 So, with this what we will do is, we will start our discussion and we will start taking questions. 1, 2, 1, 3. Sir, what is stagnation pressure and what is stagnation temperature, sir? So, the question is about what is stagnation pressure and what is stagnation temperature. We discussed this actually during the lecture. So, let me just try to explain it again. What you can imagine is that you have a situation such as a 1-D isentropic type flow in a duct and you are looking at one particular cross section. At that cross section, let us assume that the flow conditions are temperature equal to T and pressure equal to P. Now, from this set of conditions, if you assume that you bring the flow to rest, meaning that you bring the flow to zero velocity in an isentropic manner, whatever value of temperature and pressure that you will achieve at the end of this isentropic deceleration to a zero velocity is what is called as the stagnation pressure and stagnation temperature. So, that is the formal definition of the stagnation quantities. Thank you. Sir, can you explain choking of nozzle once again, although you explained, but I will be very thankful if you explain again that choking of nozzle. You explained by some figure, sir. Yeah. So, the question is on choking of nozzle and let me go through this again. So, what happens in case of a nozzle and for the sake of simplicity, I will choose the purely convergent nozzle, but the phenomenon is more or less similar in case of a convergent divergent nozzle. So, let us assume that the convergent nozzle is operating and we are continuously reducing the back pressure. What ends up happening is that if you reduce the back pressure to a certain value that corresponding to that value, the exit plane pressure becomes equal to P star or the critical pressure corresponding to whatever stagnation pressure you have, in which case the exit mark number becomes exactly equal to 1, which then means that the flow velocity is also exactly equal to the sonic velocity. Now, beyond this if you want to reduce the back pressure, what ends up happening is that a sound disturbance or an acoustic disturbance is generated at the exit plane, which tries to move upward into the nozzle, thereby trying to change the condition. However, it has to move against the exit plane flow and since the exit plane flow has already reached the sonic value, what happens is that the acoustic disturbance is simply not able to move against the oncoming sonic flow and therefore, nothing can change inside the nozzle, because this acoustic disturbance is simply unable to travel inside the nozzle. So, one thing that you want to keep in mind is that whenever you change the back pressure, in particular whenever you reduce the back pressure, acoustic disturbances are generated at the exit and usually they are able to propagate up in the nozzle as long as the exit flow is subsonic. But once the exit flow becomes sonic, the acoustic disturbance is simply not able to propagate against the sonic flow at the exit and thereby the conditions in the nozzle are not going to be changed at all, which is what formally we call a choked nozzle. Thank you. Then that sonic flow will be converted to subsonic flow. That is a really good question. So, the question is that if we increase the back pressure, what will happen? So, it turns out although to be honest with you, we do not have the luxury of going into such kind of detail in this course, but since you ask this question, if you increase the back pressure instead of generating an acoustic disturbance, what happens is that actually a shock like disturbance is generated at the exit plane and the shock like disturbance is able to propagate against the oncoming sonic flow and in that case what ends up happening is that the conditions within the nozzle will get changed. So, that is a really good question and I would like to reiterate here that once you have reached E star in the exit plane, if you reduce the back pressure, acoustic disturbance is generated which cannot propagate in the nozzle, but if you increase the back pressure back up, then a shock like disturbance is generated which is actually able to propagate all the way inside the nozzle and change the conditions back to a completely subsonic situation. So, such details unfortunately we cannot cover in the thermodynamic course, but in case you are interested, what I will put up is a list of couple of compressible text books, compressible flow text books which can provide you more details on this situation. So, thank you for the really nice question. Sir, what is limiting subsonic as you said in convergent, divergent nozzle, can you explain, sir, please? Yeah, so the question is about my usage of the terminology, the limiting subsonic operation condition. So, what I mean by the limiting subsonic operation in case of a convergent, divergent nozzle is that the flow within the convergent section is fully subsonic, reaching a Mach number of just about 1 at the throat and the flow within the divergent section is also fully subsonic. If you travel from the throat location all the way to the exit location, the Mach number will continuously decrease from the value of 1 which was reached at the throat to a successively lower and lower subsonic value throughout the divergent section. So, what ends up happening is that the entire nozzle is operating in a completely subsonic mode of operation with the maximum Mach number of exactly equal to 1 at the throat, both the convergent section and the divergent section are subsonic. This is what I am calling a limiting subsonic situation. 