson case (1932) where the House of Lords turned down a previous law in which liability for careless behavior existed only in a number of separate, specified circumstances. The House of Lords asserted that general duty entails taking reasonable care to avoid acts or omissions which one can reasonably foresee would likely injure your neighbor. A Neighbor in this context refers to persons who are so closely and directly affected by a another’s act that they ought to have them in contemplation as being so affected when another is directing his/her mind to the acts or omissions which are called into question (McLaughlin 63). In addition to establishing a duty of care, Hartman must further prove that the damage she suffered was foreseeable. This concept was advanced in Caparo v. Dickman (1990) case where it must be established that there was proximity between herself and the three companies. Contributory n egligence defense In this case, Dangerfield, continental and Sandman Corporations have a defense in that they did owe a duty of care to Hartman. However, Hartman was not responsible for her own safety as she was negligent by walking in front of her car knowingly. As such, the three corporations can establish that Hartman was negligent and it is for that reason that she suffered the accident. Moreover, the defendants have a defense that Hartman did not read the contents of the receipt that indicated that the management was not responsible for damages incurred by valet parking customers. This concept is generally referred to as the plaintiff’s default or contributory negligence. For this defense to be relied, the defendants have to show that Hartman is to blame for her suffering. Dangerfield, continental and Sandman Corporations must prove that; Hartman exposed herself to the danger of being hit by walking in front of her car Hartman was negligent Hartman’s negligence/fa ult contributed to her suffering. These conditions have been met as explained above. Although contributory negligence is a popular defense in tort, the defense does not free the defendants from liability. It acts to reduce the amount of damages payable y the defendant to the extent of the plaintiff’s contribution. Once Hartman establishes that the three companies owed her a duty of care, she has to prove that the defendants were at fault. That means that Dangerfield, cont

Conventional Approaches To Strategic Management

Conventional Approaches To Strategic Management The aim of this essay is to critically analyse and evaluate the application, validity, limitations and uncertainties of the conventional approaches of strategic management in this rapidly changing business context. It briefly outlines strategic management as it is traditionally taught, studied and practised and how organisations determine what strategies are apt within various business environments. In keeping with the goal, the essay disputes the validity and applicability of the traditional approach in todays deconstructing situation where the opportunities and challenges make any kind of logical strategic planning fail. Through the arguments stated in this paper, a combination and a right mix of prescriptive and emergent approaches is essential and needs to be incorporated in the strategic management process for continuity. Thus conventional approaches with its pros and cons, still prevail in todays economic business context. In any business venture, strategy is a vital factor for the efficient functioning, growth, development, continuity and success of a firm. It aims to achieve a set goal and embarks a direction for the future. Organisations require collaboration, cautious planning and the mindful implementation of planning. To maximise the effectiveness of strategies and to ensure the smooth functioning and success of the business, they have to be managed skilfully. So what is strategy? What role does strategic management play in this global economic world? The word strategy has been implicitly used in various ways even if it has been conventionally defined in only one. It is widely accepted that there is no single or universal definition of strategy, however the various descriptions of strategy allows people to manoeuvre and manipulate through this difficult pitch. Mintzberg(1994) defines strategy in 5 different ways. Plan A consciously intended course of action to ensure objectives are achieved. Ploy Basically a subset of plan and is a trick intended to outsmart or overcome an opponent or a competitor. Pattern Series of action which involves consistent behaviour over time which may or may not be intended. Position Locating the organisation within a environment. Perspective It is conceptual as well as cultural and is concerned with how an organisation itself sees and perceives the business environment. The above 5 Ps may be applicable in vastly different areas and can also be interrelated. Johnson Scholes (2008) defines strategy as the direction and scope of an enterprise over the long term; which achieves advantage for the firm through arrangement of resources within a demanding environment, to meet the needs of the