Mental health and health needs of asylum seekers and refugees

Mental health and health needs of asylum seekers and refugees INTRODUCTION 1.1 Background Asylum seekers and refuges is a growing problem affecting many European countries as well as the UK. In the recent years the number of asylum seekers and refugees entering UK has increased, attracting the attention of the media, politicians as well as ordinary people. It is a controversial subject leading to intense debate and discussions and unsurprisingly to different views and perspectives. The increase in the numbers seeking asylum has led to governments and the international agencies grappling with the problems of providing adequate humanitarian assistance in the third world and avoiding floods of asylum seekers arriving at their doorstep (Timothy et al 2009). This has also led to changes in asylum policies with the governments responding to the rising problem with a range of measures aimed at deterring asylum applications. Mental illness is one of the leading causes of illness around the world and estimated to affect up to a third of the British population. It is especially common amongst asylum seekers and refugees, which may be due to them having experienced loss, bereavement, torture, rape etc. Their mental health can then be exacerbated due to displacement and their situation in the UK. There is a lot of stigma attached to mental illness, and the mentally ill still face discrimination in many ways, which results in many not seeking treatment. The exact cause of mental illness is a subject doctors still argue about. Society has been known to play a key role, but recently there has been a growing concentration on the role of genes. 1.2 Who are Asylum-seekers? An asylum seeker is someone who has fled their country to find a safe place elsewhere. Under the 1951 Convention on Refugees, an asylum applicant must be able to demonstrate a well-founded fear of persecution in their country of origin for reasons of political opinion, religion, ethnicity, race/nationality, or membership of a particular social group (Burnett 2002). They must also be able to show that they are unable to obtain any protection or help from their own national authorities (Burnett 2002). The Refugee or Person in Need of International Protection (Qualification) Regulations 2006 updates parts of the convention. Asylum applications in the UK are sent to the Home Office. Over the last ten years there have been several pieces of legislation introduced which has created an ever changing climate of policy on refugees and asylum seekers. This is a result of the significant numbers of rejected asylum seekers who have had all means of support withdrawn from them and are now destitute in the UK. Asylum seekers represent a vulnerable population due to a host of pre- and post-migration risk factors. Pre-migration factors include torture and refugee trauma, which may result in mental and physical illness. Moreover, asylum seekers often come from conflict areas, without access to adequate health services. Post-migration factors also play a role for health. They include detention, length of asylum procedure, language barriers, and lack of knowledge about the new health care system. Destitute asylum seekers are those people who are unable to access support for their basic needs from the government or from their own resources. The position of rejected asylum seekers is appalling, with many unable to return to their country of origin for reasons beyond their control and yet they are not allowed to work and support themselves (Dumper et al 2009). Below is a table showing the various definitions of refugee status: Asylum seeker Someone who has submitted an application for protection under the Geneva Convention and is waiting for their claim to be decided by the Home Office. Refugee status Someone whos claim has been accepted and has been granted Indefinite Leave to Remain, and is also eligible for family reunion. Exceptional Leave to or Remain (ELE/ELR) The Home Office accepts that there are strong reasons that the person should not return to their country of origin. ELR is discretionary and for varying periods depending on the age of the applicant and other circumstances Refusal Someone whos application for refugee status has been rejected. 1.3 Reasons for seeking Asylum The causes of refugees and asylum flows are many from the effects of conflict and wars, political upheaval, to economic problems and search for a better life. These displaced people face many problems such as oppression, poverty and disease. Some of them have been held captive and tortured in their own countries; some have been prosecuted because of their political or religious beliefs and some because they belong to a minority ethnic group. 1.4 UK Asylum Policy Services offered to refugees and asylum-seekers in the United Kingdom are largely determined by national legislation that in turn informs policy and practice. The introduction of the National Asylum Support Service (NASS) at the end of the 1990s was accompanied by several Acts of Parliament that have been added to by further legislation, the most recent being the Asylum and Immigration Act 2004. While historically UK has a long tradition of providing refuge to people fleeing from prosecution, the Government has recently sought to affect the behaviour of asylum-seekers through legislation intended to discourage asylum-seekers from coming to the UK. For example the support withdrawn from asylum-seekers who have exhausted their claim is designed ultimately to either persuade people to return to their country or make it easier for the Home Office to remove them. In the same way, provision of support to asylum-seekers is often conditional on their agreeing to be dispersed to different parts of the country (Johnson 2003). 1.5 Statistics of asylum seekers in the UK The main source of data on the UK asylum process and flows of individuals through it is the Home Office RDS units. Throughout the asylum process, administrative data is entered into a number of computerised databases, which are supported by a small number of manual systems. The Case Information Database (CID) records information on applications, decisions, appeals, removals (including voluntary assisted returns), persons held in detention and persons leaving detention. The Asylum Seekers Support System Database (ASYS) records details of asylum seekers applying and receiving support (ICAR 2009). The UK received 25,930 applications for asylum in 2008, compared to 23,430 in 2007 making it an increase of 11%. The highest level of asylum applications, in the last decade, was in 2002, with levels falling significantly after that. It was not until 2008 when the number of applicants started increasing once again. The chart below shows the number of applicants received in the UK between 2000 -2008. The chart was taken from the Information Centre about Asylum Seekers and Refugees (ICAR) Statistics paper. Figure 1: Applications for asylum in the UK excluding dependents 2000-08 (ICAR 2009). The main countries of origin of asylum applicants in 2008 were Afghanistan (14%), Zimbabwe (12%), Iran (9%), Eritrea (9%), Iraq (7%) Sri Lanka (6%), China, (5%), Somalia (5%), Pakistan (5%) and Nigeria (3%) (ICAR 2009). The majority of people seeking asylum in UK are single men under the age of 40 who come from countries in conflict (Burnett et al 2001). Figure 2: Showing age and gender breakdown of UK asylum seekers (Refugee Council 2009) The above diagram shows the break down of the gender of principle applicants to the UK. Males under 35 are the majority, whilst females seeking asylum are only a ration of twenty percent. 1.6 Rational for the study Asylum seekers and refugees have been the subject of media as well as political attention for many years. However, they receive bad publicity and majority of the time are stigmatised. They are perceived to come to the UK to take advantage of the welfare system and to receive host of benefits and entitlements. However, this could not be more wrong as asylum seekers and refugees flee their country not because of choice but due to circumstances and a search for sanctuary and help. They are not allowed to claim benefits and are forced to live 30% below the poverty line (Kirklees Council 2007). Furthermore, most of the asylum seekers come from well off backgrounds; and it is only the rich and well off that are able to make the long journey, and hold skilled jobs in their native countries (FPH 2008). Asylum seekers and refugees are most vulnerable groups of people at risk of developing mental problems (FPH 2008). Although there is awareness that asylum seekers and refugees are more likely to experience psychological problems factors such as asylum and immigration policies as well as social and economic exclusion and racism all exacerbate their mental condition. Having experienced all kinds of atrocities from torture, rape, imprisonment, witnessing killings, loss etc., they are faced with further problems once arriving in the UK and their mental state further deteriorates. Although refugees and asylum seekers physical health needs are usually no greater than the host populations this is not the case in relation to mental illness. There are many gaps in our knowledge about the extent of mental health issues affecting asylum seekers and what should be done in addressing these concerns. There is hardly any scholarly literature available on this topic and the general population need to be more aware of the issues and challenges faced by asylum seekers, and what effect it has on their mental health. 