1 0 double 9, go ahead if you have a question. Sir, what is the practical use of Mach number? Can you give example? Where it is used? So, the question is about what is the practical use of Mach number? See the Mach number is one of the most important parameters to quantify a compressible flow. So, we discussed this yesterday as well that a compressible flow can be subsonic or sonic or supersonic and whether the flow itself is having a velocity less than the speed of sound or equal to the speed of sound or higher than the speed of sound is signified through the value of the Mach number being less than 1 equal to 1 or higher than 1. I have also mentioned yesterday briefly that if you look at the square of the Mach number, the square of the Mach number can be interpreted as the ratio of the bulk kinetic energy to the thermodynamic internal energy contained within the flow and usually you will see that when we talk about these high speed compressible flows, the usually the bulk kinetic energy is not really negligible in comparison with the thermodynamic internal energy and this is what is signified through the value of the Mach number as well. If you look at the purely incompressible flow type situations we can more or less formally show that the bulk kinetic energy is usually really really small in comparison with the thermodynamic internal energy, but when it comes to compressible flow they are comparable and the measure of the relative strength of let us say the bulk kinetic energy to the thermodynamic internal energy is given by the Mach number, the square of the Mach number. So, in that sense it has a reasonably good physical interpretation also. Thank you. Another question, under the expanded condition in a convergent nozzle, what will be the effect physical effect there? The question is about under expanded operation of a convergent nozzle and what would be the physical effect. What ends up happening is that when you reach the design condition and if you go below in terms of the back pressure you get into this under expanded situation. What I tried to explain during the lecture is that the mass flow rate remains exactly the same. However, outside the nozzle there is a further reduction of pressure through the expansion waves that are generated. Usually what ends up happening because of that is that there is a slight alteration in the thrust that is generated on the nozzle. So, depending on whether the nozzle is operating under design condition or an under expanded type situation there is a slight difference in the thrust generated on the nozzle. So, I think my understanding is that this is the most reasonable practical implementation or implication of the nozzle being under expanded. Thank you. One more thing sir, actually when we are analyzing this nozzle we are saying that reducing the back pressure, but in practice how we can reduce the back pressure because suppose it is connected to the turbine that back pressure will be the almost at most pressure or the back pressure. Yes. So, that is a that is a really good question and the question is about the characteristics of the nozzles that we have discussed in the form of a constant P naught stagnation pressure and reducing the back pressure. Whereas in reality it is usually the exact opposite that happens. Normally what we have is a constant value of the back pressure and usually the stagnation pressure is what is changing. It turns out that that is correct what you are pointing out is absolutely right. Usually that is what happens in reality. However, as far as just description of the operating characteristics of the nozzle is concerned it does not matter whether you are describing it with respect to constant back pressure and changing the stagnation pressure or keeping a constant stagnation pressure and reducing the reducing the back pressure. So, it turns out that for whatever reason authors have decided to describe the operating characteristics with a constant value of P naught and reducing value of the back pressure, but your point is absolutely well taken. In fact, what I will point out is that problem number 14 in the compressible problems describes the situation which you are referring to where the back pressure is kept constant, but the stagnation value of the pressure is changing and you can see that overall the operating characteristics can be described either way. So, that way there is no problem. Thank you. On 1 5 0 go ahead if you have a question. Hello sir, my question is regarding compressible flow. Sir, when we consider the cross section of the throat, may I know is there any the concept of cross sectional analysis of a throat having square area, rectangular area, triangular area, circular or two holes, two circular cross sections in a throat connected side by side. So, the question is about the nature of the cross section of the throat whether we are referring specifically to a triangular cross section or a rectangular cross section or a circular cross section or any other sort of cross section and the answer is actually no, we are not referring to any specific kind of cross section, but perhaps what is implicitly understood is that we are talking about a circular cross section although that is not really an issue at all. What ends up happening is that the entire discussion that we have gone through and the description of the nozzle does not really affect or get affected by the kind of cross section that we are talking about. So, in that sense whatever discussion we have had is equally applicable whether you have a cross section which is rectangular or circular. Now whatever discussion we have gone through is really a very ideal situation and in reality you should be expecting reasonable amount of changes with respect to this ideal situation that we have talked about, but as per as the ideal discussion is concerned it really does not take into account any specific kind of area cross section. So, in that sense it is equally applicable for a rectangular or a circular cross section. Thank you. Sir, when you are considering the throat itself and if its inner surface is having thread like profile on both sides and what will be the effect by normal plane tube like throat and that thread profile like internal thread profile like surface. Yeah, so the question is about if in particular at the throat level if you have any surface imperfections and in particular something like a thread like situation if it exists what will happen. See typically what happens is that you will generate lot of extra waves typically of the shock type waves and these shock type waves will deviate the flow from being ideally isentropic into a non-isentropic situation. So your nozzle performance will be going away more and more away from the discussion that we have done. So any surface imperfection that you may have for the inner surface of the nozzle whether it is at the throat or even in the divergent part will typically create shocks of various strengths depending on the extent of your surface imperfection and because of this shock generation you will see that the performance of the nozzle will degrade in comparison with what the ideal performance should be. So, that is what I would think. Thank you. Sir, according to your