As you know, ethics has been one of the central theme or one of the branches of philosophy. So, today in my lecture, I would be discussing mostly on the Philosophical Foundation for Environmental Ethics. Now, when we look at ethical issues, what is that now takes us to discourse on environmental studies. That is the central theme of our talk today. So, before we begin our discussion, we need to know what is ethics. Ethics as you all know is about the theory of morals and every human endeavor tries to look at the other aspect of the world or the other members in the society and theorize them. So, the theoretical aspects of philosophical discourse on ethics, something which we are going to discuss in the beginning of today's lecture. And I am sure you would like it in the sense that it will invite a lot of questions and during our discussion, we will have a fruitful discussion. So, that is what is expected from this course. Now, when I say that ethics is about the theory of morals, morals refer to custom, conduct, activities that are looked upon as good, bad, right, wrong, correct, incorrect. So, mostly whenever we talk about our activities, our actions and it is inevitable that we will perform various kinds of actions and we will be engaged in doing things. So, this whole interactive process of human life needs to be evaluated and ethics plays a role there to support us in evaluating our deeds, our actions. And therefore, ethics talks about right and wrong, correct or incorrect, right action, wrong action, correct action or incorrect action. So, we do praise an action saying that it is good or bad. So, the ethics is all about the study of morals in this sense that our actions are being evaluated and it has been consistently evaluated so that we live a meaningful life. So, far as the meaningfulness of life is concerned, we need to understand the theoretical underpinnings of this debate on ethics in general and environmental ethics in particular because our discussion should link to the debate on environmental issues. So, in that context we need to see how ethical principles are operating in our society and how these principles are being conformed by various institutions that regulate our activities. So, therefore, it is important that how values are guiding principles of human actions and how do they regulate human actions. Being the guiding principles, they have the power to regulate human actions. In that context, we need to understand the notion of ethics, the notion of values, etc. So, as I said that it is all about human activities, human conduct and human judgment. So, whenever we are performing any action, we need to judge. So, this capacity to judge, the capacity to digest certain things pertains to the discourse of ethics. So, human beings per se has this ability to perform not only actions, but ability to perform valued actions. So, and this is indeed or is total says is a rational ability. Now, we need to understand how does human rationality has made an important role in understanding nature, in understanding human environment, etc. Is there a flow in that understanding? Is there a lecuna in that understanding? Because that is important unless we are very self-critical about our everyday engagement with the world, we will not be able to create a new ideas, new value system or new principles, which will be the guiding source of guiding source. So, it is in that context, we need to talk about how human ability, rationality as a human ability plays a very important role in formulating moral principles, not only at an individual level, but also at a collective level. So, and we will come back to that discourse on human rationality little later on. So, when I talk about the theorization of morals, I do give importance to this idea that certain values are to be practiced, certain values do exist. It is about the existence of values, it is about the practicing the values and it is about the preservation of values. So, how do we preserve certain values? Because values we practice find at every societal context, values are do practiced, but at a higher realm of this discourse, we need to talk about how values remain as one of the guiding principle as I suggested earlier. So, therefore, preservation of values is important and values can be only preserved if and only if we give importance to these institutions are not only the regulatory bodies, but these institutions are being created to maintain values. So, that is what I mean when I talk about existence of values, practice of values and preservation of values for the future. So, it is in that context we need to talk about values. Why there is a need to talk about values? We understand that our whole engagement is value centric, but what is the need of talking about values? What is the need of talking about or theorizing morals? Now, the need is basically this as Anna Petition writes, I quote Anna Petition's words in the beginning of his very famous book on everyday ethics and social change, she writes that we all live in a difficult time. We face social and environmental problems that are massive in scope for which effective solutions are elusive at best. These problems are well symbolized by global warming which threatens non-human spaces, unique ecosystems and human communities equally. Now, if you look at this writer, this quotation, one understands that global warming is one of the central issues that environmental studies deals with or climate change is one of the central issues that environmental studies deals with. Pollution, soil erosion, etc will be equally an important topic of our discussion on environmental ethics. But it is also depressing that whenever we talk about the future generation, whenever we talk about the future of humanity, these questions makes us very depressed because we do not have a hope for future. The future looks like a kind of a blank sheet because we do not know what it will lead to. So, it is in that context, the whole idea of hope for living, living a meaningful life as I mentioned earlier is coming to stop. So, it is in that context we need to discuss that why ethics are important, why do we need ethics. So, therefore, Petition says that there are several things in our social life which are very depressing, which are making human living hopeless. And similarly, there are several things at the realm of environment, one finds very depressing.  Now, the question is what does ethics do? Now, ethics tries to, as I said, tries to talk about values, try to theorize values, what is good, what is bad, what is right, what is wrong, what is correct, what is incorrect, what is to be condemned, what is to be praised. So, all these become part of our ethical studies. But then when we talk about ethics or values as a guiding principle, we also need to look at that whether there is any evidence to justify our moral claims. Is there any evidence to justify my judgment? Is there any evidence to justify the decision that I take or the act that I perform? So, therefore, it is important to look for a justification. So, the whole idea that human beings are capable of formulating judgment, the whole idea that human beings are capable of making enlightened choice very informed argument in various platforms implies that they have justification to support their actions or their choices. So, therefore, we always look for a justificatory reason. So, therefore, at the same time we try to be critical about it. So, a critical evaluation and a reevaluation becomes part of this rational discourse of value formulation, value redesigning, reformulation etc. So, therefore, in every society one finds that there is an up and downs. There is a kind of a movement from traditional society to modern society as we find nowadays that this whole idea of a post-modern society becoming more relevant to various theoretical understanding of the world. So, therefore, it is important that how such progress is maintained in our theoretical discourse in our understanding of the world. So, we also need to initiate this question here that how such progress can be made when we talk about environment as our subject. Environment is a kind of a subject of our study. So, therefore, our scope of morality has to be enlarged, has to be enhanced so that we can accommodate, we can include various entities that are not only living entities, but are also non-living entities which are precious for human living. And where we talk about sustainable development in the context of social sciences, in the context of economics, we also try to see that how such an engagement will be a value-related engagement. So, therefore, we need to broaden our discourse on morality because morality is not all about human engagement with other human beings. It also is an engagement with various biotic beings and various entities that are living, that are existing in and around us. So, therefore, we need to talk about what kind of duties, what are our obligations and what kind of virtue we need to maintain in our everyday life so that this meaningful living is possible. So, it is in this context I have quoted Light and Ralston who writes, I think extends all our duties, obligations, virtues and the vices as we interact with each other. See, this interaction, I will come back to this idea of interaction, as the interaction seems to me is a very technical term. So, we do interact with our fellow beings.  So, that is the question which we need to address because we all know that living things are important for us. We all know that there are species which are in extinct day by day and they are important for us, but how deep is this understanding? That is the question which environmental ethics raises in the context of deep ecology which we will be discussing tomorrow. But I emphasize on this idea of interaction or engagement which has to be ethical, which has to be deep enough to understand the value of the other. Unless we reflect on this, unless we are sensitive enough, reflect on this, we will fail to recognize the value of other. It will not be a logical failure, it will be a moral failure. So, there are two kinds of failures which you all know that sometimes when we are doing some calculation, we fail to calculate and we do not get a result. That would be a kind of a logical failure because either you are wrong in adding something or subtracting something, but when we perform a wrong action, when we are committed to something, but we do not show our commitment, we do not show our obligation to those facts. So, it is in that context, our failures are indeed moral failures. So, to live a meaningful life, one has to re-enchant what kind of personality he is. One has to re-enchant his own self. Unless until we re-enchant our own self, we will not be able to understand what we are. So, one of the questions that I will be discussing today in the second part of my lecture is the question about what we are. It is precisely because this question will help us renewing or help us in searching an answers to this idea that further whatever action that we perform in our everyday life is something significant. So, unless such a renewal is welcomed, unless such a renewal is initiated at an individual level, ethics has no meaning. Particularly, the kind of ethics that we will be discussing today has no meaning. So, therefore, it is