1.7 Aims Chapter two 2.1 Method A review was carried out of studies investigating the mental health of asylum seekers. The results and findings of carefully selected and reliable studies, searched systematically from databases and published sources were summarised. Other sources included NHS, Home Office, charity organisations, books, newspapers and magazines, and finally a general internet search was conducted. The following electronic databases were used CINHAL, Medline, BMJ, Cochrane, Pubmed, Academic search complete, and psycho info. The task of reviewing was done very methodically, with step to step plan being implemented, which involved: * the way existing studies are found * how the relevant studies are judged in terms of their usefulness in answering the question. The following search was performed, searching the title, abstract and any subject heading fields in each database, for example asylum seekers, mental health, health effects of detention. Studies published in journals were selected that involved asylum seekers and mental health, irrespective of whether the research question was addressed directly. Abstracts were screened against set criteria, and if they met the criteria full copies were obtained and looked at and relevant information extracted. Cited references were also looked at. Chapter three Results and Analysis 3.1 Health needs of Asylum-seekers The basic health needs of refugees and asylum seekers are generally similar to those of the host population, although due to poor and lack of healthcare they may have many conditions untreated. Figure 3: Most common health issues affecting asylum seekers. (Wilson 2002). The above graph, taken from a report done by Northern and Yorkshire public health observatory (Wilson 2002) shows the most frequent health issues encountered by asylum seekers. The general/minor health issues includes coughs, colds, flu, viral infections etc. Mental health issues are the most common and include anything from depression, anxiety, stress, loneliness, to torture related psychological problems, post traumatic stress etc. (Wilson 2002). People seeking asylum come from different countries and cultures, and have had range of different experiences affecting their health and nutritional state. Once in the UK they face further problems affecting their health such as the effects of poverty, dependence and lack of cohesive social support. On top of this they face racial discrimination which can result in inequalities in health and also have an impact on opportunities in and quality of life. Their experiences also shape their acceptance and expectations of health care in the UK (Burnett et al 2001). Those from countries with not so well developed health care system may expect hospital referral for conditions that in the UK are treated in primary care. This can result in refugees and asylum seekers feeling disappointed and health workers feeling irritated and overwhelmed by the many and varying needs of asylum seekers (Burnett at al 2001). Most refugees experience difficulties in expressing health needs and in accessing health care. Poverty and social exclusion have a negative impact on health. Initially refugees and asylum seekers will need help to make contact with health and social support agencies. Professional interpreters are also essential, as they help to overcome both bi-lingual and inter-cultural communication and as a result able to understand the specific health needs of asylum seekers (Bhatia et al 2007). Although the health needs of asylum seekers and refugees should be a priority, the availability and capacity of healthcare services should also be considered. There is a general feeling amongst healthcare providers that the decision about where to disperse asylum seekers are based purely on the availability of accommodation and factors such as the capacity of healthcare services are not taken into account (Johnson 2003). However, healthcare providers agree that the presence of asylum seekers highlights existing weaknesses in healthcare provision and does not necessarily create new problems (Johnson 2003). Due to the complex and confusing legal status of asylum seekers, the majority of healthcare providers are unsure how asylum status relates to healthcare entitlements. NHS staff are usually ignorant about the rights and entitlements of immigrants, and are also not adequately trained (Johnson 2003). 3.2 Mental Health and its causes Mental Health is defined as a state of well-being in which every individual realizes his or her own potential, can cope with the normal stresses of life, can work productively and fruitfully, and is able to make a contribution to her or his community (WHO 2010). Mental Illness is defined as any disease of the mind; the psychological state of someone who has emotional or behavioural problems serious enough to require psychiatric intervention (Save the Children 2010). The very nature of seeking asylum or human rights protection in the UK means that a person has suffered in some way in their country of origin and is looking for protection and safety in the UK. Nearly all those seeking asylum have experienced some form of atrocities that mental health issues are almost always intrinsically bound with their personal circumstances and nature of their claim (Burnett et al 2001). However, due to the stigmas and taboos associated with anyone suffering from any problems of the mind most people do not mention their mental suffering (Save the Children 2010). Most see mental illness as an enduring problem from which there is no recovery. It is therefore evident that those dealing with asylum seekers must address mental health issues with each applicant, making it clear to them that there is support and treatment available to them. It is crucial that asylum seekers feel safe and supported in order for them to reveal details not only crucial to their claim but also crucial to letting the person assisting them identify and provide assistance for the persons particular need (Save the Children 2010). Majority of the asylum seekers will show signs and symptoms of psychological distress, but this does not necessarily mean that they are suffering from mental illness. Asylum seekers may show symptoms of depression and anxiety, panic attacks, poor sleeping patterns, nervousness and anxiousness (Burnett 2002). They may also develop behaviours to avoid stimuli that reminds them of past experiences, with some also experiencing memory and concentration problems (Burnett 2002). Such symptoms are often reactions to their past experiences and current situations. Many of them will have been forced to leave their family behind or may even not know the whereabouts of their family. Their state of mental health may worsen due to social isolation, poverty, hostility and racism, which all have a negative impact on their health (Burnett et al 2002). Arrival, detention and uncertainty, practical issues, e.g. housing, lack of employment, living in a climate of prejudice, family dislocation and reunion, domestic violence and living in the shadow of deportation are all reasons identified that contribute to the poor mental state of asylum seekers and refuges (Burnett 2002). Majority of the asylum seekers have suffered some sort of prosecution and harassment in their country of origin, enduring torture, rape or bereavement. They have also experienced the stress of flight and exile. Psychological morbidity has been extensively documented among refugee populations (Burnett et al 2002). The experience of detention compounds the misery of refugees. Captivity is stressful in any context, but is particularly debilitating when it occurs over an indeterminate period and to people who have had previously traumatic experiences of detention (Burnett 2002). Some asylum seekers show signs of anxiety, depression, guilt and shame as a result of the atrocities they may have suffered. Such symptoms are common responses to grief and distress and should not be viewed as psychiatric illness. Common experiences in asylum seekers and refugees after trauma include poor sleeping patterns, distressing dreams, headaches, palpitations, sweating, loss of concentration, jumpiness, low mood and frequent crying, irritability etc. Symptoms such as consistent failure to carry out daily tasks, frequent expressed suicidal thoughts and ideas, social withdrawal and self-neglect, and behaviour that is abnormal or strange are symptoms that may require specialist help (Burnett 2002). 