information that there is no practical application of such profiles inside the throat system. Sir, my understanding is that you know if you want to maintain a performance as close to the ideal as possible it is probably a good idea to avoid such kind of surface imperfections and have as smooth a surface as possible that is what my understanding would be. Thank you. Sir, I am clear and what about if the throat is 0 and if throat length is some 5 centimeter or 10 centimeter like that what is the effect on flow process if the throat length is increased? Yeah, so if the see typically what is going to happen is that the longer the length that you have in general whether for throat or for the convergent part or the divergent part what ends up happening is that frictional effect will become more and more dominant which we have completely neglected as you can see from our analysis and with the frictional effects being more and more dominant again the performance of the nozzle will go away from the ideal performance. In that sense if you have calculated let us say a design Mach number of let us say 2.5 you will not obtain that 2.5 and you will obtain typically a lower value than that because of the additional frictional effects that will come in because basically you are increasing the length of the nozzle. Thank you. Sir say 0 length of the throat is the ideal one sir. I would think so because you know that what that will do is that in general it will make sure that the wall length that the flow has to travel against is as low as possible which will make sure that the frictional losses are kept to a minimum although to be honest with you a couple of centimeters here and there at the throat is not really going to degrade your performance significantly. However in general you want to avoid that as much as possible. Thank you. Sir when we are considering the aero plane and the jet plane while it is moving with higher speed and the jet plane is taking the air inlet and what is the application of the compressible flow concept as well as the nozzle profile or design we can say when we are considering in those space crafts. Sir so the question is about the aircraft engines and how we can utilize these compressible flow concepts in analyzing those. So if you are talking about a gas turbine type situation gas turbine type aircraft engine what happens is that there is an intake at the front air intake and it goes through the compressor where also the flow is essentially compressible because it is typically a high speed flow that goes through it following which there is a combustion chamber where you will burn the fuel along with the air that you have that you have taken in and in all these aspects you can utilize the concepts of compressible flow for example in the combustion chamber we normally utilize a flow model called the Rayleigh flow model which we have not discussed in this course but if you take a course on compressible flow you will go through a Rayleigh flow model which can be used for the analysis of the combustion chamber and then once you form the combustion products in the combustion chamber those are normally exhausted through a nozzle like the nozzle that we have talked about. So all these basic concepts that we are going through are more or less directly utilized in the analysis of a gas turbine type engine for an aircraft. Thank you. Sir when you are considering the speed of planes in that case we are specifying the sonic speed supersonic speed especially for fighter planes if the plane is moving with higher supersonic speed it is not visible like that and somehow recently I have heard that some fighter planes are designed such that they are not visible or they are not identifiable. Then what is the logic band is there? Are they using the compressible flow concept for producing some vibrations acoustic disturbances like that system? So the question is about stealth fighter type planes which are supposed to be undetectable actually that undetectable stealth fighter type technology has nothing to do with compressible flow ideas. It has to do with radar technology and the detection through radars is somehow avoided by using typical shapes that they come up with along with some sort of a special material that they use for the plane. The plane is going to travel supersonically and if you want to analyze the flow situation past the plane you will end up utilizing the compressible flow concept but as far as the stealth detection part is concerned it is a completely different idea and it has to do with radar technology and not really to do with compressible flow. Thank you. Sir, when you consider the jet plane when the air inlet is occurring and suddenly the exit will be giving the minute solid ice particles because of throttling process. So I have heard like this, is it true sir? The outlet will be the ice particles because of throttling process. Is it true sir? And can we apply it day to day life, practical life? I am not really qualified to answer this but roughly speaking it appears that it is possible depending on how moist is the air that you are intaking and how low the pressures can get at the exit. It is possible that the kind of situation that you are describing can occur although to be honest with you I am not an expert to comment very seriously on this. So sorry about that. Similar condition will be occurring while we have kept the compressor on for smaller exit allowance so that the air is going out and the water particles will be there, those are observed. So like that I am thinking so sir. Yeah again I am sorry I am not too sure if I am qualified to answer this but it appears that it can be possible. Whatever else questions you may have in particular related to application type situations it is good chance that I may not be able to answer those if they are specific and applications to aerospace type situations. Feel free to upload those on on Moodle and what we have observed is that many times some other participants who are quite familiar with such end application type situations will be able to actually answer some of your questions. So my request is that feel free to upload some of these questions on Moodle as well. So 1116, as you said is in your. I will follow up on my earlier interest in entropy from yesterday. So we have this term along with entropy, entropy generation also that comes about in these processes and there are three cases