very, the urge here is that we need to initiate certain sensitive outlook and therefore, to do that we need to renew our self. We need to revisit our self and see whether our understanding has been a correct understanding, whether our understanding has any significance at all for the society. So, it is this kind of thing that I need to look at along with you and I hope that you will have some understanding of ethics. Now, as I said in the beginning of my lecture, ethics is all about theorizing morals. It deals with the study of human action and it regulates human conduct and it helps us performing better actions. It rescues us from committing certain moral failures. So, if ethics is all about that, there are several parts in ethics. One idea is that there is a general study about ethics in the form of goodness, where we talk about what is good and how the concept of good is been generally formulated, etc., etc. And we have another kind of a discussion where we talk about study of right action. But we are not really interested today to discuss all about that. We are rather interested to talk about applied ethics and environmental studies particularly environmental ethics deals with applied ethics or is a part of applied ethics. So, it is in that context. Now, let us have a brief discussion on this point that what is general study of this notion of goodness that we talk about. When we talk about goodness, we do initiate a question, what are the components of good life. I was talking about what is meaningful about life. So, I was rather interested and that 21st century is interested in initiating this debate that whether the life that we are living is meaningful life. And you may recollect, some of you may recollect when you had come here for the training program, we were talking about Socrates. Socrates is one of the very famous slogan that an examined life is worth living. In other words, an unexamined life is not worth living. This is what Socrates had said, an unexamined life is not worth living. So, one can revisit this Socrates debate on a meaningfulness of life. And this revisiting possibly we will do in our course of studies that how meaningful it is to talk about environment. And how does environment affects us and how we are being affected by the crisis that the environment is facing today. So, is this crisis harming our meaningful living is something that is very important. In that context, one can think of how meaningful the life is. One can also think of various things that what are the classical sources of ethics. I have pointed out the three major points. One is about the religious ethics. All traditional society or we will talk about religion as a source of morals. There are also debates about duty-based ethics which has been initiated by Kant. And there are there are a number of people who have related this Kantian notion of ethics. You have heard of Immanuel Kant, the name of Immanuel Kant, whose idea is about that duty for duty sake, not duty for deity sake. A religious understanding of ethics will promote the idea that whatever duty that we perform, it is for deity sake, not for duty sake. So, there is a difference which Kant is making. And many people, many philosophers have tried to relate the Kant's understanding of values with the Bhagavad Gita's understanding of values, particularly the notion of niskam karma. Now, how an action has to be performed without contemplating on its consequence? So, action has to be performed or duty has to be performed for duty sake. So, that is what is the geontological ethics all about. Now, the consequentialists on the other hand are utilitarians. So, they give importance to the consequence. Now, in ethics, one very interesting concept is this that there is, now the whole idea is about means and end. Now, the consequentialists give importance to the notion of end and becomes their primary goal, whereas the geontologists who argue that if the means is good, then the end will be good. So, that is the basic difference between the geontologist and consequentialist. The consequentialist, we suppose that if something is good, then it should be good for large number of people or the maximum happiness for maximum number of people. So, this is what is their slogan. So, they try to quantify the notion of goodness. So, it is in that context. Now, this means and end relationship are something relevant here, because every as I said that whenever we perform an action, we try to see that there is an evidence to it and this evidence is nothing but a kind of a just. So, the whole idea is that whenever we to perform any action, we look for some justificatory reason. Now, so therefore, our the reason plays two roles here. One is the role every individual is rational, that is one kind of reason, which is called theoretical reason. Then the second type of reason is practical reason. So, the second kind of reason is called practical reason. There is a theoretical reason and another one is practical reason. And theoretical reason is that every individual human being is a rational being. That is the theoretical pre-supposition. The practical reason is that that every action is performed with some reason in mind keeping some reason in mind. So, that reason is a reason which makes our action valid action. That reason is something which makes our action moral action good, bad, right, wrong, correct, incorrect. So, there is a practical reason which plays an important role and this practical reason prepares a kind of a means that why I should perform action. Now, what kind of benefit it will give me if I perform action? Will that be beneficial for my colleagues? Will that be beneficial for my students? Will that be beneficial for the entire community which living in a campus or the entire society which is a part of mind? So, this extension, the scope can be enlarged. So, the whole idea is that what kind of means that an individual adopts to perform action and that means is very important and that is the part of the practical reason. So, when we talk about values or curation of values it is important that we make a distinction between means and the end. The idea here is that there are several kinds of ethical theories where the first could be a religion and or the theories are like deontological theory. There are also schools who believes in emotive theory but I have not discussed all that. I am planning my plan is to give a kind of a general account of ethics and how does environmental ethics fit into that discourse that is the whole agenda here today and the other one is the utilitarian ethics which we will go back to the kind of utilitarian studies maybe tomorrow. So, environmental ethics as I mentioned to you that is an applied ethics. Now, what is an applied ethics? Applied ethics is that where we ethical principles include particular area of concern such as environment, medicine, engineering, business, biotechnology etcetera. So, the scope of moral discourse is very limited when we talk about a specific notion of values and value engagement. So, environmental ethics is an applied ethics or is part of an applied ethics. So, we need to study, we need to understand that environmental ethics as an applied ethics. So, who counts morally? We said that our whole engagement has to be a meaningful engagement. Our whole engagement is will be meaningful if and only if we reexamine ourselves, we try to relook at certain relations interactions which we have been you know engaged with. So, therefore, the question is that who counts morally and why do we if at all we count morally then why do we count morally? Morally about our engagement with endangered spaces or our engagement with or our interaction with at this whole activities called a deep frustration which has been going on or the pollution whether it is water pollution or air pollution or the loss of biodiversity, loss of soil etcetera. So, these activities or these events if we encounter in our everyday life how we are being affected by those events or what kind of approach, what kind of ethical relation we have when we encounter such things. So, therefore, environmental ethics if I sum up this whole idea that and the whole environmental ethics is going to reexamine human nature relationship. The idea is we want to reexamine this whole engagement between the human on the one side and the non-humans or the environment on the other side. So, or the nature as a whole on the other side. So, this is what is about environmental ethics. Can we have some questions? Is it clear to all of you? I can take up one or two questions here. Is there any doubt? Good afternoon sir. Good afternoon. So, you are talking about environmental ethics. Yes. And you talked something about Nishkama Yoga in Gita. Yes. And means I just really want to appreciate the effort that you put in this lecture sir, but I have a small doubt that you talked about the reason. I mean what is the motive behind a particular action? Yes. So, that decides the what do you say whether the action is good or bad. Yes. Sir, can you put some what means can you please explain that in some broader concept? Yes. This whole idea about action being good or bad. Now, when we judge a particular action, we try to judge it keeping a standard in mind. Now, who decides that standard? Does the individual himself the performer himself decide the standard? If yes, then the source is the self itself. So, in that context, I asked my concerns or I look at my individual rational ability to judge a particular action or to justify why I have done it. But if the source the standard the source of the standard is some religion, let us say.  