3.3 Mental health of dispersed asylum seekers One of the major initiatives introduced by the Asylum and Immigration Act 1999 is the dispersal of asylum seekers requiring provision of long-term accommodation form London and the South-East to other parts of the UK (Cornelius 2007). This is due to the fact that long term accommodation is more readily available and cheaper and also to lessen pressure on services and resentment by local communities. However, it is believed that dispersal of asylum seekers is associated with higher rates of psychiatric disorder (Heptinstall et al 2004). Other issues such as loss of newly established support networks, racially motivated crime against dispersed asylum seekers are also common (Heptinstall et al 2004). Although most asylum seekers cope quite well with dispersal, there are those however that become distressed and show signs of dispersal-related mental disorder (Cornelius 2007). Supporting such individuals can be challenging for most mental health clinicians. Asylum seekers referred because of dispersal-related mental disorder can be divided into two broad categories: mild to moderate psychiatric disorder and severe psychiatric disorder (Cornelius 2007). The majority of affected individuals are likely to experience mild to moderately severe psychiatric disorder with no major risk concerns, whereas a small proportion of individuals may have severe psychiatric disorder such as psychosis or a severe depressive episode associated with risk of harm to self or others (Cornelius 2007). The differing severity, complexity and risk profile of these two groups suggest that mental health strategies for support are likely to be different (Cornelius 2007). Clinicians should undertake a detailed assessment of the needs and risk profiles of asylum seekers, with the aide of interpreters with knowledge of mental health issues. If the outcome of the assessment shows the individual to have forms of mild to moderate severe psychiatric disorder with no major risks then the mental health support should be focused on helping the individual accept and adjust to dispersal (Cornelius 2007). However, individuals may show signs of being acutely psychotic and severely disturbed with risk of harming themselves and others and such individuals should not be dispersed. There is evidence to suggest that abrupt cessation of psychiatric treatment can result in serious deterioration of the individuals mental health and compromise long-term recovery (Cornelius 2007). 3.4 Children and Adolescents Although the majority of asylum seekers and refugees are adults, there are however many children who arrive in the UK seeking refuge. While some arrive with family, there are those that arrive alone as unaccompanied asylum-seeking children. These children are likely, at an emotional level to have experienced some sort of terror, grief, shame, guilt etc. (Burnett 2002). They may have experienced imprisonment, beatings, rape, they may have witnessed others subjected to violence, or been subjected to torture due to their political or religious belief of their parents, their colour of skin, and may have lost or been separated from their family. All these experiences and events have different impacts on children. Refugee Children and asylum-seekers are more likely to develop psychological problems due to their experiences (Mind 2009). These children may experience both physical and psychological symptoms that trouble them such as sleep disturbances, feeling of loneliness, isolation, difficulty in learning and a general feeling of unhappiness and anger. They may experience anxiety, aggression, nightmares, poor concentration, withdrawal, and behaviour such as bed-wetting (Burnett 2002). Although unaccompanied children are most likely to suffer from mental health problems, children with families present may also suffer from mental health problems as a result of finding themselves feeling unsupported and having to fend for themselves due to absent parents as a result of work or other problems. Furthermore, parents dealing with their own emotional problems are unlikely to care for their children properly, which can result in psychological and physical problems (McCormack et al 2005). 3.5 Health implications of detained asylum seekers Health professionals world wide are concerned about the potential detrimental effects detention has on the mental health of the detainees (Procter 2005). An experiment carried out by Sultan and OSullivan in which they observed participants inside an immigration centre found that 32 of 33 detainees displayed symptoms of major depressive illness (Procter 2005). The majority also showed deterioration in their mental state as the length of detention increased. Detained children also showed signs and symptoms of mental distress, which included anxiety, disruptive conduct, nocturnal enuresis, sleep disturbances, nightmares, sleepwalking as well as cognitive development (Procter 2005). Once released the detainees mental illness is likely to deteriorate and it is known that adult asylum seekers who have been in immigration detention display a threefold increase in mental illness subsequent to their release (Procter 2005). Trauma, upsetting memories about detention, feeling of hopelessness and sadness are the common symptoms experienced by those detained. These symptoms were also present among detainees in an investigation carried out by Dudley (2003), who also found rioting, violence, and hunger strikes common inside immigration detention facilities with 264 incidents of self-harm reported over an 8-month period among detainees (Procter 2005). Once the detainees are released from immigration detention, they face new challenges and stresses in the context of existing mental health problems (Procter 2005). In another study carried out by Thompson and colleagues found that Tamil asylum seekers detained during 1997 and 1998 found the detainees experiencing high levels of depression, post-traumatic stress, anxiety, panic and physical symptoms compared to those asylum seekers living in the community (Steel et al 2004). This study found detention to be injurious to the mental health of asylum seekers with mental health deteriorating with increased length of detention. The study also indicated that adults and children are regularly distressed by memories of detention and feeling of immense sadness and hopelessness about being in detention. Parents of children also felt they were unable to care for or support and control their childrens behaviour (Steel et al 2004). Hundreds of children are detained in immigration centres every year in the UK because their families face deportation. Medical experts say this can have harmful health implications on the children. The Royal Colleges of Paediatrics, GPs and Psychiatrists say other countries have found alternatives to detention and want the British government to take a different approach to stop the physical and psychological damage suffered by children (Wilson 2009). These children are among the most vulnerable and detention causes unnecessary harm to their mental and physical health. The average stay of children at Yarls Wood, the UKs largest immigration removal centre, is fifteen days but a third are detained for more than a month. Detaining children for any length of time is a frightening experience that can have lifelong consequences (Wilson 2009). As well as the potential psychological impact, these children invariably experience poor physical health as they cannot access immunisation and preventative services (Wilson 2009). 