typically that are considered greater than zero, less than zero and equal to zero. Can you elaborate quickly on what is the significance of less than zero? Are you talking of the case for entropy generation? I did not know which case are you talking of now? Which less than zero and what quantity is less than zero? Right. So typically we have this sigma that is known as entropy production generation. So we typically have three cases considered greater than zero and equal to zero and along with less than zero and less than zero is the one that is considered not possible. So from engineering perspective or mechanical engineering significance what is the usefulness of that less than zero case? The only significance is that that case cannot exist at all. So if you have found some equation or some situation where suddenly you find that your entropy generation term is coming out to be less than zero then you can safely assume that you have done something totally wrong and you will have to recheck all your calculations or recheck what else you have done. So such a case cannot come at all. That is the whole idea. So it is an impossible thing under the second law condition. Thank you. Very quickly. So what is it that I am at loss with this number with entropy generation term that I calculate to begin with in any numerical problem? So how should I interpret that value, that number and how is that tied with irreversibility that seems to be the source of it? Yeah. So that term has only been invented to tell you whether a process is reversible or not. So if the entropy generated was zero then you say the process is reversible. If the entropy generated is greater than zero then you say the process is irreversible and that is about it. It is only telling you whether you were or how close to reversibility you were because if the number is greater than zero and it is pretty less then you know how close to reversibility you were. So that is about the only thing you will get using the absolute magnitude. Otherwise as I said the term better be zero or greater than zero and in fact in all practical cases it will always be greater than zero. If you have made a mistake you will probably get less than zero. So that is about it. If I do have this number from a calculation and if I use it for say IC engine or the steam turbine or any of these power generating devices will I be able to use this number to improve the say performance parameters or efficiency of the system. So very honestly speaking I am still not able to see the actual significance of either this generation term. Okay see the term was only introduced to tell you what is a reversible process and what is an irreversible process. You can also use it in a turbine but you know you have another factor there called isentropic efficiency which anyway tells you how you know how much away you are from the reversibility because typically a turbine is assumed to be an adiabatic system. So an adiabatic isentropic situation would be reversible. So if it is not isentropic automatically it is not reversible also if it is adiabatic and what you realize is that you have gone away from the ideal and you are not extracting as much energy as possible you know ideally and you can try to see what is wrong with the design or what else you can do to come closer to the isentropic situation. So similarly if you have a large operation term you can try to see the process is extremely reversible so what is it that you are doing wrong so that you can come closer to reversibility because that is when you would in an adiabatic situation that is because that is when you will come to you know extracting as much work out of the whole system as possible. So basically it will tell you how far away from the ideal situation you are and whether you know it is possible to get towards the ideal situation that is what you know thank you. True very true so that seems to be closer more to the first law conservation rather than any sense that we are getting out of this term entropy that is basically what my interest is coming from this term has been coming along all along and it will continue to come up along now again in future topics like availability and exergy and combustion and every which way but it is still not really giving any sense of engineering relevance but what should I do with this number and why is it not tied rather with conservation of energy and more with this term which is very vague that we understand. No see I think somehow there seems to have been a disconnect this whole thing has nothing to do with conservation of energy okay you can always write or you know come up with a system which is conserving energy or you can say it is probably obeying the first law but you can go totally off and despite see you can always write total process where you know q is equal to delta u plus w but do you know whether it is reversible or not that is the key question okay do you know whether it is isentropic or not that is the key question I mean I can always have a system where everything I put in q hardly anything w comes out okay and I want to know what is the maximum w that I can get out of the system so that is when you use such term to figure out whether it is feasible how much closer or how much what is the best value of w I can come up with so this is only telling you how how much of you know how close you can come to ideality as possible the first law is always going to be conserved irrespective of this thing okay so there the equality will always hold here what you did was just you took the inequality introduce this entropy generation term to create an equality and that entropy generation term is just telling you how far away from ideality you are and it could have been anything as long as it is 0 or positive whereas in the first law the equality always has to be satisfied here you just introduce that term to tell you how far away from ideality you are and whether you can work towards going towards ideality or not so it is a very very practical thing for engineers as far as I can see I mean and I do not see any relation to first law so I am not sure why you are bringing the first law here thank you full of stirring a paddle wheel in a in a closed system or a pressman cylinder assembly and we have this friction that comes about in this process now this friction gets to be termed as irreversibility that leads to this sense of entropy and entropy generation