markets and accomplish the expectations of the stakeholders. The process of strategic management includes analysis of the internal and external environment, formation of strategy, implementation of strategy, and evaluation of strategy. The theory of strategic management is analysed within an integrated model of context, content and process. There are two approaches for organisational change: The Prescriptive Approach which works best in a stable environment and Emergent Approaches which is used in an unpredictable fashion. These approaches are the widely known strategic models and must be examined thoroughly within the context of the fast paced, highly competitive and increasingly dynamic business environment. The prescriptive approach, also known as deliberate strategy is a traditional approach to strategic management. It is a deterministic and systematic plan of action designed to achieve a specific goal for the long term. It is usually the responsibility of the top management to establish lucid strategic directions through analysis and evaluation and then implement them through the successive layers of the organisation. Porter(1996) states that competitive strategies are about an intended course of action of being different from the rivals and differentiating yourself in the eyes of customer by doing various unique activities which add value and by positioning yourself competitively in the environment. Porter maintains that deliberate strategies are intentional and planning ahead is important and should be formulated and articulated by leaders in a predictable and controlled environment to achieve the goals and objectives. Porter also states that trade-offs and operational effectiveness are an integral part for sustainability. Conversely, Mintzberg (1994), one of the biggest critics of prescriptive approach developed the emergent approach to strategic management. He states that in emergent strategies the final objective is unclear and it a process of evolution, adaption, alternation and continuity. Emergent strategies are more successful in this chaotic world as they are unintentional and are the result of impromptu response to unforeseen situations which emerge over time. For example, Sam Walton, the founder of Wal-Mart, decision to open his second store in a rural area rather than a big city, for convenience of logistics and management efficiency was a fantastic winning emergent strategy. Also as there was less competition and people would travel to buy products which offered value at the lowest prices, made the business successful. An emergent strategy increases flexibility in times of turbulence and allows the firm to respond to opportunities and make the most of the threats. Mintzberg argues that the emergent strategies are the result of constant learning, adjusting and experimentation of different variables. Many of the world discoveries have happened accidently and would not have taken place if it was dictated by formal planning of strategy. On a negative note, as the emergent strategy is not a systematic and linear process, formulation and implementation occur simultaneously which would lead to slow, messy and jumbled development. Brews and Hunt points out that overdependence on emergent strategy can lead to underperformance of the organisation. On the other hand, deliberate strategies are planned and put into action, however due to the unrealised and unpredictable changes in the business environment; most of the planned strategies are not implemented. SWOT gives an insight on the internal and external factors which are helpful and harmful for achievement of a specific objective of an organisation. PESTLE is an analysis of the macro environment in which the firm operates. VALUE CHAIN ANALYSIS points out the primary activities which are directly related to production of products (eg logistics, sales) and the secondary activities (eg Human Resource, technology) which are not directly involved in production, but are essential for the efficiency and effectiveness of the process. It defines the core competencies of the firm and its helps to figure out the competitive advantage over cost and its competitors by adding value to the various activities. PORTERS 5 FORCE framework is an simple but powerful tool to understand the context in which the firm operates and analyse the attractiveness and economic performance of an industry which would lead to more sustainable financial returns to the stakeholders. According to Porters bestselling book Competitive Advantage, the forces that influence the profitability of an industry in a business environment are the entry of new competitors, the bargaining power of suppliers, the threat of substitutes, the bargaining power of buyers and the rivalry amongst existing competitors. The above four are important tools in the strategic management process. Porter states that strategic management is all about plotting a way through the mesh of threats and opportunities mounted by external competitive forces. The uncertainty, chaos and instability that characterise global market contest any kind of predictibilty, which