So, in that context, the religion decides what is good and bad. Human reason, you know is submissive. Human reason does not play much role there. But if you talk about say that the social principles, the moral principles, the standards are been socially formulated or collectively formulated, meaning thereby that the whole principles are formulated by one particular community. Then that is that becomes the source. It is in that context. Is that clear? Yes. So, I just wanted to one thing why this problem of ethics is more coming from last 30-40 years, the time we had more we have more urbanization in India. So, why this is that? We are living with the nature in harmony with the nature since long. What had happened over the period of time in just 30-40 years? Just kindly throw some light on that. Yes, yes. You were right. Now, this whole, you know, if you if you read Blackwell anthology on environmental ethics says that environmental ethics as a discipline, the theoretical discipline is started from last 30 years. You were right. Now, last 30 years there are visible effects in our society. The visible effect in terms of if you look at the kind of diseases that humanity is encountering, the visible effects in the form of climate that we experience in our everyday life either in the form of global warming or in the form of pollution, which is again related to disease. And then there is a kind of an alarm situation. We need to respond to that. The question is human humanity has always you know felt that they are responsible for the things that are happening in and around them. So, this whole idea is to develop certain mechanism ethics. We will talk about certain to develop certain normative mechanism rather so that we do not encounter the kind of problem that we are encountering today. So, today if we are talking about environmental ethics or if our concern has becoming double it is not only for ourselves but also for our future generation that what kind of society we are you know or we will be giving to our future community or future generation. So, that has become you know a major concern for us and ethic helps us or guides us in preparing a kind of an normative framework in which we all not only conduct ourselves but also help in developing or a kind of a good society which will or good environment which will be good for the future generation. So, it is in that context ethics is important today. Thank you sir. Yeah, welcome. Is there any ethics in context to the pollution control of air and water or code of conduct to reduce the pollution? See at present I am talking about what is ethics, how these standards are being made. Now, if you look at that then the whole idea is to stop polluting water to stop or restricting the air pollution etc. But the kind of society in which we are we all live does not allow us to do that is not it because the form of life that we have adopted is not allowing us to stop. So, for example, I keep on using my bike the industry keep on you know plumping waste to the river etc. Because we need to develop certain mechanisms, we need to develop certain similarly a normative mechanisms so that we restrict the kind of actions that we are habituated to perform. So, I am not saying that you stop it today and that is how things will be stopped. No and it is in that context people are talking about the whole academia is talking about sustainable development. So, we need to develop some kind of a mechanism some kind of a golden means so that everything is possible within our rational meaningful legal. I hope it is clear. One more question is there sir though we are following our ethics, but others are not following the ethics. In this situation what should be the our action? Now, you are being ethical and others are your colleagues are not ethical. You can always suggest them to become you know ethical persons. You can always influence them people will follow. See once look at Gandhi. Gandhi was so influential because he was a performer he was performing action. Ethics today in 21st century is not about ideas. Ethics is about action. Now the situation is such that people are really admiring those performer who are performing it in their everyday life. Suppose I am being ethical then automatically the surroundings in which I leave people will be influenced that yes he is ethical. If I can influence at least one person is that not enough? If we think about country to country the ethics of India, ethics of China and ethics of America like that but in this contest Indian psychology will be different, Indian physiology will be different, China is different. In that constant if we see towards the environment then how it is possible to maintain all the peoples in a single contest. No no we so far as environment is concerned we cannot subscribe to any relative models. So for example it is their ethics or it is China's ethics it is American ethics it is Indian kind of ethical model okay. We cannot really subscribe to that kind of methodology or framework whether what we can do and what is ought to be done here is this that we need to prepare a kind of a universal model because environmental crisis is affecting everyone.  Look at the Indians who are living in America because today you are a global citizen you are no more a citizen of this country alone. You are somehow economically, academically no related to a citizen to some other country is not it. If you develop a good paper will it not be read by Americans or Chinese? Of course it will be read it is not it. So we are all global citizens today and therefore we need to improve ourselves in a global model and it is in that context look at our search of earth mission. How meaningful it is can we say that our psychology is like this we should not improve our psychology we ought to improve our psychology otherwise we will be victim of several diseases that will affect our life is not it directly or indirectly the problem is we when we throw darts we do not care for it this is not mine this is not my job to do it it is somebody else but when my own son or daughter is affected or when my neighbor is being affected when my student is been affected then oh this is wrong don't we say that. So that kind of ethical sensitivity need to be cultivated among ourselves so that we live up to the 21st century demands is not it. So we are global citizens we are no more a citizen of this nation only. Yes sir thank you sir. Welcome yes sir. Good afternoon sir. Good afternoon. My question is what is metaethics and how it is applied in EIS study environmental impact study. No no no as I told you that there are several parts in ethics one branch is metaethics another branch could be moral psychology another branch could be what is good life. So there are several branches in ethics environmental ethics is part of applied ethics not metaethics. So now let me clarify what is metaethics since you have initiated this question it is important maybe for somebody else and yourself that metaethics is when we talk about ethical principles and existing ethical principle. Now those existing ethical principles need to be explained through certain logical presuppositions okay otherwise we cannot explain any ethical principles. So the presupposed normative principles is something to do with our metaethics and our human theoretical reason helps us explain metaethics but environmental ethics is part of applied ethics not metaethics. Sir my question is who is major theory of environmental ethics tells that the environmental deserves a kind of direct moral consideration that is merely derived from human interest. Yes now we will be discussing I gave a general account of ethics. Now in my next slot I will go back to this idea of a anthropocentric approach and non-anthropocentric approach the anthropocentric approach has been damaging the environmental concerns. So therefore the 21st century people are more concerned to develop a new ethics called life-centric ethics that will be helpful to understand environmental problems more clearly and significantly. This will be last question then we will go to our next you know part of the lecture. A reporter was banned alive in UP while they were reporting on wet filling of land. Okay. So in this what is the importance of studying ethics and ethical value of Indian people because we know most of our politicians and others are corrupted. Many of them has communal cases against them. Okay. Almost 40 percent when the parliament has communal cases against them. So how we educate our next generation about ethical value? How can we? Is it only a classroom activity or is it does it have any real practical implication on it? Of course it has you know I think we should I will take up this question and then we can go back to our previous sections where now I would I would like to suggest this that corruption has been part of human society since long. Okay. And there are several kinds of corruption. One very important aspect of corruption is the moral corruption. When people try to think you know below the standards the below the the ethical values then they try to corrupt the society. So societal values deteriorate starts deteriorating when individual himself does not follow it in the everyday life. This is one thing. Now to make a general statement that our politicians are corrupt and we are not it is it is not always true. We are equally corrupt in many realms. Okay.  Say for example now I should not beat my children. Okay. Let us take this as a kind of a moral statement that it is not advisable to harm now physically you know the children's but I do beat sometimes when I am angry. Is that not a moral corruption? So corruption happens at various realms of individual thinking. One possibly which is more visible in a the outer world is the the political corruption which were but there are several realms in which corruption happens. So we need to restrict ourselves and therefore my basic urge was that we need to renew our own self. So this kind of a renewal will bring back our original self the benign self which is a responsible self which is a committed self which is a moral self after all and once we are capable of you know uncovering that self I do not think in a society or in a family there will be any such trouble. There will be no chaos in any society in any institutions once capable enough rationally to restrict their corrupting attitudes. Thank you. Rafa Khan sir. Yes sir. Sir my question to you is related to sustainable development. Whatever we have learned for last two weeks regarding the sustainable development in economics has been an important part of that. Of course. And today's after your wonderful session I will say ethics without ethics we could not dream of a sustainable development. Thank you. And what we personally feel is that ethics economics and sustainable development these three things are merely opposing each other. So how we could make a perfect balance and we could have a dream sustainable development. Yes the question will be like this how we can redefine our approach so that we live not only a sustainable life but our values will sustain for long values will sustain for not only for all future generation to come. I think that would be you know the question. Now if that is the question then the we need to reform ourselves first. We need to know what we want because for last say 100 years or so people have accepted a kind of a life where there are mass consumption where there are you know a massive kind of a you know as an effect of mass consumption you have generated a waste and we do not know how to dispose the waste. We don't know but slowly if you look at for last several years 30 40 years people have started you know contemplating on renewal energy people have started contemplating on how to reuse waste etc etc. So there is a sense of development. There is a sense of good development rather happening in our economic modern and it is also due to the fact that our whole engagement with the society has changed. So that economics is only one reflection now when somebody else was talking about a political corruption. Now today look at it is not that corruption is happening today there were societies which were you know which have encountered rampant corruptions but if you take the statistics corruption has been restricted been you know to some extent and it is possible to restrict it. It is possible because we look for an alternative model we look for a more developed society so that we live a better life. So it is in that context our alternative outlook is something for future generation again is something praise over the and since we and humanity always like to develop think of a society which has not aspired for development. Development in all prospective not only economic prospective but in all perspectives I think is that clear. Yes sir thank you very much sir. Thank you let us go back to our lecture. So let us come back to our discussion on environmental ethics as an applied ethics. Many people have had a misunderstanding