so right now right here we are moving away from first law conservation and attaching this idea more to this term entropy or entropy generation rather than basically saying that this friction has literate in some amount of heat generation which we have not been able to conserve which has slipped away since it was not a perfectly insulated system and that is where my ultimate loss is coming from so I do not see where my any of my loss is coming from this second law idea so I think again you are what you can check let us see you are running a ranking cycle and you assume an adiabatic turbine and you know the most ideal case is isentropic case where you know it is a reversible case and the entropy at the exit of the turbine is the same as entropy at the inlet and now if you move further and further away what you said is true I mean friction introduces this irreversibility and you know for sure that you have created a lot of irreversibility and it is up to you to figure out how to reduce those irreversibility now of course you are what you are doing is that you are just equating friction with heat and that is something that you would absolutely not advise you to do do not look at it in this fashion you have done some work or there is some you can say in a way it is work you could not have you could not extract so you know for sure that you can do something about it and maximize your work that is the whole idea here so there is no loss of any energy all energy is in there so it is just that you were not able to extract as much work as possible so and this is as far as the turbine goes now you can always come up with system like for example people come up with separation system which using the first law everything seems fine you know you have a total energy balance and you figure out that q is delta u plus w but once you do this entropy calculations you realize that the net entropy at the exit or if the entropy production term is calculated it comes out negative and whatever you thought was so easily feasible you suddenly realize that it is an infeasible process so you suddenly realize that you have to backtrack and try to figure out what went wrong so these are special situations which you will have to analyze to figure out first law will always be valid but you have to figure out so this the entropy generation term is just another way second law so all you are trying to see whether the second law is being satisfied if it is being satisfied how far away from the reversibility am I and whether I can get closer to it or not so as that is what I said as far as we are concerned as engineer we just have to figure out how far away from ideality we are and try to see if we can get closer there the problems involving paddle wheel etcetera are just there for illustration but finally when you come to turbines etcetera or compressor you have to figure out yes there is some increase in entropy and we have to figure out what is exactly causing this whether it can be reduced or not so that is all up to how we have designed the blade shape what is the distance between the blade so we can do lot of calculations and come and see whether we can reduce all those extra irreversibility that we have created and ensure that we get closer and closer to the ideal case so that is up to us as engineers to do so we once we realize how far away from ideality we are we know that we have a lot of work to do to get it back towards ideality and that is the I would say the practical aspect of checking how big this entropy production is so thank you thank you for all your answers is there any way I can ask any further questions later after your sessions on this yes sure I think the professor has already announced that you can submit your questions on Moodle there will be a class group and we can keep on asking more and more questions and keep on giving answers on this chat session and as long as all of you participate it will help everyone of us because you will come up with certain questions which we will find difficult to answer and try to figure out what to do similarly everyone else will know what everyone else is thinking and what kind of questions crop up so that is a very useful forum according to me so I would like all of you to actually log on to that forum and you know answer these or ask these questions and look at the answers that are being given thank you just a quick comment so as part of major applications of thermodynamics for mechanical engineering in terms of IC engines or turbines primarily being energy converting devices or power producing devices again very quickly the primary interest comes for an engineer is what is the input that goes into these devices in any of these forms of chemical energy and what is the actual output that you get out of it and what is the laws associated with that so it one way or the other coming closer to the conservation law or first law and in any way I am not able to use any information or the primary definition of entropy or entropy generation term that I can use to investigate the performance or improve the performance of any of these devices so that is just one basic thought and one more quick thought so this further leads us to the idea of increase of forever entropy principle is there any again straightforward relevance or application to mechanical engineering or any of these power producing devices that we are working with other than say universality of this definition I am not very sure what because is it in a way you have reworded your original question that is how are we going to use entropy is that what your question is I mean so one of the thoughts that I am getting is it is much celebrated term that we have been using in many of the topics of thermodynamics and for many different aspects but again for mechanical engineering alone if you look at it now even the further topics like exergy availability and combustion and some of the compressible flow that was covered earlier today so all of this has a content of entropy entropy change, entropy generation and unless we are absolutely clear what is the primary relevance or significance of this term say at least from mechanical engineering perspective and from these energy converting devices it just seems to be a monotonic repetitive exercise of just calculating numbers after numbers and not really knowing what we really mean to us. So probably it comes with experience I mean if you