is a requisite base of many a traditional process of strategic management (Pitts, 2000). Brown Eisenhardt (1998) states that traditional approaches to strategy often collapse in the face of rapidly and unpredictability changing industries. The technological advances have accelerated the process of communication and globalisation has expanded significantly. The shift and restructuring in government policies and the recent terrorist attacks have impacted companies. The challenges of formulation and implementation of strategies within a framework where global catastrophic events have an undulating effect on local market conditions, has been underestimated by management, according to researchers. Trends in the biophysical ecosystem has changed and threatened humans and other species in various geographic areas. Events such as the terrorist attack on the twin tower building in New York on September 11, 2001, or the Tsunami in Japan has an undermining effect on the global financial markets. The rational approach to strategic management which is a top down approach helps to resolve the complexities of a firm in its stable environment. It is considered as a logical and continuous process which involves defining the mission and setting long term objectives, systematic and exhaustive analysis of the competitive environment, creating and evaluating alternative strategies, implementing the various strategies and finally monitoring the performance. Ansoff(1965) states that it helps to organise complex activities and employ a greater control over various business units which leads to domination of marketplace. This approach is founded on the idea that firms are adapted to cope with changes in their environment by taking rational and comprehensive decisions (Chaffee, 1985). Due to incapacity of predicting the future, this approach is very linear and unrealistic and is based on the thinking and assumptions of the upper level management. In a complex and unstable environment the values and the role of mainstream strategies are still unclear and may lead to more complications rather than solutions. It may weaken the flexibility of the firm to cope with prospective changes taking place in its environment (Wally Baum, 1994). In Mintzberg(1994) opinion, rational methods of strategic management leads to inflexibility, encourages excess bureaucracy and confines creativity and spontaneity. On the contrary, Ansoff(1991)argues the fact that conventional strategies are much more effective than a trial and error process when it comes to collecting and analysing relevant data and aligning the firm with its internal and external environments. Porter(1996)maintains that mainstream strategies can cleverly play a vital role in determining a suitable strategic direction for the firm. It can significantly help companies to avoid expensive errors and survive and sustain in a highly competitive environment (Aram Cowan, 1990). Adopting the conventional strategic approach, would help in ensuring a systematic assessment of numerous plausible options, encouraging creative thinking and ideas, enhancing internal interactions and communications, increasing motivation and commitment of staff, identifying pertinent opportunities, ensuring coordination of organisational activities and anticipating potential change. The size of a firm is a factor of high importance when it comes to adopting strategies. Often, strategic planning and management is considered a major tool for large enterprises. Due to its complexity, a comprehensive strategy is needed, as compared to, small and medium sized firms. In (Mintzberg, 1994)opinion, smaller firms operates in less complex environments and their internal operations and procedures are manageable by a smaller hierarchy, hence they abandon the formal strategy process. Smaller businesses would do well if they adopt emergent strategies especially in turbulent periods. The conventional strategies are based on a sole quantitative purpose and are very cold and give little or practically no consideration to human factor (Muchinsky, 2000). It fails to utilise people as the competitive advantage of the firm. Due to the traditional approaches to strategy, many organisations fail to realise the potential of their people, inspite of the rhetoric claim that people are the firms real strategic asset (Gratton,2000). Truss(1999) argues that a healthy organisation can be formed by incorporating humanistic principles and by aligning strategic human resource management with the rational conceptualisation of strategies, thereby evoking behaviours necessary to individual growth and effectiveness of the organisation. Along with the Human Resource of a firm, leaders too play a central role in achieving people based competitive advantage in modern organisations. The conventional approaches to leadership either is transactional reward the employee in exchange of desir able results or contingent identify leaders based on the circumstances of the firm and execution of specific strategies(Landrum, Howell Paris, 2000). Eisenbach, Watson Pillai(2000) states that these approaches are