that it is about metaethics no it is not about metaethics it is an applied ethics where certain rules and standards are applied to limited areas of research or problematic areas like environment like the use of medicine like our engineering activities business activities etc etc. So when we restrict our scope we scope of ethical engagement we talk about applied ethics. So it is so our concern here is environment and how meaningfully we can engage ourselves with the environment and this meaningful engagement will help us enlightening about our approach towards the environment. So it is in that context I was talking about environmental ethics as an applied ethics. Now this re-examination is basically the re-examination between the nature and human engagement is basically to talk about how this problem further pollution loss of biodiversity etc. Figure in disciplinary approach because we are all academicians we try to understand the society we try to understand the world in a particular way. So therefore academic understanding a disciplinary approach is necessary otherwise you ask any common man they know that yes I am polluting everyday when I take my bike out when I take my car out I am contributing to that pollution but that is not the question which and the pollution is something wrong that is a you know yes or no question but when we are engaged in academic activities our approach is little different we try to understand theoretically how good it is to study environment and what kind of philosophical foundation that is necessary to talk about a proper environmental ethics or where have we gone wrong in talking about ethics because the kind of problem that we encounter today we find that yes something is wrong then where we have gone wrong in understanding reality. So therefore environmental ethics as I said is a branch of ultimately branch of philosophy and we need to look at how what kind of philosophy is necessary to understand environment meaningfully. So therefore our understanding is about the human non-human and the nature for all in danger it is not that environment is a concept which we are trying to understand we in the environment we also figure the human does figure within and the realm of the environment so and the non-human of course non-human also is part of that so environment is a very you know if you define environment it is very large the scope is really large and how our life is been threatened how we as a community okay because when I say that it is not harmful to human beings therefore we will do it now that kind of approach has not been very successful it in fact it has failed it has shown that where we have morally gone wrong. So therefore environmental crisis today is a threat to the entire community it is not that human humanity alone is experiencing the crisis the non-human do experience the crisis and so also the nature who speaks to us in different language. So therefore the environmental ethics has to change its language in order to speak to the people in order to speak to in order not to communicate the real issues of environment. So environmental crisis is a threat to the entire community it does not leave one community and embraces other actually it embraces all of us together. So therefore the practical approach will to know resources to which need to conservation or creation of national park or ecological movements have been very very significant in this regard. Now how ethics has been studied how values are carried by nature could best be described often asking whether nature is morally considerable in itself rather than only indirectly morally considerable. See so far we have treated the environment or the nature as a whole as something outside us something which does not include us this consideration has been the reason for our moral failures. So therefore we need to revisit us we need to prepare a ground so that we not only protect ourselves we know we protect our own well-being the human well-being and also protect the non-human non-humans which are living within an around you know this environment. So the whole issue of moral foundation has to be changed the whole concept of moral foundation has to be changed in order to prepare a kind of environmental norms or in order to control pollution we in order to save the end endangered spaces we need to revamp the whole foundation of morals that has been you know accepted as something relevant. So it is in that context I will bring this concept of anthropocentrism in a anthropocentric world view where humans are considered as morally only morally significant and everything in the universe everything in the nature are only for human use. So that kind of approach that kind of moral foundation has created this crisis okay we will go into it in details after some time. So my basic idea here is that the change of moral foundation will not only protect the end endangered species but also will help us seeing or envisioning a kind of a new world where we will find that everything is everything will be better than the existing one. So there you know to to have a better outlook about the better world we need to see this concept of environment in in two ways scientifically we have been looking at it environment as an objective phenomenon that something a particular river say Ganga has been polluted and that affects people who are living in its surrounding okay. So so there is a kind of a causal relation in which we all live with our environment. When we have this kind of understanding we treat environment as a kind of an objective phenomenon okay because environment is real environmental issues are real and environment affects us you know this kind of interaction this kind of engagement has been very is a causal engagement but there is another mode of engagement which human lives you know which human lives in their everyday life where they treat environment as a field of significance. Now how human beings are living in that field is something very important if we would like to change the very foundation of morals morals of anthropocentric worldview then we I think we need to look at environment as a field of significance. Now this field doesn't believe in a causal relation alone I am not saying that we should give up this idea of a causal relation the scientific vision of understanding the reality I am not saying that I am saying that the scientific vision of understanding the environment or the reality as a whole must go along with the understanding of an intentional relationship with environment. So when I say environment as a field of significance human beings are intentionally connected with the environment say for example when somebody is dying the the reporter the as our fellow participants said the reporter is dying because of some reason. Now that has affected us that has been affecting us and this is an intentional effect because I am able to relate myself to that individual who has been doing his job well who has been committed to to his profession. So this is an intentional relation and I said that when we talk about and moral sensitivity if we try to uncover that real self I was talking about uncovering the real self the renewal of the self or the reenchantment of the self I was really keeping this in mind that we are all intentionally related people around me trees and objects around me are not only physically related but also intentionally related we have been really not taking into account this intentional relations. So environment as a field of significance talks about an intentional relation where the environment is intentional object. So this idea of one of the very famous philosopher David Cooper talks about it in his paper called the idea of environment. Cooper essay has been published in 1992 and there are critiques who have also talked about it but Cooper has been very important in this regard that he is bringing to us a new way of addressing environmental crisis. Now look at this example that I have been cited now our engagement a student who goes to school every day it is not about what he studies there and what kind of lesson he is learning that is part of his schooling activities but apart from that he is also associated and very deeply associated with the physical structure the physical environment of schooling the trees the plants the garden the playground etc and the walls of the classroom so there and that is very important and that creates a very binding relationship this intentional relationship that I was talking about which is relevant to human form of life and human form of you know valued living also incorporates this that how deeply we are and how intentionally we are connected to our physical surroundings after 10 years of schooling when I go back to my school I find that yes this is where I was sitting and this is the world of blackboard which you know our teacher used to write and we used to have fun writing something else so this is familiarity is something which brings the self you know to a physical reality and the physical reality is no more a physical object there it is it becomes an intentional object the object starts living in my experience and that is what is called a field an intentional field and that association that familiarity is something significant significant to construe what would be our normative relationship with the world in general or our surroundings in particular and this is what you know see in the in the beginning of my lecture today I refer to Anna Peterson's that how dangerous the life is and the kind of life that we are living now I bring back to another important statements of Peterson where he says that we know relations of love and solidarity even if these are fragile and fragmentary we know connectedness with other people and with members of other spaces we play freely and joyfully we feel satisfaction in taking care of those need us and being cared for now this is what a human being is now you cannot really as my fellow participant was on a pointing out now this is what this is how Indians leave this is how a Chinese my fellow Chinese leave and this is how my you know Americans leave now we cannot divide our society the humanity like this when it comes to ethical questions when it comes to our basic concern for life life as a whole we need to dream for a good society keeping this in mind that what kind of relationship we make with our fellow beings with our institutions and how what kind of solidarity we exhibit in our everyday life it may be fragmentary it may be temporary but we do create relations are we not creating relations every day do we not make friends and friendship is not a fragile bond it is not fragile precisely because if at all our interest is genuine we can keep sustaining it we can keep preserving it as we preserve values as we preserve our antique things now this is now you may be knowing suppose I have seen my grandfather sitting on the armchair I tried to see that armchair now is now after my grandfather's death I do not really see is an empty chair whenever I look at that chair I see that my grandfather is swinging there sitting relaxing and in a happy mode and that is what is you know renews myself in a better way so it does not make really it does not make an individual a fragile being rather it it actually consolidates our understanding