have thought cycles and how turbines work you realize that this term becomes very important because we use it all the time to see whether thing is possible and if it is too much deviation we know there is something wrong with the design of the turbine and that is why people keep doing these experiments with turbine blades and see what kind of pressure losses come in and they come up with better and better designs using CFD primarily because we know that we have deviated so much we just look so you have to actually do a physical experiment figure out what your entropy is at the end or at the exit of the turbine compared to what is at the inlet you get various things so for example let us say you are not adiabatic you say you ensure that the insulation is such that you are adiabatic in spite of this if you are deviating far away from the isentropic case you know there is something wrong and you will get down and ensure that your blade design is changed so this is where the engineers come in and I am not sure so for example all our calculations regarding turbines and we always will ensure that what is it that we do with the entropy depends on if I am at the isentropic case I know exactly the outlet of the turbine or the compressor without knowing the isentropic case I can go either way on the T S diagram and satisfy my first law and come up with any kind of ridiculous number for my work and you will realize that this is easily possible if you didn't know the second law so I mean I can just draw the T S diagram draw my curve in any way I want and come up with any value for the work so this is where you are finally going to use entropy so and this is the only time when mechanical engineers use entropy that they look on the steam tables they look on the T S diagram for an ideal gas and try to figure out which is the possible cases and which are the possible cases and what are the works available and you can draw any amount of lines which are also impossible but you know that you can't draw them at all whereas if you give it to a layman you will say ok I know the first law I will draw whatever line I want and get my work output and you can get any kind of ridiculous number that you want so this is where you will actually start using thank you thank you for all your questions like I said if I have any 4 questions I will ask you at other forum thank you MRP Sir I have a question related to combined cycle which is connected to the gas turbine and the steam turbine system and the HRSG is the boiler right so sir can we increase the operating parameters or the optimize the operating parameters of the HRSG by the input or by the same mass flow rate of the gas turbine I am not very sure what you mean by optimizing so I am sure that you know there are many ways to optimize whatever you want but the question is I don't know what exactly you are looking at ok so you can have one kind of mass flow rate and you know get the best results but I am not sure what is it you are exactly looking for so if you could be more specific that would be helpful and I will see if I can answer such a question then thank you sir can we can we really can we redesign the bit-quit and the approach point of the HRSG after when we are doing the optimization of the system so I don't understand what do you mean by redesign you want to change the placement sir if the HRSG is connected to the free pressure as design right manufacture according to high pressure, media pressure and the low pressure then if we want to optimize that parameter of the HRSG then it can we redesign that bit-quit and the approach point of the system so I am very sure that you know if you are placing an HRSG at some point where you are so if you can tell me what the design would be I mean how is it that you are looking at different pressure turbines do you have various stages in the turbine and the HRSG is only providing the steam to one of the stages or is it provided into all the stages so unless that is specified I wouldn't be able to answer such a question however I am sure that if you have many stages you can always based on what your gas turbine exit temperature is you can always optimize the placement of the HRSG to you know get the best performance so I don't see any harm in trying to shift the positions of the HRSG to optimize whatever you want sir what happened if we want to increase the efficiency of that combined cycle that if the system will run into the open cycle system then the efficiency of the gas turbine unit will be the maximum that is mean gas circuit and if we want to increase the efficiency of the combined cycle then the gas turbine efficiency will be decreased and the steam turbine efficiency will be increased so nowadays the scientists are connected to that result how we increase that kind of the increase efficient increase the efficiency of the combined cycle okay so I see so what you are aiming at is you want to increase the back pressure of the gas turbine or adjust it so where the back pressure of the gas turbine is that what your question is yes sir I have sir due to the same mass flow rate into the gas turbine can we increase the efficiency of the combined cycle unit yes sir Michael well I would think so depending on how we have done it because if you are exit pressure of the gas turbine can be adjusted and the work output there will reduce if you slightly increase the back pressure but how it is affecting the efficiency of the HRSG the higher pressure in the HRSG if it is making the that is the boiler that is the HRSG more efficient I am sure that you can do an optimization in it you only have to figure out how the HRSG will behave at different pressures and whether the efficiency of the whole HRSG boiler system will improve so if you have some practical knowledge on that I am sure you can do some optimization thank you sir can we do the exergy analysis going into the system yes I am sure you can do all of this and we will cover the exergy topic tomorrow and day after but all of this can be done so I do not see any reason why you cannot do it so I think we will move on to another center now 1, 2, 6, 5 mother institute go ahead we can hear you hello hello sir what is the effect of temperature of over the wet bulb temperature this pressure based on the previous class so see the whole process of measuring the wet bulb temperature is such that whatever is the steady state temperature of the wick