3.6 Previous research/studies on health of asylum seekers Knowledge about asylum seekers health and access to health care services is still limited. Literature on asylum seekers health mainly concerns mental health problems and infectious diseases. Burnett Peel reviewed the literature and found that one in six asylum seekers had severe physical problems and two-thirds had experienced mental problems. Prevalent physical problems included tuberculosis, HIV/AIDS, hepatitis A and B, parasitic diseases, and non-specific body pains (Burnett et al 2001). Mental health problems include depression and Post Traumatic Stress Disorder, which are due to traumatic experiences, including torture. Asylum seekers are at the risk of having many and severe health problems of a varied nature. Literature on asylum seekers use of health care services and the barriers they face when seeking care is hard to find. Asylum seekers, however, find themselves in a difficult situation as they are residing in a country, sometimes for years while waiting for a decision in their case, without necessarily having the same legal rights as citizens. They may face limitations on access to health care compared with the citizens. This combined with the asylum seekers already vulnerable health and with possible restrictions on access to care may result in their health deteriorating (Burnett et al 2001). Studies carried out in the UK have found that one in six refugees has a physical health problem severe enough to affect their life with two thirds having experienced anxiety or depression. Medical screening of newly arrived asylum seekers exist in the majority of the EU countries as well as the UK. However differences exist in the way medical screening is carried out. In the UK medical screening is only carried out in the so-called induction or reception centres. Newly arrived asylum seekers who do not enter these centres access medical screening randomly. Medical screening may be available for asylum seekers living outside the centres, but using it depends on individual initiative and there might be a number of barriers. Medical screening programmes also differ in their content from one EU country to another. For example, TB screening was included in the screening programmes of all countries but one, whereas screening for mental health problems was carried out in less than half the countries (Norredam et al 2005). Overall, medical screening programmes appear to have two aims. One is to secure the well being of asylum seekers, and the other to guarantee the safety of the population in the host country. The content of the screening programmes is likely to depend on how the country priorities these aims. For example, screening for infectious diseases seems more related to the safety of the host population and mental health screening more to the well being of asylum seekers (Norredam et al 2005). Regarding access to health care, the study shows that access was restricted to only emergency care at the time of arrival in 10 countries (Norredam et al 2005). The results, however, do not show, if some countries offered alternative measures in case of chronic illness. The study also found that asylum seekers faced a number of practical barriers when seeking health care. Most of the barriers were concerned with immigrant populations in general, and are related to language, culture, and lack of information about the health care system in the host country. However, practical barriers specific for asylum seekers were also identified. The most severe of which include waiting for months or years on paperwork that will ensure access to health care, while only having access to emergency care in the meantime. The literature also shows that asylum seekers access to health care may be compounded by other barriers, such as confinement in detention centres, and dispersal policies leading to dis ruptive and compromised care (Norredam et al 2005). The study also shows how legal access to health care services have changed over time for asylum seekers in three countries. Asylum seekers rights to health care are immediately restricted to emergency care if their application is refused (Norredam et al 2005). Failed asylum seekers may also be stripped of the other rights in an attempt to force them out of the host country. Failed asylum seekers include persons who cannot return because their countries are deemed unsafe by UNHCR. UK is one of the countries using increasingly restrictive measures towards failed asylum seekers. Failed asylum seekers used to have free access to NHS, but since 2004 they cannot obtain free secondary health care (Norredam et al 2005). In another study in which the impact of detention on asylum seekers was examined, found that detainees are rendered hopeless and powerless in detention (Pourgourides 1997). The unknown duration and reasons for detention mean they are unable to make sense of their predicament and deal with it in a meaningful way. The unpredictable outcome of detention, in particular the fear of deportation is a constant cause of stress. Detention denies asylum seekers the resources to cope with adversity, blocks adaptation to the host society and impairs psychological healing (Pourgourides 1997). Depression, anxiety, demotivation and despondency are all responses to detention as well as misery and suffering (Pourgourides 1997). The study highlighted high levels of stress and distress amongst detainees. The detainees appear to be able to cope for the first month or two in detention but then after that they become increasingly frustrated, demotivated and apathetic. They start showing signs of psychological symptoms such as sleep and appetite disturbances, symptoms of post-traumatic stress, psychosomatic symptoms etc

Cengel Solutions

Chapter 4 Fluid Kinematics Solutions Manual for Fluid Mechanics: Fundamentals and Applications by Cengel & Cimbala CHAPTER 4 FLUID KINEMATICS PROPRIETARY AND CONFIDENTIAL This Manual is the proprietary property of The McGraw-Hill Companies, Inc. (â€Å"McGraw-Hill†) and protected by copyright and other state and federal laws.By opening and using this Manual the user agrees to the following restrictions, and if the recipient does not agree to these restrictions, the Manual should be promptly returned unopened to McGraw-Hill: This Manual is being provided only to authorized professors and instructors for use in preparing for the classes using the affiliated textbook. No other use or distribution of this Manual is permitted. This Manual may not be sold and may not be distributed to or used by any student or other third party.No part of this Manual may be reproduced, displayed or distributed in any form or by any means, electronic or otherwise, without the prior written permission of McGraw-Hill. 4-1 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics Introductory Problems 4-1C Solution We are to define and explain kinematics and fluid kinematics. Analysis Kinematics means the study of motion.Fluid kinematics is the study of how fluids flow and how to describe fluid motion. Fluid kinematics deals with describing the motion of fluids without considering (or even understanding) the forces and moments that cause the motion. Discussion Fluid kinematics deals with such things as describing how a fluid particle translates, distorts, and rotates, and how to visualize flow fields. 4-2 Solution We are to write an equation for centerline speed through a nozzle, given that the flow speed increases parabolically. Assumptions 1 The flow is steady. 2 The flow is axisymmetri c. The water is incompressible. Analysis A general equation for a parabola in the x direction is u = a + b ( x ? c) General parabolic equation: 2 (1) We have two boundary conditions, namely at x = 0, u = uentrance and at x = L, u = uexit. By inspection, Eq. 1 is satisfied by setting c = 0, a = uentrance and b = (uexit – uentrance)/L2. Thus, Eq. 1 becomes u = uentrance + Parabolic speed: ( uexit ? uentrance ) L2 x2 (2) Discussion You can verify Eq. 2 by plugging in x = 0 and x = L. 4-3 Solution location. For a given velocity field we are to find out if there is a stagnation point.If so, we are to calculate its Assumptions 1 The flow is steady. 2 The flow is two-dimensional in the x-y plane. Analysis The velocity field is V = ( u , v ) = ( 0. 5 + 1. 2 x ) i + ( ? 2. 0 ? 1. 2 y ) j (1) At a stagnation point, both u and v must equal zero. At any point (x,y) in the flow field, the velocity components u and v are obtained from Eq. 1, Velocity components: u = 0. 5 + 1. 2 x v = ? 2. 0 ? 1. 2 y (2) x = ? 0. 4167 y = ? 1. 667 (3) Setting these to zero yields Stagnation point: 0 = 0. 5 + 1. 2 x 0 = ? 2. 0 ? 1. 2 y So, yes there is a stagnation point; its location is x = -0. 17, y = -1. 67 (to 3 digits). Discussion If the flow were three-dimensional, we would have to set w = 0 as well to determine the location of the stagnation point. In some flow fields there is more than one stagnation point. 4-2 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-4 Solution location. For a given velocity field we are to find out if there is a stagnation point.If so, we are to calculate its Assumptions 1 The flow is steady. 2 The flow is two-dimensional in the x-y plane. Analysis The velocity field is ( )( ) V = ( u, v ) = a 2 ? ( b ? cx ) i + ? 2cby + 2c 2 xy j 2 (1) At a stagna tion point, both u and v must equal zero. At any point (x,y) in the flow field, the velocity components u and v are obtained from Eq. 1, Velocity components: u = a 2 ? ( b ? cx ) 2 v = ? 2cby + 2c 2 xy (2) b? a c y=0 (3) Setting these to zero and solving simultaneously yields Stagnation point: 0 = a 2 ? ( b ? cx ) 2 x= v = ? 2cby + 2c xy So, yes there is a stagnation point; its location is x = (b – a)/c, y = 0. Discussion If the flow were three-dimensional, we would have to set w = 0 as well to determine the location of the stagnation point. In some flow fields there is more than one stagnation point. Lagrangian and Eulerian Descriptions 4-5C Solution We are to define the Lagrangian description of fluid motion. Analysis In the Lagrangian description of fluid motion, individual fluid particles (fluid elements composed of a fixed, identifiable mass of fluid) are followed. DiscussionThe Lagrangian method of studying fluid motion is similar to that of studying billiard balls and other solid objects in physics. 