about the world and we find that we are even if somebody is absent we connect ourselves to that so even if suppose you know I was given another example of the and the people who goes to the school in the example of a schooling life now even if you find that a particular tree is cut suppose the mango tree is cut is no more existing there we feel very sorry about it because we fail to connect we fail to connect so that failure is something you know creates a crisis in my life because I cannot really consolidate myself I cannot really gather myself in in in a holistic way so it is when we talk about an intentional field the field which helps me understanding a holistic world view the the field which really helps me needing all the beings together and create a kind of a world where the world in which I live the environment in which I live I care for it and when I start caring as my fellow friend was saying that I am only moral and others are not that is not true moment I start doing things rightly and I enjoy doing it and I care for it I also find that others have done it and we have n number of moral exemplars look at Gandhi look at Buddha look at Martin Luther King I mean how many examples you you will find many examples go back to the history now these exemplars the moral exemplars are the person who have shown us you know who have directed us in a better path okay so they have been successful in directing us because connected themselves with the other in our approach today in 21st century when we talk about globalization when we talk about a global economy we only emphasize that what is good for me what is valuable for me I me becomes the primary concern what I will gain out of it and this sense of individualism has in fact driven us in a wrong direction what Charles Taylor calls is a malaise is one of the malaise of 21st century that is individualism is a threat to better world we need to renew ourselves we need to connect ourselves to the world we need to connect ourselves to our neighborhood to our family members in such a way that we cherish a good life and once we start caring ourselves others will also look at us so so this is a kind of now an intentional relationship which we need to assert in our understanding of the environment so and living in an environment in in this connection is like living at home this is the famous phrase of Martin Heidegger one of the 20th century leading philosophers of the world who says that every species lives in his own world okay every person has his own world now when we start living in the world we do not it it gives a immense strength it gives an immense strength of connectedness okay where the individual spaces or an individual being knows how to live I mean one does not really consciously do any action unconsciously performs better action once I I take up that habit that speaking truth is something valuable then I start speaking truth consciously but eventually after few years I will be only you know speaking truth because I have started living in that world of truthfulness so this is what is very important and each species when starts living in an environment they live you know a carefree life they live they do not care what others think they do not really care how others value it because they live a valued life and that is very important I think that one has to keep that in mind that how relevant the kind of knowledge is and how practical it is to live an unreflective lifetime and create a sense of familiarity in our surroundings so this is I think you know is very important when I talk about non-human species for example now look at you all know that now the IIT Powai has a lake called Powai Lake is situated near a lake there are several kinds of species living there and they live freely they do not take into consideration whether we are living here or not like we all live freely we do not take into account whether somebody else is living there or not now this is something a very important way of relating and interacting with the environment we will reflect on it and my next episode of of this lecture called environment and ecological self so I as I told you that there are two ways of understanding the notion of environment one is looking at the subjective way the intentional mode in which we try to reform our attitude we try to develop new attitude or to try to cherish our you know moral attitude and the kind of feelings that we have for the beings or the entities which are around us and there is a causal relationship in which one is you know being engaged so there are two ways and the environmental ethics does not leave the causal way of understanding the environment rather this kind of ethics which I will be talking about is called the life-centric ethics it incorporates it involves the intentional the field significant which I was talking about now somebody pointed out can we have a universal ethical principles my response is yes and this is this is a better response actually this is a better response which gives by which is given by rollstone and light this is if we do not practice that universally then our approach will be only an anthropological survey and environmental ethics is not an anthropological survey it is not about any community not about any particular you know end dangered species rather it is about the end endangered species as a whole rather it is about the humanity as a whole and what kind of you know interaction or engagement the humanity will have with the world so so so it looks at the entire reality you know from a holistic perspective this much thank you


Boys and girls, today I have a fun game for us to play, and we are going to use some dice. And we will count the dots and we will decide how many turns we can take or how many numbers or we will look at the set of dots and we will count them and decide if there are more dots, less dots or the same. So let's just look at one of these and just look around at it. Okay, here we have how many dots? One. Let's see if we can find this one. How many? Two. And what's here? Four. Good. Now we did them in order, didn't we? One, two, three, four, five, six. Six is the largest set on there. In the game today, we're going to think about the words more, less and the same. Okay? And I've written them right up here on the board. This is more, this is less. The same. Same. Good. You could read those words. Excellent. So we're going to compare the sets of dots as we play the game. The game is going to go like this. I'm going to be playing against all of you. And so we're going to roll two dice and I'll look at mine and whoever's, which one of you is playing with me will look at yours. And I will say a sentence about mine. Let's, and let me give you an example of that. Let's just pretend that we roll them right here and I'm blue. So I rolled a five and let's say the person that was the student, like Ty, rolled a two. My sentence would be five is more than two. And Ty's sentence would be two is less than five. And then I will write that on the board. Now just so that we can make a game out of this, I'm going to see if I roll the dots that have more, more times than you do. And if at the end of ten rolls, and we'll count ten times that we do this, if I have more times that I roll more dots than you do, then I win. But if you have more times than you win, so that's how we'll play the game. And as they come on up, okay, we'll roll it on the floor, we'll say one, two, three roll, and then we'll pick it up and I'll say my sentence and then you say your number sentence and then we'll write it, okay? All right? All right, ready? One, two, three roll. Pick yours up and show your friends. Let's show them the number that you rolled. Okay, my sentence is two is less than six. Okay, what is your sentence? Six is more than two. Six is more than two, that's so true. Okay, so I'm going to write down, that's so true. So mine was two is less than six. Oh, remember, we forgot to show that this is less than, and this is the symbol for more than, and this is the same, that's that equal sign that Leo was talking about. Okay, so did I get more this time? No. No. I'm, this is, I'm going to underline, and you guys are always going to be in this row and you've got the first win. Okay, Shelby, come on up. Thank you, Claire, for sitting right down. One, two, three, roll. Oh my goodness, I have a four and she has a, go ahead and hold it so everybody can see. My sentence is four is the same as four. What's your sentence? Four is the same as four. Good job. We're keeping. Let's see if we need a tie breaker. Four equals four. Okay, Ty, come on up. I don't know if I'm going to get him, Ty. No, either. One, two, three, roll. Oh, this is what I got. Yes. What did you get, Ty? So my sentence is two is less than three. What's your sentence? Yes. Three is, no, three is more than two. Good job. I like the way you said that. Thank you. Did I have two? No. Yeah, you had two. And I had three? No, I had three. Yeah, that's right. I wrote my number first. I can put a pink. Oh, you get that pink because it shows that you won. Okay.


We were looking into some examples to illustrate the use of the Reynolds transport theorem for working out problems related to that. We will continue with some more examples. Let us take an example where let us say you have a solid body say a solid body of whatever shape maybe circular shape if you wanted to be so and fluid is flowing it is coming from a free stream with a velocity uniform velocity say u infinity and because of the presence of the solid the velocity is disturbed and if you go a little bit away from the solid and if you draw the velocity profile say the velocity profile is obtained something like let us make a sketch of how the velocity profile is there. Let us say that the velocity profile varies in this way. In one of our later chapters we will see that what are the factors that will determine that what should be this velocity profile or what should be the nature of variation of this velocity profile but for the time being let us say that this is the this is a qualitative sketch of how the velocity profile varies. Assume that it is totally symmetric with respect to the centre line and the velocity profile is such that say like at the middle like if you draw it totally in a symmetric manner at the middle it is like a minimum and then it increases in both sides comes to almost u infinity at a given height. Let us say that this height at which it comes to almost u infinity is a and let us say this velocity profile is given in terms of the x and y coordinates. Let us say that x is the axial direction and y is the transverse direction and the velocity profile say is given by u by u infinity say is equal to sin this is given okay not that it has to be like this this is just an example. We are trying to satisfy the condition that when y equal to a u equal to u infinity that is how this velocity profile is there. So the question is that what is the total drag force on the solid body exerted by the water or the fluid. Let us assume that the density of the fluid is rho and we have to find out based on these dimensions. So how do we go about this? We worked out a very similar problem when we were considering flow over a flat plate. This is not flow over a flat plate this is flow past some body of arbitrary contour but