that is going to be your wet bulb temperature so those are going to be equal so initially you will just put at room temperature there on the wick and once you start blowing air over it finally you will reach a steady state and the temperature of the wick is the same as the temperature of the wet bulb because that is what the thermometer is actually measuring sir one more question sir it means if the wick temperature is lower and lower the wet bulb temperature goes lower and lower ok so let me draw this diagram I am not sure what your question is but yesterday we had drawn this T S diagram and we said that the point was here the view point was here if I begin here I will reach a particular wet bulb temperature ok so but if I begin somewhere else at a lower temperature I will reach a lower wet bulb temperature so that is definitely bound to happen thank you it means sir one thing I want to say that if suppose it means there should not be a single wet bulb temperature for a given dry bulb temperature no no no there is not a single wet bulb temperature for a dry bulb temperature it is a mixture of what the vapor temperature is and what the dry bulb temperature is so for a given combination there is only one wet bulb temperature but for one dry bulb temperature you can have any number of wet bulb temperature depending on what your vapor pressure of the moist air is so if the surrounding moist is very dry then you will have a much lower wet bulb temperature if the surrounding is very very moist or wet you will have a pretty high wet bulb temperature for your dry bulb temperature thank you if the Mach number is greater than one what will be the shape of nozzle and diffuser yeah so the question is if you are dealing with a supersonic flow situation what will be the shape of the nozzle and the diffuser so this you can answer if you look at the area velocity relation itself if you remember we saw that if you are dealing with a subsonic flow if you want to accelerate in the form of a nozzle we have to go with a convergent-divergent nozzle so exactly the opposite will happen if you are dealing with a supersonic flow so if your supersonic flow is the inlet flow and if you want to accelerate this you actually would like to go with a divergent-convergent type situation thank you 1016 KJ Somaia please go ahead if you have a question my question is basically based on the CF 15 in this problem AE equal to 2 throats 2 times of T throats and back pressure is reduced by factor 4 in this problem shall I take the back pressure 101 KPI yeah so the question is on one of the problems in the compressible flow exercises specifically CF 15 and you are asking whether you can take the back pressure as 101 in fact any value of back pressure is not required to be assumed at all what you can do is based on the information provided in the problem you just assume a P0 that is the upstream stagnation pressure and with respect to the upstream stagnation pressure all calculations can be done so in terms of P0 and there also you are not assuming any specific value of P0 just in terms of the symbol P0 you can calculate the entire problem so there is absolutely no reason to assume any particular value this problem is to be honest with you is not that obvious and this will require a little bit more thinking than what we have covered in the lecture so as I had announced earlier what I am going to do is I am going to actually put up the entire solution over on Moodle so my request is if you do not mind waiting for a couple of days and then in case you have any more trouble in understanding that solution then you can write it on Moodle and we will be able to answer it thank you 1176 Sir can you define the standard conditions in the process of combustion with regard to the STP and NTP so I think I did tell that as far as combustion is concerned the standard conditions are one atmosphere and 25 degrees 10 degrees so this is what is considered standard for combustion and all values of H or all reference values are referred to this value so that is about it I mean as far as combustion is concerned this is where the reference lies in other topics the reference can lie elsewhere that is about it I mean we should not try to connect what could be standard elsewhere to what is standard here in some cases people talk of normal temperature and pressure where 0 degrees is taken as the normal case but as far as combustion is concerned the standard is set at 25 degrees and the pressure is 1 as far as here thank you I think both for products and reactants how do you correlate these products and reactants enthalpy of the species with regard to the whole enthalpy or the universal enthalpy what you can call that so I am not sure what you would mean by universal enthalpy because this is totally irrelevant for enthalpy as far as we are concerned we are only bothered about differences so it is up to us what is the standard anywhere that we want and measure any difference that we have and hence you will realize that in combustion we have decided to put elements in the natural state as 0 at the standard state which is 25 degrees and everything else we are calculating based on how much energy we require to get to that state and then after that you realize that the H is just Cp delta T you integrate Cp delta T you know change delta H is just Cp delta T what you can see is that all we have done is that 25 degrees we have just assigned numbers to the Cp so that the enthalpy of reaction can be calculated now as long as you have done it consistently you could have used any other numbers as long as the enthalpy of reaction would come out correct at 25 degrees after that everything calculated correctly as Cp delta T everything else also will be correct so what is really important is to assign correctly some differences which are logical at 25 degrees after that it is just purely using Cp delta T thank you there is one more question related to the psychometric chart knowing the geographical locations of the place and also knowing the standard conditions like pressure and temperature to prepare the psychometric chart for a location yes sure I mean if you know the pressure at a particular place you can use that and create a psychometric chart for that particular place so that is perfectly fine in fact it is best to do that if you want to have accurate calculations for your refrigeration and air conditioning is there any practical