4-6C Solution We are to compare the Lagrangian method to the study of systems and control volumes and determine to which of these it is most similar. Analysis The Lagrangian method is more similar to system analysis (i. e. , closed system analysis). In both cases, we follow a mass of fixed identity as it moves in a flow. In a control volume analysis, on the other hand, mass moves into and out of the control volume, and we don’t follow any particular chunk of fluid.Instead we analyze whatever fluid happens to be inside the control volume at the time. Discussion to a point. In fact, the Lagrangian analysis is the same as a system analysis in the limit as the size of the system shrinks 4-3 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-7C Sol ution description. We are to define the Eulerian description of fluid motion, and explain how it differs from the LagrangianAnalysis In the Eulerian description of fluid motion, we are concerned with field variables, such as velocity, pressure, temperature, etc. , as functions of space and time within a flow domain or control volume. In contrast to the Lagrangian method, fluid flows into and out of the Eulerian flow domain, and we do not keep track of the motion of particular identifiable fluid particles. Discussion The Eulerian method of studying fluid motion is not as â€Å"natural† as the Lagrangian method since the fundamental conservation laws apply to moving particles, not to fields. -8C Solution We are to determine whether a measurement is Lagrangian or Eulerian. Analysis Since the probe is fixed in space and the fluid flows around it, we are not following individual fluid particles as they move. Instead, we are measuring a field variable at a particular location in sp ace. Thus this is an Eulerian measurement. Discussion If a neutrally buoyant probe were to move with the flow, its results would be Lagrangian measurements – following fluid particles. 4-9C Solution We are to determine whether a measurement is Lagrangian or Eulerian. AnalysisSince the probe moves with the flow and is neutrally buoyant, we are following individual fluid particles as they move through the pump. Thus this is a Lagrangian measurement. Discussion If the probe were instead fixed at one location in the flow, its results would be Eulerian measurements. 4-10C Solution We are to determine whether a measurement is Lagrangian or Eulerian. Analysis Since the weather balloon moves with the air and is neutrally buoyant, we are following individual â€Å"fluid particles† as they move through the atmosphere. Thus this is a Lagrangian measurement.Note that in this case the â€Å"fluid particle† is huge, and can follow gross features of the flow – the ballo on obviously cannot follow small scale turbulent fluctuations in the atmosphere. Discussion When weather monitoring instruments are mounted on the roof of a building, the results are Eulerian measurements. 4-11C Solution We are to determine whether a measurement is Lagrangian or Eulerian. Analysis Relative to the airplane, the probe is fixed and the air flows around it. We are not following individual fluid particles as they move. Instead, we are measuring a field variable at a particular location in space relative to the moving airplane.Thus this is an Eulerian measurement. Discussion The airplane is moving, but it is not moving with the flow. 4-4 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-12C Solution We are to compare the Eulerian method to the study of systems and contr ol volumes and determine to which of these it is most similar. Analysis The Eulerian method is more similar to control volume analysis.In both cases, mass moves into and out of the flow domain or control volume, and we don’t follow any particular chunk of fluid. Instead we analyze whatever fluid happens to be inside the control volume at the time. Discussion In fact, the Eulerian analysis is the same as a control volume analysis except that Eulerian analysis is usually applied to infinitesimal volumes and differential equations of fluid flow, whereas control volume analysis usually refers to finite volumes and integral equations of fluid flow. 4-13C Solution flow. We are to define a steady flow field in the Eulerian description, and discuss particle acceleration in such aAnalysis A flow field is defined as steady in the Eulerian frame of reference when properties at any point in the flow field do not change with respect to time. In such a flow field, individual fluid particle s may still experience non-zero acceleration – the answer to the question is yes. Discussion ( a = dV / dt ) Although velocity is not a function of time in a steady flow field, its total derivative with respect to time is not necessarily zero since the acceleration is composed of a local (unsteady) part which is zero and an advective part which is not necessarily zero. 4-14C SolutionWe are to list three alternate names for material derivative. Analysis The material derivative is also called total derivative, particle derivative, Eulerian derivative, Lagrangian derivative, and substantial derivative. â€Å"Total† is appropriate because the material derivative includes both local (unsteady) and convective parts. â€Å"Particle† is appropriate because it stresses that the material derivative is one following fluid particles as they move about in the flow field. â€Å"Eulerian† is appropriate since the material derivative is used to transform from Lagrangian to Eulerian reference frames. Lagrangian† is appropriate since the material derivative is used to transform from Lagrangian to Eulerian reference frames. Finally, â€Å"substantial† is not as clear of a term for the material derivative, and we are not sure of its origin. Discussion All of these names emphasize that we are following a fluid particle as it moves through a flow field. 4-5 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.Chapter 4 Fluid Kinematics 4-15 Solution We are to calculate the material acceleration for a given velocity field. Assumptions 1 The flow is steady. 2 The flow is incompressible. 3 The flow is two-dimensional in the x-y plane. Analysis The velocity field is V = ( u , v ) = (U 0 + bx ) i ? byj (1) The acceleration field components are obtained from its definition (the material acceleration) in Cartesian coordinates, ? u ?u ?u ?u +u +v +w = 0 + (U 0 + bx ) b + ( ? by ) 0 + 0 ?t ?x ?y ?z ?v ?v ?v ?v ay = + u + v + w = 0 + (U 0 + bx ) 0 + ( ? by )( ? b ) +0 ?t ?x ?y ?z ax = (2) here the unsteady terms are zero since this is a steady flow, and the terms with w are zero since the flow is twodimensional. Eq. 2 simplifies to ax = b (U 0 + bx ) ay = b2 y (3) a = b (U 0 + bx ) i + b 2 yj Material acceleration components: (4) In terms of a vector, Material acceleration vector: Discussion For positive x and b, fluid particles accelerate in the positive x direction. Even though this flow is steady, there is still a non-zero acceleration field. 4-16 Solution particle. For a given pressure and velocity field, we are to calculate the rate of change of pressure following a fluid Assumptions 1 The flow is steady. The flow is incompressible. 3 The flow is two-dimensional in the x-y plane. Analysis The pressure field is P = P0 ? Pressure field: 2U 0 bx + b 2 ( x 2 + y 2 ) ? 2? ? (1) By definition, the material derivative, when applied to pressure, produces the rate of change of pressure following a fluid particle. Using Eq. 1 and the velocity components from the previous problem, DP ? P ?P ?P = +u +v + Dt ?t ?x ?y Steady ( w ?P ?z (2) Two-dimensional ) ( = (U 0 + bx ) ? ?U 0 b ? ? b 2 x + ( ? by ) ? ? b 2 y ) where the unsteady term is zero since this is a steady flow, and the term with w is zero since the flow is two-dimensional.Eq. 2 simplifies to the following rate of change of pressure following a fluid particle: ( ) DP 2 = ? ? ? U 0 b ? 2U 0 b 2 x + b3 y 2 ? x 2 ? ? ? Dt (3) Discussion The material derivative can be applied to any flow property, scalar or vector. Here we apply it to the pressure, a scalar quantity. 4-6 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permi ssion. Chapter 4 Fluid Kinematics 4-17 SolutionFor a given velocity field we are to calculate the acceleration. Assumptions 1 The flow is steady. 2 The flow is two-dimensional in the x-y plane. Analysis The velocity components are Velocity components: u = 1. 1 + 2. 8 x + 0. 65 y v = 0. 98 ? 2. 1x ? 2. 8 y (1) The acceleration field components are obtained from its definition (the material acceleration) in Cartesian coordinates, ? u ?u ?u ?u +u +v +w = 0 + (1. 1 + 2. 8 x + 0. 65 y )( 2. 8 ) + ( 0. 98 ? 2. 1x ? 2. 8 y )( 0. 65 ) + 0 ? t ?x ?y ?z ?v ?v ?v ?v + u + v + w = 0 + (1. 