the policy or the philosophy remains the same. So we have to basically find out we have to identify a control volume and see what is the net force on the control volume. So to identify a control volume see what part of the control volume will have some inlet and some outlet. So one inlet is this one which is straight forward that the flow is entering outlet this is straight forward and you can see that outlet is interesting only up to y equal to a or y equal to minus a because beyond that the velocity is uniform. So if we take a control volume say something like this where we consider one inflow boundary one outflow boundary and across other boundaries we do not want any flow. So what should be the edges of the other boundaries? There should be streamlines so that there is no flow across those. So let us say that we consider a streamline like this and these are not horizontal lines these are inclined ones. Let us just magnify those a little bit to represent that. Let us say that this is one extreme streamline this is another extreme streamline. So these are streamlines. Keep in mind that these it is not necessary to choose a control volume which has which contains streamlines but only elegance it gives to us is that we do not have to bother about the cross flows. But if we just take say some horizontal lines at the top and the bottom and constitute say a rectangular piece as the control volume then there will be flow across that and one has to make calculations related to that. So it is just a matter of convenience for choosing the control volume maybe you consider only the water in the control volume so you exclude the solid part. Now let us write the expressions for the mass and the linear momentum conservation for the control volume. So one thing that remains unknown is that what is this height h because we have constructed a streamline from the right from the edge of this layer where u becomes u infinity this is not a boundary layer. We will discuss later that what is the difference between this and the boundary layer as such. So when we have the streamline starting from the edge the streamline will end up here at some arbitrary point which is not known to us so we have to find that out. So let us say that we mark the edges as a b c d and try to identify that what are the expressions for the conservation of mass. So if you write the conservation of mass you have the dm dt for the system I am just writing it straight away without going for the explanation of different terms because we have already encountered that. So dm dt for the system in the left hand side is 0 then we assume that it is a steady flow not changing with time. So the right hand side you have first term 0 and then the term integral of rho vr.n da so that term we have to basically write. So what will be the corresponding expression here? So you have one outflow and one inflow so there is no flow across these 2 that is the advantage of taking the streamline. So what will be this term for the outflow? Say rho what is da, da you can take as dy into the width. Let us say w is the width perpendicular to the plane of the figure that is the width of this body. So rho into u dy into w that is the total when integrated from say y equal to minus a to plus a that means 2 into y equal to 0 to a that is the outflow and then the inflow that is there that is with a minus sign because velocity is along the positive x outward normally is along the negative x. So what will be that minus again 2 rho u infinity into h into w right. So from here you can get what is h because that is the unknown that you have to find out mass conservation tells us how to find out that. So h equal to integral u dy 0 to a divided by 2 infinity. Next conservation of linear momentum what it will tell us the resultant force which is acting on the control volume. So what is the resultant force that acts on the control volume? There is a pressure distribution but because it is open to the ambient the pressure is same all around. So the net effect of pressure distribution may be 0 but in reality it is it may be so that here the pressure is not same as the atmospheric pressure but something which is different from that. But let us assume that there is a uniform pressure distribution just for simplicity. Then the only force that remains along x so let us say we are bothered about the linear momentum transport along x. The only force that remains important is the drag force is equal to again the unsteady term is not there in the right hand side first and then basically these things will be multiplied with another u. So it will be plus 2 rho integral of u square dy w then minus so you can substitute the value of h here sorry this is u infinity square. 2 rho we have already taken as common so that will be the corresponding expression right. So what we have done is we have replaced h with this expression okay. Now what does this force represent? This is the force exerted by what on what? This is the force exerted by the solid body on the fluid control volume and you can easily see it say you do not know it but the mathematical sign will tell you see u square is less than u infinity. So this integral when it is evaluated it will be negative. So that means you have a negative force that means force which is along the negative x direction. So what force is there along the negative x direction? It is definitely force exerted by the solid on the fluid because it is trying to resist the motion of the fluid. On the other hand the force exerted by the fluid on the solid is equal in magnitude to this but opposite in sense. So that is along the positive x direction that we also call as drag force on the solid object. There are certain interesting things that we can observe from this problem. One interesting thing is it appears as if this force does not depend on the shape of this object but that is an illusion. Why? Where the effect of the shape of the object comes into the picture? The velocity profile. So the velocity profile will very much depend on what is the shape of the object. So we have assumed the velocity profile but this is like it does it is not that it is it comes just arbitrarily. This whatever is the velocity profile that velocity profile should come from the shape of the body and therefore that is where the shape of the body becomes critical. Now the other thing is that it will also appear as if the force does not depend on the viscosity of the fluid. It appears so. So it is a it is a it is a kind of like not an intuitive thing that you expect the force due to viscosity because if there is no viscous effect perhaps there would be no drag but there is no there is no viscosity here. There is no there is no there is no presence of the parameter viscosity here. So what what is the viscosity doing here or the question may be posed in this way that is it always necessary that viscosity will directly come into the picture for the drag force calculation. See viscous effect is there. There are 2 important effects which are important which are prevalent here. One is the viscous effect another is the contour of the body as the fluid is flowing over the contour of the body there is a change in pressure. So one is the geometrical effect another is the viscous effect and this velocity profile is a combined consequence of what has taken place. So once you are given a velocity profile you may be abstracted of anything else but where from the velocity profile has originated for that viscosity may be important but once you get a velocity profile see that is what the integral balance is giving integral balance is the net effect. It is not microscopic looking into what has happened at individual points but it has got a gross consequence. What what is the consequence some velocity profile at the outlet and this kind of gross consequence is important because you can measure it experimentally. Experimentally point to point measurement is difficult it is not impossible but it is it is always more expensive to do that but experimentally you can at least find out velocity profile on a given section. So you can have different probes also may not be as simple as a pitot tube probe but you you may have any velocity measurement along this section that is not difficult and uniform velocity which which is the free stream velocity that you know. So from the experimental understanding of what is the velocity profile at the inlet and at the outlet you may be in a position to experimentally calculate or rather to calculate from the experimental data what is the drag force and the limitation of that is it does not pinpoint that how how the flow feel varied from one point to another point to give rise to the drag force but it gives the total effect in an integral sense. Now how it varies from one point to another point for that we have to look into the corresponding differential equation for viscous flows that we will do in our next chapter. Now let us look into another problem let us say that there is a pipe like this it has to be fitted with another pipe which is like this I am trying to give you an industrial perspective of the problem rather than just stating the problem as it is. So the problem is you have to connect these pipelines it is very common that no matter whatever plant you visit you will see that there are lots of pipelines and pipelines are not always straight because they have to connect different systems and there are space constraints and so on. So the pipeline has to be bent many times. So there must be some fitting which connects this pipe to this pipe there are 2 things which have happened one is the direction has changed may be the axis of these are oriented at an angle 90 degree it is not required or necessary that it has to be 90 degree but let us say that the angle between these 2 is 90 degree plus there is a reduction in cross sectional area that also is not a mass sometimes cross sectional area may remain the same or may even may increase but one has to just have a fitting to fit that and that fitting in industry is known as an elbow. So what an elbow does it basically tries to have a fitting like this to fit or match with pipelines of different orientations and different sections. If the angle between these 2 axis is 90 degree it is called as a 90 degree elbow like that. So if we assume that this angle is 90 degree we call it 90 degree elbow. Now this elbow it cannot be free in air because we will see that there is a lot of force that is being exerted on this elbow because of the change of linear momentum of the water that is entering and leaving and because of that there is a force on the elbow and it has to be supported. So it must be supported with a support that provides some necessary reaction force which balances those forces exerted by the water on the elbow so that it is in equilibrium otherwise it might have a tendency to move or to get deflected from its equilibrium configuration and that will disturb the entire stability of the structure. So when you design a structure you have to be careful of what are the support forces that need to be sustained by that structure. For that the support force has to basically balance the force exerted by the fluid on the structure. So we have to know what is the force exerted by the water on the pipe bend. So that is our objective of solving this problem