insufficient and advocates transformational leadership as the apt approach. Guest Schepers,( 1997, p 37) considers a transformational leader as a person who brings about change by formulation of a vision for the future and means of realising this mission by communication and necessary action. A leaders vision should also consider the essential interests of the key stakeholders of the organisation along with the employees needs such as growth and motivation (Ford Ford,1994). Beugre(2006) states that a transformational leader should exhibit individualised attention, positivity, encourage logical thinking and inspire the followers for team unity. Steve Jobs of Apple and Bill Gates of Microsoft are classic examples of transformational leaders who have achieved momentous s uccess with a articulate vision which have persuaded their followers (Giladi, 2000). Participation of share holders in formulation of strategies is crucial. Freeman (1984) defines stakeholders as any individual or group who can affect or is affected by the achievement of an organisations objective. It is intended to explain and guide the structure and operation of the established organisation. Many traditional strategy tools have ignored some shareholders, sidelined others and constantly traded off the interests of others against preferred shareholder group. This approach may be suitable in stable environments. However, in a dynamic, volatile and fast changing business world, the limitation of this approach becomes increasingly evident. Integration of shareholder interests into the very rationale of the firm and exploring, managing and balancing relationship with shareholders must be managed in a lucid and strategic fashion to ensure long term success of the firm. Incorporating value based management system, understanding morality and ethics play a significant role i n the enhanced performance and profitability of the firm in the long run. Ansoff(1965) contrasts that stakeholders might be a barrier on the objective and actions of the enterprise and might constraint the development of the firm. With the advent of the 21st century and the emergence of digitisation, globalisation and new technology traditional strategic tools like value chain analysis, Porters 5 forces, have become less useful. In todays varied business world, there is a need for strategists to develop more comprehensive and reasonable measures for better performance and must consider a wider array of industry organisations, bases of competitive advantage and higher level of complexity and uncertainty. As the industry conditions progresses or changes, strategies should also evolve. Scenario Analysis differs from the traditional approach and is a contemporary approach to strategic management which analyses the possible future events by taking into consideration alternative plausible outcomes that the future may unfold. It is not about predicting or projecting the future but a means of learning and improving our understanding of the long term global effects of the current trends and their interrelation considering the uncertainties and volatilities in the business context; which helps a company to make flexible long term plans. The traditional approaches rely on the notion that the future will be very similar to the past and present and works in a relatively stable environment, however scenarios help managers to prepare for the future and improve their decision making ability by stimulating out of the box thinking. The well known example of this methodology would be of Royal Dutch Shell, who by implementation of scenario planning was the only energy company to su rvive and sustain the oil price crisis in the 1970s. Scenario techniques if combined with other approaches can In summary, the traditional approaches to strategic management provide a structured and orderly approach to decision making in the strategic making process. These approaches still constitute a basic indispensable and feasible framework; however it is not sufficient alone for the profitability of a firm. Contemporary strategic approaches should be incorporated in the base model to make it more entrepreneurial and adaptable. Though the dynamic approaches can prevent control over action and may jeopardise a lack of direction, it considers the uncertainty of the future and emphasises on the flexibility of reaction to enhance the functionality of the organisation in this fast growing, turbulent and uncertain world. In essence there is no one size fits all or best approach to strategy. The organisations should adapt and align the conventional strategies such as internal and external analysis with the real time techniques to ensure continuity and facilitate organisational and individual lea rning. The management should seek the best way of combination, customisation and balance of elements from both the approaches for survival and sustainability in this tumultuous world. Rather than using the approaches individually and in isolation, they should complement each other in order to handle the intricacies of the business and still succeed over the changing conditions.