1 + 2. 8 x + 0. 65 y )( ? 2. 1) + ( 0. 98 ? 2. 1x ? 2. 8 y )( ? 2. ) +0 ay = ?t ?x ?y ?z ax = (2) where the unsteady terms are zero since this is a steady flow, and the terms with w are zero since the flow is twodimensional. Eq. 2 simplifies to Acceleration components: ax = 3. 717 + 6. 475 x a y = ? 5. 054 + 6. 475 y (3) At the point (x,y) = (-2,3), the acceleration components of Eq. 3 are Acceleration compone nts at (-2,3): ax = ? 9. 233 ? -9. 23 a y = 14. 371 ? 14. 4 Discussion The final answers are given to three significant digits. No units are given in either the problem statement or the answers. We assume that the coefficients have appropriate units. 4-18 SolutionFor a given velocity field we are to calculate the acceleration. Assumptions 1 The flow is steady. 2 The flow is two-dimensional in the x-y plane. Analysis The velocity components are Velocity components: u = 0. 20 + 1. 3 x + 0. 85 y v = ? 0. 50 + 0. 95 x ? 1. 3 y (1) The acceleration field components are obtained from its definition (the material acceleration) in Cartesian coordinates, ? u ?u ?u ?u +u +v +w = 0 + ( 0. 20 + 1. 3 x + 0. 85 y )(1. 3) + ( ? 0. 50 + 0. 95 x ? 1. 3 y )( 0. 85 ) + 0 ? t ?x ?y ?z ?v ?v ?v ?v + u + v + w = 0 + ( 0. 20 + 1. 3 x + 0. 85 y )( 0. 95 ) + ( ? 0. 50 + 0. 95 x ? 1. y )( ? 1. 3 ) +0 ay = ?t ?x ?y ?z ax = (2) where the unsteady terms are zero since this is a steady flow, and the terms with w are zero since the flow is twodimensional. Eq. 2 simplifies to Acceleration components: ax = ? 0. 165 + 2. 4975 x a y = 0. 84 + 2. 4975 y (3) At the point (x,y) = (1,2), the acceleration components of Eq. 3 are Acceleration components at (1,2): ax = 2. 3325 ? 2. 33 a y = 5. 835 ? 5. 84 Discussion The final answers are given to three significant digits. No units are given in either the problem statement or the answers. We assume that the coefficients have appropriate units. -7 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-19 Solution We are to generate an expression for the fluid acceleration for a given velocity. Assumptions 1 The flow is steady. 2 The flow is axisymmetric. 3 The water is incompressible. Analysis In Problem 4-2 we found that along the centerline, u = uentranc e + Speed along centerline of nozzle: ( uexit ? uentrance ) x2 (1) ?u ?u ?u ?u +u +v +w ?t ?x y ?z (2) L2 To find the acceleration in the x-direction, we use the material acceleration, ax = Acceleration along centerline of nozzle: The first term in Eq. 2 is zero because the flow is steady. The last two terms are zero because the flow is axisymmetric, which means that along the centerline there can be no v or w velocity component. We substitute Eq. 1 for u to obtain Acceleration along centerline of nozzle: ax = u ( uexit ? uentrance ) 2 ? ( uexit ? uentrance ) ?u ? = ? uentrance + x ? ( 2) x ? ? ?x ? L2 L2 ? (3) or ax = 2uentrance Discussion ( uexit ? uentrance ) L2 x+2 ( uexit ? uentrance )L4 2 x3 (4) Fluid particles are accelerated along the centerline of the nozzle, even though the flow is steady. 4-20 Solution We are to write an equation for centerline speed through a diffuser, given that the flow speed decreases parabolically. Assumptions 1 The flow is steady. 2 The flow is axis ymmetric. Analysis A general equation for a parabola in x is General parabolic equation: u = a + b ( x ? c) 2 (1) We have two boundary conditions, namely at x = 0, u = uentrance and at x = L, u = uexit. By inspection, Eq. 1 is satisfied by setting c = 0, a = uentrance and b = (uexit – uentrance)/L2. Thus, Eq. becomes Parabolic speed: Discussion u = uentrance + ( uexit ? uentrance ) L2 x2 (2) You can verify Eq. 2 by plugging in x = 0 and x = L. 4-8 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-21 Solution We are to generate an expression for the fluid acceleration for a given velocity, and then calculate its value at two x locations. Assumptions 1 The flow is steady. 2 The flow is axisymmetric. AnalysisIn the previous problem, we found that along the centerline, u = uent rance + Speed along centerline of diffuser: ( uexit ? uentrance ) 2 L x2 (1) To find the acceleration in the x-direction, we use the material acceleration, Acceleration along centerline of diffuser: ax = ?u ?u ?u ?u +w +u +v ?z ?t ?x ?y (2) The first term in Eq. 2 is zero because the flow is steady. The last two terms are zero because the flow is axisymmetric, which means that along the centerline there can be no v or w velocity component. We substitute Eq. 1 for u to obtain Acceleration along centerline of diffuser: ( uexit ? uentrance ) x 2 ? ( uexit ? entrance ) x ?u ? = ? uentrance + ax = u ? ( 2) ? ?x ? L2 L2 ? ? or ax = 2uentrance ( uexit ? uentrance ) 2 L x+2 ( uexit ? uentrance ) 2 4 L x3 (3) At the given locations, we substitute the given values. At x = 0, Acceleration along centerline of diffuser at x = 0: ax ( x = 0 ) = 0 (4) At x = 1. 0 m, Acceleration along centerline of diffuser at x = 1. 0 m: ax ( x = 1. 0 m ) = 2 ( 30. 0 m/s ) ( ? 25. 0 m/s ) ( ? 25. 0 m/s ) 3 (1. 0 m ) + 2 (1. 0 m ) 2 4 ( 2. 0 m ) ( 2. 0 m ) 2 (5) = -297 m/s 2 Discussion ax is negative implying that fluid particles are decelerated along the centerline of the diffuser, even though the flow is steady.Because of the parabolic nature of the velocity field, the acceleration is zero at the entrance of the diffuser, but its magnitude increases rapidly downstream. 4-9 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics Flow Patterns and Flow Visualization 4-22C Solution We are to define streamline and discuss what streamlines indicate. Analysis A streamline is a curve that is everywhere tangent to the instantaneous local velocity vector.It indicates the instantaneous direction of fluid motion throughout the flow field. Discussion If a flow field is steady, streamlines, pathlines, and st reaklines are identical. 4-23 Solution For a given velocity field we are to generate an equation for the streamlines. Assumptions 1 The flow is steady. 2 The flow is two-dimensional in the x-y plane. The steady, two-dimensional velocity field of Problem 4-15 is Analysis V = ( u , v ) = (U 0 + bx ) i ? byj Velocity field: (1) For two-dimensional flow in the x-y plane, streamlines are given by Streamlines in the x-y plane: dy ? v = dx ? along a streamline u (2) We substitute the u and v components of Eq. 1 into Eq. 2 and rearrange to get dy ?by = dx U 0 + bx We solve the above differential equation by separation of variables: dy dx = by ? U 0 + bx Integration yields 1 1 1 ? ln ( by ) = ln (U 0 + bx ) + ln C1 b b b (3) where we have set the constant of integration as the natural logarithm of some constant C1, with a constant in front in order to simplify the algebra (notice that the factor of 1/b can be removed from each term in Eq. 3). When we recall that ln(ab) = lna + lnb, and that –lna = ln(1/a), Eq. 3 simplifies to Equation for streamlines: y= CU 0 + bx ) ( (4) The new constant C is related to C1, and is introduced for simplicity. Discussion Each value of constant C yields a unique streamline of the flow. 4-10 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-24E Solution For a given velocity field we are to plot several streamlines for a given range of x and y values. 3 Assumptions 1 The flow is steady. 2 The flow is two-dimensional in the x-y plane. Analysis From the solution to the previous problem, an equation for the streamlines is 1 Streamlines in the x-y plane: y= C (U 0 + bx ) (1) y0 (ft) Constant C is set to various values in order to plot the streamlines. Several streamlines in the given range of x and y are plotted in Fig. 1. The directi on of the flow is found by calculating u and v at some point in the flow field. We choose x = 1 ft, y = 1 ft. At this point u = 9. 6 ft/s and v = –4. 6 ft/s. The direction of the velocity at this point is obviously to the lower right. This sets the direction of all the streamlines. The arrows in Fig. indicate the direction of flow. Discussion -1 -2 -3 0 1 2 3 x (ft) 4 5 The flow is type of converging channel flow. FIGURE 1 Streamlines (solid blue curves) for the given velocity field; x and y are in units of ft. 4-25C Solution We are to determine what kind of flow visualization is seen in a photograph. Analysis Since the picture is a snapshot of dye streaks in water, each streak shows the time history of dye that was introduced earlier from a port in the body. Thus these are streaklines. Since the flow appears to be steady, these streaklines are the same as pathlines and streamlines. DiscussionIt is assumed that the dye follows the flow of the water. If the dye is of nearly th e same density as the water, this is a reasonable assumption. 