that is we want to know that what is the force exerted on the elbow. What are the data given? Let us try to list that force on the elbow. Let us say that you have points 1 and 2 or let us call these as sections 1 and 2. So at the section 1 say there is a equivalent pressure P1 which is given, area of cross section is given. At the section 2 you have P2 and A2 these are given. Let us say that the velocity profile is uniform. If it is not uniform at least you know what is the average velocity. So you know the average velocity at section 1, you know the average velocity at section 2. Where from you know the average velocity is experimentally what you can always find out it what is the flow rate. And if you know the area of cross section say it is a circular one you know the diameter. So you know the area of cross section. So A into the average velocity is the flow rate. From that you can find out the average velocity. If you neglect the viscous effects then the average velocity is same as the velocity at any point. So you may neglect that let us say that neglect non-uniformity in velocity profile. What else is given that what is the weight of the elbow say it is equal to w. Weight of the elbow is a solid. So it has its own weight. So we are considering that weight and we are given the density of the water which is there inside. Rho is the density and what else we require. Let us say the angle between this inlet and the outlet. So the water is entering like this it is leaving like this. The angle is 90 degree. If it is not 90 degree then also like if it is inclined it will have its horizontal and vertical components of the flux velocity and so on. Now we are interested to write the expression for the force component along x and force component along y. Sometimes you see that the pressure at 1 is given but pressure at 2 may not be given. But if you assume an inviscid flow and you connect a streamline say from the center of the section 1 to center of the section 2 you can use the Bernoulli's equation to find out what is the pressure and if you assume that the pressure is uniformly distributed over the section then that will be the pressure throughout the section 2. You have to keep in mind that what can create a non-uniformity in pressure. So if you have pressure at the center line say at p1 what can make it deviate if you go to different location in the cross section curvature of the stream lines. So if stream lines are almost parallel to each other then the change in pressure is very very small or negligible. So then we are assuming that stream lines here and here are almost parallel to each other. See if you take that on the bend that is not valid. So we are considering the section 2 which has actually crossed the curvature part of the elbow. This is an assumption. In reality the piece may be short so that may not be a very good assumption but this is what we are assuming otherwise you have to also consider a non-uniformity in pressure across the section which itself adds to the complexity. We are not going into the complexities but I am trying to highlight the complexity because these are important, these may be important in some realistic conditions. So 2 important complexities may be non-uniformity of velocity over each section and non-uniformity of pressure over each section and when non-uniformity of velocity over each section is occurring then that means that and it is always there until unless it is a highly turbulent flow where the velocity profile due to high mixing is almost uniform. Otherwise if there is a velocity profile it gives an important understanding that yes viscous effects are important and when viscous effects are important you cannot apply Bernoulli's equation along a streamline between 1 and 2. Still you can use a1 v1 average equal to a2 v2 average that is a conservation of mass that does not depend on how viscous forces are occurring or not but you cannot really relate the pressure at 1 with pressure at 2 using the Bernoulli's equation. One has to solve the viscous flow equations to find out that. Now when you write the resultant force along x, so let us try to write the resultant force in a vector form. So we are using the Reynolds transport theorem, the right hand side the first term due to unsteadiness that is 0, next term is integral of rho v. When you are writing this force f, what is this force f? Let us now write what are the constituents of this? One force is the force exerted by the elbow on the water, so that is the f reaction. Then what other force is there? Force due to pressure is there plus force due to 2 weights. One is the weight of the elbow itself, another is the weight of the water which is instantaneously there within the elbow. So f due to water weight and plus f due to elbow weight, okay. So let us try to write these expressions of these forces, of course this is what you are interested to find out every action, so this is an unknown. Force due to pressure, how do you find out what is the force due to pressure? What is the force due to pressure on the control volume? P1A1 for section 1 along x, P2A2 for section 2 along y like that, it is not like that. I have mentioned it earlier y, when you have a pressure distribution on a surface you have to consider the force due to gauge pressure only because atmospheric pressure is there from all sides and that is nullifying the total force when it is integrated over a closed contour. So when you are writing the force due to pressure it should be the net force because of the pressure over and above the atmospheric pressure. So to calculate the force P1 has to be converted into the gauge pressure at 1, so P1 gauge has to be evaluated that is P1-P atmosphere. Similarly this has to be converted into gauge pressure. These are subtle but very important things. These are places where like in most of the cases students will make mistakes. Of course if you practice enough problems you will never make such a mistake but general tendency is like before the exam you just look into worked out examples. So when then these things are not highlighted, you just look into the gross formula but these are very important things that you have to keep in mind. Do not just take it as a formula, keep in mind that why it should be so that why you have to take the gauge pressure for evaluation of the force. So force due to the pressure what should be the corresponding expression P1 gauge into A1 that is the net force due to pressure at section 1. So in a vector notation we call it this i cap then plus P2 gauge into A2 j cap. You have to keep in mind that pressure is always into the surface. In whatever phase you are considering pressure is always acting towards that okay. Then force due to the water weight what is that? It is not impossible to calculate what is the volume of this given this contour. Let us say the volume of the water is given that is the volume of the elbow basically. So if the volume of the water is given then it is the what is the mass rho into volume of the water that into g is the weight, g is acting along negative y then this is minus of this j and the elbow weight what is the elbow weight minus w j and the right hand side the integral of when you are considering this integral first is what are the surfaces across which fluid is flowing 1 and 2. What is the control volume that we have taken? Since we have represented the elbow weight we have considered the elbow also as a part of the control volume. So the control volume let us draw the control volume. So till you express explicitly that what is the force, what is the resultant force that you are having? It may not be so straight forward to say that what is the resultant like what is the control volume that you have taken? So if you say if you take this as the control volume that means this excludes the elbow and then f elbow weight is not there but once f elbow weight is there you have basically taken including the elbow. So it is elbow plus the water that you have taken as the control volume. So the question is then when you have taken this as the control volume the outer one as the control volume say which includes both the elbow and the water the question is then what is this for f reaction this is provided by it is now not provided by elbow by the water. So what is this? So it consider there is a support which is there outside which exerts the force on this elbow plus water system. So there is some support which is there which is not drawn in the figure but it is highlighting that support. So now for that particular control volume we are having how many inlets and how many outlets we have one inlet and one outlet and let us write that. So the right hand side first let us write for the section 1 for the section 1 if you assume a uniform velocity profile then like this entire integral will be based on the velocity say v1 which is over uniform over the section 1. So rho then for v1 it is v1 i cap and then into v1 a1 so with what sign plus or minus right. You can clearly see that if there is a velocity variation along y then this expression is not valid then you have to integrate the velocity profile and that would give a net momentum flux this is this like a momentum flux. So the net momentum flux will be different and if one assumes a uniform velocity profile and it is really not so then that is an error and one has to adjust that error with some momentum correction factor maybe but here because of uniform profile assumption that such a correction is not necessary otherwise if the velocity profile is given to you you can integrate it to get this expression then there is no correction factor necessary. Then for the surface 2 plus rho what is the velocity at the section 2 let us say v2 it is directed along which direction minus y so minus v2j into this is plus. So the left hand side is equal to the right hand side and that will give you what are the components of the reaction force. This is the force exerted by the support on this system. So it should provide an equal and opposite force on the support and the support must be good enough to sustain that force okay. So if it is unsupported then because of some resultant force see it with the elbow may start moving okay. Let us look into one more example let us say there is a cart like this and a water jet is striking on the cart and it is changing its direction let us say this angle is theta. Let us say that the velocity of the water jet is v and the corresponding area over which the jet is moving here is a cross section area and let us assume that this is smooth. So if this is smooth that means there is no friction that the fluid is encountering as it is moving along the cart only its direction is getting changed. The first question that we would like to answer is that will it be possible to keep the cart stationary if such a water jet falls on it and changes its direction. For simplicity let us assume that this is a frictionless surface and may be assume that the cart is having a particular weight but that is not of great concern for us because we are interested to consider the motion along x whether there will be any motion along x or not. First of all let us say that what do you expect to be the velocity at which the water leaves the cart. Say it enters the cart at 1 and leaves the cart at 2 what is the velocity that we expect if the