Pride in Greenleaf and Spotted Horses :: Greenleaf Spotted Horses Essays

Pride in Greenleaf" and Spotted Horses Pride is a feeling that most people in the world have always shared. Pride can be a great thing to have, but when a person has too much pride, the situation becomes very different. Pride can cause a person to do things he would not do under normal circumstances, and it can cause a person unhappiness. Mrs. May in "Greenleaf" and Henry Armstid in "Spotted Horses" both have a sad type of pride that leads to untimely death and demise. In Henry's case, his pride is the direct cause of his injuries done by the horses, and Mrs. May's is somewhat more indirect. In "Greenleaf," Mrs. May thought that she was a blessing to the world. She thought that everything good that happened was her doing and that everything she did was good. At one point in the story she says, "I work and slave, I struggle and sweat to keep this place for them and as soon as I'm dead, they'll marry trash and bring it in here and ruin everything. They will marry trash and ruin everything I've done." Although she hates the dairy farm and her two sons do not live up to her standards, she still has a sense of pride about them causing her to be so preoccupied with what she has done for them. The bull, a prominent symbol for what Mrs. May cannot control, meanders throughout the story and clashes and conflicts with her pride. The two are intertwined: she constantly visualizes and hears the bull in the day and sleep. In one of her dreams she talks of being "aware that what ever it was had been eating as long as she had the place and had eaten everything from the beginning of her fence line up to the house and now was eating the house and calmly with the same steady rhythm would continue through the house, eating her and the boys, and then on, eating everything but the Greenleafs." The bull symbolizes what she cannot do in life, what she cannot control, and what she has not done, and it is what makes her take the last step before her death by bringing out her pride and causing her to try and take control over the unknown, over itself. She is then gored to death by the bull, and this proves the point that she should not have concerned her whole life with her pride and what she had done and what she could not ultimately control.

Steam Jet Refrigeration Cycle

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. 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 a t 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 correlations 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, SOx, 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: [email  pro tected] 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 unit 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 sin gle 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 an d 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) t he suction chamber; and (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. 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, wher e 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 of 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 e jector 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-114 86; ? 8; 30 Increase in ejector perfo rmance 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; 30–60Effect 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 pressure. [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 Engineer ing and Processing 41 (2002) 551 – 561 1. The motive steam expands isentropically in the nozzle. Also, 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*2Te/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 entrai ned ? uid at the nozzle exit 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 + me = 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 fol lowing 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 re peated 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 met hod 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 acquired 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 condenser 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 comp ression 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 – 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 ab ove 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 satisfactory 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 andThe 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 3Range of design and experimental data used in model devel opment 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 4Summary 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. 2 3 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. 87 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

Edgar Allan Poe Life Outline

Nick Arleo3/11/13 I. Introduction Edgar Allen Poe was a very dark writer of poems and short stories. His writings terrified many. His whole life and the unfortunante events that occured during it can tell a person why his writings were the way they were written. II. Body- Poe's early life, marriage, works, later years A. Early life in Boston,MA 1. Poe's family a. his father left his family early on in his life, and his mother passed away when he was 3 years of age. 2. Poe's foster family a.Poe lived with John and Frances Allan, a successful tobacco merchant and his wife in Richmond,Virginia. 3. Poe's marriage a. Poe married his 13 year old cousin Virgnia or ‘Sissy' as he called her when he was the age of 27. b. ‘Sissy' grew ill with tuberculosis and with no cure, she passed away in 1842. 4. Poe's Collegient years a. Poe started out studying at the University of Virginia. b. Poe later on transfered to the Naval acadamy at West Point and joined the military. B. Poe's works 1. Short stories: a. The Angel of the Odd† (1844) Comedy about being drunk b. â€Å"The Balloon Hoax† (1844) Newspaper story about balloon travel c. â€Å"Berenice† (1835) Horror story about teeth d. â€Å"The Black Cat† (1845) Horror story about a cat e. â€Å"The Cask of Amontillado† (1846) A story of revenge f. â€Å"A Descent Into The Maelstrom† (1845) Man vs. Nature, Adventure Story g. â€Å"Eleonora† (1850) A love story h. â€Å"The Facts in the Case of M. Valdemar† (1845) Talking with a dead man i. â€Å"The Fall of the House of Usher† (1839) An old house and its secrets 2. Poems A DreamA Dream Within A Dream A Valentine Al Aaraaf Alone An Acrostic An Enigma Annabel Lee Bridal Ballad Dreamland Dreams Eldorado Elizabeth C. Poe's Later years a. After the death of his wife, Poe became very depressed. This depression inspired most of his pieces. b. Poe began an even bigger alcoholic after years of being a heavy drinker . c. Poe also began the search for a new wife in order to restore his happieness and cure his depression. d. Poes writings at the end of his life were his most depressing. e. Poe eventually died on October 7th 1849.