4-26C Solution We are to define pathline and discuss what pathlines indicate. Analysis A pathline is the actual path traveled by an individual fluid particle over some time period. It indicates the exact route along which a fluid particle travels from its starting point to its ending point. Unlike streamlines, pathlines are not instantaneous, but involve a finite time period. Discussion If a flow field is steady, streamlines, pathlines, and streaklines are identical. -27C Solution We are to define streakline and discuss the difference between streaklines and streamlines. Analysis A streakline is the locus of fluid particles that have passed sequentially through a prescribed point in the flow. Streaklines are very different than streamlines. Streamlines are instantaneous curves, everywhere tangent to the local velocity, while streaklines are produced over a finite time period. In an unsteady flow, streaklines distort and t hen retain features of that distorted shape even as the flow field changes, whereas streamlines change instantaneously with the flow field.Discussion If a flow field is steady, streamlines and streaklines are identical. 4-11 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-28C Solution We are to determine what kind of flow visualization is seen in a photograph. Analysis Since the picture is a snapshot of dye streaks in water, each streak shows the time history of dye that was introduced earlier from a port in the body.Thus these are streaklines. Since the flow appears to be unsteady, these streaklines are not the same as pathlines or streamlines. Discussion It is assumed that the dye follows the flow of the water. If the dye is of nearly the same density as the water, this is a r easonable assumption. 4-29C Solution We are to determine what kind of flow visualization is seen in a photograph. Analysis Since the picture is a snapshot of smoke streaks in air, each streak shows the time history of smoke that was introduced earlier from the smoke wire. Thus these are streaklines.Since the flow appears to be unsteady, these streaklines are not the same as pathlines or streamlines. Discussion It is assumed that the smoke follows the flow of the air. If the smoke is neutrally buoyant, this is a reasonable assumption. In actuality, the smoke rises a bit since it is hot; however, the air speeds are high enough that this effect is negligible. 4-30C Solution We are to determine what kind of flow visualization is seen in a photograph. Analysis Since the picture is a time exposure of air bubbles in water, each white streak shows the path of an individual air bubble.Thus these are pathlines. Since the outer flow (top and bottom portions of the photograph) appears to be ste ady, these pathlines are the same as streaklines and streamlines. Discussion It is assumed that the air bubbles follow the flow of the water. If the bubbles are small enough, this is a reasonable assumption. 4-31C Solution We are to define timeline and discuss how timelines can be produced in a water channel. We are also to describe an application where timelines are more useful than streaklines. Analysis A timeline is a set of adjacent fluid particles that were marked at the same instant of time.Timelines can be produced in a water flow by using a hydrogen bubble wire. There are also techniques in which a chemical reaction is initiated by applying current to the wire, changing the fluid color along the wire. Timelines are more useful than streaklines when the uniformity of a flow is to be visualized. Another application is to visualize the velocity profile of a boundary layer or a channel flow. Discussion Timelines differ from streamlines, streaklines, and pathlines even if the flo w is steady. 4-32C Solution For each case we are to decide whether a vector plot or contour plot is most appropriate, and we are to explain our choice.Analysis In general, contour plots are most appropriate for scalars, while vector plots are necessary when vectors are to be visualized. (a) A contour plot of speed is most appropriate since fluid speed is a scalar. (b) A vector plot of velocity vectors would clearly show where the flow separates. Alternatively, a vorticity contour plot of vorticity normal to the plane would also show the separation region clearly. (c) A contour plot of temperature is most appropriate since temperature is a scalar. (d) A contour plot of this component of vorticity is most appropriate since one component of a vector is a scalar.Discussion There are other options for case (b) – temperature contours can also sometimes be used to identify a separation zone. 4-12 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution pe rmitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-33 Solution For a given velocity field we are to generate an equation for the streamlines and sketch several streamlines in the first quadrant. Assumptions 1 The flow is steady. 2 The flow is two-dimensional in the x-y plane.Analysis The velocity field is given by V = ( u , v ) = ( 0. 5 + 1. 2 x ) i + ( ? 2. 0 ? 1. 2 y ) j (1) For two-dimensional flow in the x-y plane, streamlines are given by dy ? v = ? dx ? along a streamline u Streamlines in the x-y plane: (2) We substitute the u and v components of Eq. 1 into Eq. 2 and rearrange to get dy ? 2. 0 ? 1. 2 y = dx 0. 5 + 1. 2 x We solve the above differential equation by separation of variables: dy dx = ?2. 0 ? 1. 2 y 0. 5 + 1. 2 x > dy dx ? ? 2. 0 ? 1. 2 y = ? 0. 5 + 1. 2 x Integration yields ? 1 1 1 ln ( ? 2. 0 ? 1. 2 y ) = ln ( 0. 5 + 1. 2 x ) ? ln C1 1. 2 1. 2 1. 2 here we have set the constant of integration as the natural logarithm of some constant C1, with a constant in front in order to simplify the algebra. When we recall that ln(ab) = lna + lnb, and that –lna = ln(1/a), Eq. 3 simplifies to Equation for streamlines: y= 5 y 4 3 2 C ? 1. 667 1. 2 ( 0. 5 + 1. 2 x ) 1 The new constant C is related to C1, and is introduced for simplicity. C can be set to various values in order to plot the streamlines. Several streamlines in the upper right quadrant of the given flow field are shown in Fig. 1. The direction of the flow is found by calculating u and v at some point in the flow field.We choose x = 3, y = 3. At this point u = 4. 1 and v = -5. 6. The direction of the velocity at this point is obviously to the lower right. This sets the direction of all the streamlines. The arrows in Fig. 1 indicate the direction of flow. Discussion 6 (3) 0 0 1 2 3 4 5 x FIGURE 1 Streamlines (solid black curves) for the given velocity field. The flow appea rs to be a counterclockwise turning flow in the upper right quadrant. 4-13 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation.If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-34 Solution For a given velocity field we are to generate a velocity vector plot in the first quadrant. Scale: 6 Assumptions 1 The flow is steady. 2 The flow is two-dimensional in the x-y plane. Analysis 5 y4 The velocity field is given by V = ( u , v ) = ( 0. 5 + 1. 2 x ) i + ( ? 2. 0 ? 1. 2 y ) j 3 (1) 2 At any point (x,y) in the flow field, the velocity components u and v are obtained from Eq. 1, Velocity components: u = 0. 5 + 1. 2 x 10 m/s v = ? 2. 0 ? 1. 2 y 1 0 (2) 0To plot velocity vectors, we simply pick an (x,y) point, calculate u and v from Eq. 2, and plot an arrow with its tail at (x,y), and its tip at (x+Su,y+Sv) where S is some scale factor for the vector plot. For the vector plot shown in Fig. 1, we chose S = 0. 2, and plot velocity vectors at several locations in the first quadrant. 1 2 3 4 5 x FIGURE 1 Velocity vectors for the given velocity field. The scale is shown by the top arrow. Discussion The flow appears to be a counterclockwise turning flow in the upper right quadrant. 4-35 Solution For a given velocity field we are to generate an acceleration vector plot in the first quadrant.Assumptions 1 The flow is steady. 2 The flow is two-dimensional in the x-y plane. Analysis The velocity field is given by V = ( u , v ) = ( 0. 5 + 1. 2 x ) i + ( ? 2. 0 ? 1. 2 y ) j (1) At any point (x,y) in the flow field, the velocity components u and v are obtained from Eq. 1, Velocity components: u = 0. 5 + 1. 2 x v = ? 2. 0 ? 1. 2 y Scale: (2) 6 The acceleration field is obtained from its definition (the material acceleration), Acceleration components: ?u ?u ?u ?u ax = +u +v +w = 0 + ( 0. 5 + 1. 2 x )(1. 2 ) + 0 + 0 ?t ?x ?y ?z ?v ?v ?v ?v ay = + u + v + w = 0 + 0 + ( ? 2. 0 ? 1. 2 y )( ? 1. 2 ) +0 t ?x ?y ?z 5 4 y 3 2 (3) 1 0 0 where the unsteady terms are zero since this is a steady flow, and the terms with w are zero since the flow is two-dimensional. Eq. 3 simplifies to Acceleration components: ax = 0. 6 + 1. 44 x a y = 2. 4 + 1. 44 y 10 m/s2 (4) 1 2 3 4 5 x FIGURE 1 Acceleration vectors for the velocity field. The scale is shown by the top arrow. To plot the acceleration vectors, we simply pick an (x,y) point, calculate ax and ay from Eq. 4, and plot an arrow with its tail at (x,y), and its tip at (x+Sax,y+Say) where S is some scale factor for the vector plot. For the vector plot shown in Fig. , we chose S = 0. 15, and plot acceleration vectors at several locations in the first quadrant. Discussion Since the flow is a counterclockwise turning flow in the upper right quadrant, the acceleration vectors point to the upper right (centripetal acceleration). 