velocity here is say v1 which is equal to v what is the velocity at 2 there what are the first of all if you consider a streamline that connects some point at the inlet with some point at the outlet then could we apply the Bernoulli's equation along that streamline. If it is the first question is if it is inviscid flow then like that that is the first question that you would like to ask. So assume that it is an inviscid flow if it is an inviscid flow yes provided other conditions are satisfied what are those you have density as constant and steady flow obviously although unsteady version of Bernoulli's equation is also there what let us assume that it is a steady flow. So if this is a smooth one we and the water this is quite thin and this because of the smoothness there is no such wall roughness effect that is propagated into the fluid. So it is as if like a frictionless flow although you this is a great idealization in reality the effect of the solid boundary will always be propagated into the fluid and in all cases it is likely to give viscous resistance but here we are just idealizing it by too much and assuming that that effect is not there if that effect is not there if the velocity here is v1 the velocity v2 should be equal to v1 provided that the difference in height between 1 and 2 is neglected. So we are neglecting the z2-z1 that is neglected it is really a very small height and the corresponding potential energy chain is insignificant as compared to the kinetic energies of the jets. See in engineering when we say that we are neglecting something there is a very important thing that we should keep in mind we are not actually neglecting potential energy we are neglecting the change in potential energy and that change itself may not be negligible in an absolute sense. What we are banking on is that the jet is falling on with a very high kinetic energy with respect to those kinetic energies the potential energy effect is negligible not that it is always in an absolute sense negligible and regarding the pressure both are exposed to atmospheric pressure. So the pressure is like p1 and p2 are same so if the z2-z1 is neglected and if we may apply the Bernoulli's equation with all the assumptions satisfied then you have v1 equal to v2. In general if there is a friction here v2 will be somewhat less than v1 but because the friction less nature v2 is v1 and then you can apply the continuity equation then a2 also must be same as a1. Now let us say that we are interested to find out what is the resultant force along x because that is what is going to make it move maybe. So the resultant force on x resultant force along x what is that so you have 2 sections basically so you have one section like this where the fluid is entering and you have another section at 2 where the fluid is leaving these are only the 2 flow sections. Where do you choose your control volume see since there is no friction on the ground it will not be any difference any different if you include that like all the structural part of the cart and exclude the structural part of the cart for obtaining the force along x definitely for force along y it will be mattering but not force along x. So for force along x the right hand side first the unsteady term is 0 and then integral of rho v vr.nda so this is like fx i plus fyj because this is in a vector form now let us write try to write it in terms of its scalar components at the section 2 what is v v has a magnitude v what is the direction cos theta i plus sin theta j right. So that is the v in the vector form and then the remaining is a into v that is integral of v.nda what for the section 1 for the section 1 what is the velocity vi and-av so what is the force along x you can find out only the x component of that that is rho v rho av square into cos theta-1 this is the force exerted by the solid structure on the fluid right. So if you consider say a control volume like this we just n compasses the fluid z so this is the force exerted by the cart on the fluid the fluid exerts an equal and opposite force on the cart so this force is positive or negative this negative this is along-x so force exerted by water on the cart is along-x so you have a plus fx that is there on the cart and that is quite obvious even if you do not go to go through the mathematics if there is a z striking like this it should exert a force along the x direction. So there is a fx on the cart so the cart under this force may try to move and if this is a frictionless surface it will move always if there is a friction the static friction may just balance it and keep it in equilibrium but if it is not then it has to move. If it moves the question is that then is this consideration valid that is like here we are having to use the relative velocity but we do not know what is the velocity of the cart so how we should go about it that is the first question. Second is whether this velocity then we have to use the absolute velocity or the relative velocity. So these are the questions that we will like to address in a subsequent theoretical development where we consider also the moving reference frames still now we have considered only the stationary reference frames but in the jurisdiction of stationary reference frame if you have to consider it you have to consider somehow that this is stationary. Now how can you design a system such that this remains stationary there could be many ways. Let us say let me give one alternative when you say that whether it is a good alternative or not. Let us say we have a pulley like this and let us say there is a weight mg which is there this pulley is he supported like this is it acceptable will it work no or yes it depends on what is this weight and that you can design exactly because you know what is the exact magnitude of the force. So if you draw the free body diagram of the cart what are the forces that you will see you will see a tension in the string and you will see a force fx exerted by the water on cart okay. So when you have these two of course the other y component is there so y component you have the weight of the cart then you have a normal reaction like that but for us interesting is the x component and if you want to keep it in equilibrium you have to balance t with fx on the cart and if you consider it to be all those idealistic situations that it is a frictionless pulley and then what you get is that you get this tension same as the mg. So this in turn from the mass pulley system is equal to the mg. So you know that what has to balance what so you can put the correct mass here to keep it in equilibrium okay but you can clearly see that this is this is a forceful arrangement to keep it in equilibrium but in general because of these forces it will not be in equilibrium and when it is not in equilibrium with these forces it might have a velocity the that velocity itself might change with time. So it might have a situation when the reference frame which may be attached to the cart itself is moving and moving with arbitrary velocity or arbitrary acceleration. So we have to also be equipped with an analytical ability by which we can encounter such situations that is situations where you can encounter accelerating reference frames in general. When we say an accelerating reference frame we mean accelerating frame reference frame in all respects that means it could be linearly accelerating it might have an angular velocity because of which it has its original acceleration. So we have to next go for an analysis for accelerating reference frames. So we will use certain nomenclature we will consider axis say capital X capital Y capital Z for an inertial reference frame small x small y small z reference frame as an arbitrary it may be it may be inertial may be non-inertial but it is a moving reference frame. If it is moving with an acceleration then it is non-inertial if it is moving with a uniform velocity it is still inertial. What we are interested to find out is that if we have a vector say A here in this reference frame and let us say that this reference frame is moving with an arbitrary angular velocity omega then what is the derivative of this vector with respect to the inertial reference frame. Can you show it if I ask you to show it how do you show it say you have a vector A which is there in a reference frame that is rotating with an angular velocity omega. Let us say that the angular velocity is such that the rotation is taking place in the plane of the board. The rotation will take place in some plane what is that plane the plane is perpendicular to the axis of rotation. It might not be xy plane or yz plane like that but it is some plane. So in that plane this vector A is rotating. So when it is rotating it comes to what state it comes to a new location say this is at time t it is at time t plus delta t. What we are keeping in mind we are keeping in mind this is a fixed vector in a moving reference frame. So this is a fixed vector in xyz that we have to keep in mind. It is not any arbitrary vector that means if you are sitting on this you do not see any change in the at least in the length and if you are outside although it is same in length but because the reference frame is rotating this also rotates. Let us say that it traverses an angle delta theta over this time delta t. So what is the change in the vector the change in the vector is this delta A. So what is this delta A for small delta t the delta theta is small. So this is just like an arc of a circle. So delta A in terms of magnitude is what A delta theta in terms of a vector you have to give it a proper direction and sense. So if let us say that this is A is in a direction of E1 then it should be a direction which is normal to E1 say E2. If you want to find out what is da dt if you are not mentioning any subscript capital xyz that means we are talking about inertial then it is basically we are dividing this by delta t and taking the limit as delta t tends to 0. So A E2 into limit as delta t tends to 0 delta theta by delta t which is nothing but the magnitude of the angular velocity. And what is omega cross A omega is what is the omega vector it is omega scalar times a unit vector E3 which is perpendicular to the plane of the board. So you may take E1 like x E2 like y and E3 like z just like that this cross A is A E1. So it is omega A E2 E1 E2 E3 from orthogonal basis just like x ijk. So you can write that da dt capital xyz is equal to omega E2 E3. Omega cross A but this is only for a vector A which is fixed in the small xyz reference frame. If it is moving in a small xyz reference frame then that velocity also has to be added with this. So in general for an arbitrary vector A in capital x in small xyz you have da dt capital xyz is equal to da dt small xyz plus omega cross A. So this change is felt even if A is fixed but if A is moving relative to small xyz this is an additional change. So that is the total change and this you know from your earlier studies that this is known as Chaisel's theorem. So we will take up from this and try to write an equation of linear momentum conservation for a control volume which is having arbitrary motion. It may have angular motion, it may have linear motion, it may be a non-accelerating reference. It may be a accelerating reference frame in general. So we will take that up in the next class. Thank you.