4-14 PROPRIETARY MATERIAL.  © 2006 The McGraw-Hill C ompanies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-36 For the given velocity field, the location(s) of stagnation point(s) are to be determined.Several velocity Solution vectors are to be sketched and the velocity field is to be described. Assumptions 1 The flow is steady and incompressible. 2 The flow is two-dimensional, implying no z-component of velocity and no variation of u or v with z. Analysis (a) The velocity field is Scale: V = ( u , v ) = (1 + 2. 5 x + y ) i + ( ? 0. 5 ? 1. 5 x ? 2. 5 y ) j (1) 5 Since V is a vector, all its components must equal zero in order for V itself to be zero. Setting each component of Eq. 1 to zero, Simultaneous equations: x = -0. 421 m 4 3 u = 1 + 2. 5 x + y = 0 v = ? 0. 5 ? 1. 5 x ? 2. y = 0 y 2 We can easily solve this set of two equations and two unknowns simultaneously. Yes, there is one s tagnation point, and it is located at Stagnation point: 10 m/s y = 0. 0526 m 1 0 (b) The x and y components of velocity are calculated from Eq. 1 for several (x,y) locations in the specified range. For example, at the point (x = 2 m, y = 3 m), u = 9. 00 m/s and v = -11 m/s. The magnitude of velocity (the speed) at that point is 14. 21 m/s. At this and at an array of other locations, the velocity vector is constructed from its two components, the results of which are shown in Fig. . The flow can be described as a counterclockwise turning, accelerating flow from the upper left to the lower right. The stagnation point of Part (a) does not lie in the upper right quadrant, and therefore does not appear on the sketch. -1 0 1 2 3 4 5 x FIGURE 1 Velocity vectors in the upper right quadrant for the given velocity field. Discussion The stagnation point location is given to three significant digits. It will be verified in Chap. 9 that this flow field is physically valid because it satisfies th e differential equation for conservation of mass. 4-15 PROPRIETARY MATERIAL. 2006 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. Chapter 4 Fluid Kinematics 4-37 For the given velocity field, the material acceleration is to be calculated at a particular point and plotted at Solution several locations in the upper right quadrant. Assumptions 1 The flow is steady and incompressible. 2 The flow is two-dimensional, implying no z-component of velocity and no variation of u or v with z. Analysis (a) The velocity field isV = ( u , v ) = (1 + 2. 5 x + y ) i + ( ? 0. 5 ? 1. 5 x ? 2. 5 y ) j (1) Using the velocity field of Eq. 1 and the equation for material acceleration in Cartesian coordinates, we write expressions for the two non-zero components of the acceleration vector: ax = ?u ?u +u ?t ?x +v ?u ?y +w ?u ?z Scale: = 0 + (1 + 2. 5 x + y )( 2. 5 ) + ( ? 0. 5 ? 1. 5 x ? 2. 5 y )(1) + 0 10 m/s2 5 4 and ay = ?v ?v +u ?t ?x +v ?v ?y +w ?v ?z = 0 + (1 + 2. 5 x + y )( ? 1. 5 ) + ( ? 0. 5 ? 1. 5 x ? 2. 5 y )( ? 2. 5 ) + 0 3 y 2 1 At (x = 2 m, y = 3 m), ax = 11. 5 m/s2 and ay = 14. 0 m/s2. b) The above equations are applied to an array of x and y values in the upper right quadrant, and the acceleration vectors are plotted in Fig. 1. Discussion The acceleration vectors plotted in Fig. 1 point to the upper right, increasing in magnitude away from the origin. This agrees qualitatively with the velocity vectors of Fig. 1 of the previous problem; namely, fluid particles are accelerated to the right and are turned in the counterclockwise direction due to centripetal acceleration towards the upper right. Note that the acceleration field is non-zero, even though the flow is steady. 0 -1 0 1 2 3 4 5 x

Marketing strategies of the mass-market chocolate industry Essay

This report is an evaluation of the marketing strategies used in the mass-market chocolate confection industry in the United Kingdom (UK). The four brands this report studies in detail are Cadbury, Galaxy, Kit Kat, and Maltesers. The UK mass-marker chocolate confectionary market is the biggest in the European Union and sales are heavily reliant on a solid marketing strategy. Using the four brands mentioned above this report investigated the following, segmentation, targeting and positioning, consumer buyer behaviour, promotion, pricing, product, and placement, social media strategies, and communication strategy. Finally, this report gives critiques on the effectiveness of the marketing strategy for the four selected brands and recommendations on how they might improve. Of the four brands studied, only Galaxy uses demographic segmentation by focusing on women but all four use behavioural segmentation by focusing on benefits sought from eating chocolate. Cadbury targets creative individuals, galaxy targets the indulgent types, Kit Kat targets tired employees, and Maltesers targets those in search of guilt free chocolate. Cadbury positions itself as a creative brand, galaxy as a treat, Kit Kat as a break bar, and Maltesers as the lighter way to enjoy chocolate Chocolate is an impulse good and need recognition is usually stimulated upon seeing the packaging, where as information search is usually omitted or happens very quickly. When it comes to evaluating alternatives consumers, positioning and brand personality come into play. Finally, the choice to buy or not to buy happens very quickly. Cadbury was the only brand found stay in contact with consumers post-purchase by sharing recipes that one could make with Cadbury products. Each of the four brands use adverts, sales promotion, sponsorship, and social media to increase brand awareness. However, no promotional material gives information about pricing because retail outlets set their own prices. Most mass-market chocolate bars are around the same price and can be found near tills at retail supermarket outlets as well as off-license stores across the nation. All four brands are connected to their consumers via social networks, with the exception of Galaxy and Maltesers who do not have twitter accounts. Each brand uses social networks to reinforce their positioning strategy. Cadbury uses it to encourage creativity and audience participation, Galaxy uses it to remind women of the irresistibility of chocolate, Kit Kat uses it to remind its fans to take a break, and Maltesers uses it to celebrate is 75th birthday. This report concludes by recommending that Cadbury should identify a clear branding message because currently its adverts are always open to interpretation. Galaxy should stay in touch with customers post-purchase with recipes for irresistible chocolate desserts. Kit Kat should continue having a strong focus for all communication material and Maltesers should communicate its original message, a lighter way to enjoy chocolate, more explicitly.

Muenster Pump Case Analysis Essay - 908 Words

Muenster Pump Case Analysis I. Major Facts Related to the Muenster Pump Case A. The company has cast its own pump housings for over 40 years. A competitor is now offering a cheaper alternative should Muenster choose to outsource pump housings. Terri, Purchasing Manager for Muenster, has learned that Union’s quote of $90 is one half the price it takes Muenster to manufacture their own pump housings. She’s proposed outsourcing but met with resistance on multiple grounds. B. The ownership is against outsourcing based on: a. Muenster controls the production, quality and quantity. b. Muenster’s reputation and name directly tied to product created in-house. c. Should the foundry close due to outsourcing, 16 employees would be†¦show more content†¦B. Plan B – Outsource to Union, Form an Alliance a. Overcome management’s resistance by preparing and presenting a strategic plan for an alliance between Muenster and Union. b. Choose a cross-functional team, including individuals from finance, legal, operations, production, purchasing, and other vested interest parties, to work with Union representatives on the strategic alliance. c. The alliance will share technological developments, innovations in RD, define the responsibilities and limitations of each company as required for quality, quantity and production schedules, reduce risks, lessen costs and forge a long-term relationship of trust. d. This is a more time-intensive alternative and perhaps not feasible due to the old-school environment of Muenster, but it could possibly be the best alternative to keep Muenster Pump competitive in the market. C. Plan B – Trial Period - Outsource some; Keep some production in-house. a. Based on the developments in casting used by Union, opt to test their worth by outsourcing a small percentage of castings for a trial period. b. Based on the information of new developments and substantially lower costs, secure upper management’s blessing and create a cross-functional team (upper management, production, finance, operations, etc) to outsource the minimal number of pump housings from Union. Follow-up with intensive quality