irreversible adiabatic process you want an example of an irreversible adiabatic process yes sir yes so any kind of frictional flow where you do not have heat transfer is a regular irreversible adiabatic process 1079 zeta institute please go ahead if you have a question can you give an example of quasi static process okay I mean quasi static is something which was done in such a way that you are slow enough that at every point you have equilibrium so for example you can just take a piston cylinder system and let's say the pressure is high inside but you just let it expand a small amount so that immediately you are at equilibrium again and or the pressure and temperature within can be easily defined now what happens is that in most cases let's say the pressure inside is 2 bar and outside is 1 bar if I just leave the piston it will immediately expand and during this entire expansion process the pressure inside is not defined at all because at every point things are different so that is a regular past process that occurs and this is what occurs everywhere whereas in a quasi static process you would have been able to define the temperature and pressure very very at every step you would have been able to define it so it's very rare that you can actually do this practically but we can only give examples because these are hypothetical cases that we can tell you that this is how things if you do it's a quasi static process that you let the piston expand as slowly as possible so that every time the internal pressure equilibrates and you have one defined pressure within the cylinder and hence you can calculate all its other properties so that is what you would mean by a quasi static process thank you. One question please. Sir can you tell me about the entropy only we would know that the entropy is a measure of randomness can you tell me what is the exact definition of the entropy. I think you should realize that this is something that we have kept as far as entropy was concerned you know we defined something with respect to a reversible process at dq by t so you as far as we are concerned that is it that is the definition of entropy please do not try to ascribe some kind of a physical meaning to it and unnecessarily confuse yourself I think earlier also someone did ask the same question how do we use it and I am sure that if you have taught cycles you will realize that you use it all the time to ensure or to figure out whether your process is possible or not possible and how far away from ideality you are so all your cycle analysis is entirely done using this property entropy that we have you know generated or created for our convenience based on the second law so the second law is a certain statement and we have somehow you know come up with this whole idea of an entropy which we can actually use to see whether our cycle is possible and if it is possible how far away from ideality we are so just take it think of it as a quantity that we will use to figure out whether some things are possible or not thank you please define the classes in equality with the practical example also please so I am not sure what kind of example you would want on this clausius inequality because it is something that we have created in our train of thought that is we started with second law statement and we went through these various statements just to come up with an idea of what we can use and what we could use finally was the you know some kind of quantity that we invented and we called it entropy okay so all this in between steps it would be pretty hard for me to come up with some kind of an example there but these are ideas that went in during the formation of this quantity so give me some time let me see if I can think of something else I don't think one should worry too much about what the practical significance of some of these other quantities thank you 1002 amal jyoti please go ahead my question is to phantagar sir regarding combustion while considering this rich mixtures we have considered co as a constituent of the product so while considering lean mixtures that is like excess air shouldn't we consider NOx also as a product there see it's up to us to make things as complicated as we wish okay so right now we are just taking to simple matter but the fact is that if the temperature goes high and if there is lot of oxygen available definitely NOx will be formed and we have to introduce the equation for NOx then the reaction between nitrogen and oxygen okay so such things can definitely be done but right now we were just keeping the whole topic simple so we will not delve into what to do with such extra things thank you okay one more question sir sir my question is to professor Purohit regarding the convergent nozzle what is the specification of it how to be specified a convergent nozzle we have got upstream pressure as well as the downstream pressure suppose we take the ratio of the stream and downstream pressure is there for a particular ratio all convergent nozzles will be behaving performing the same manner yes so if you want to describe the convergent nozzle in a universal fashion you can describe it in terms of the ratio of the back pressure to the stagnation pressure see remember that if you go to the isentropic flow table for example for a given ratio of the back pressure to the stagnation pressure you will actually get the same Mach number so it does not matter whether you are talking about one type of convergent nozzle or other type of convergent nozzle as long as the convergent nozzle that you are dealing with is conforming sufficiently to a quasi one-dimensional situation then we can say that all convergent nozzles are described in the same manner at least that is what my understanding is that thank you then how can we control the back pressure sir we will be discharging somehow so the question is on how to control the back pressure and that is the really important question actually see what ends up happening is that we describe the operation of these nozzles with the concept of keeping the stagnation pressure the same and controlling the back pressure in particular reducing the back pressure so in the laboratory setting you can do that what you can do is you can provide a vacuum pump on the downstream reservoir side and then using that vacuum pump you can actually create lesser and lesser back pressure while keeping the upstream stagnation pressure constant however typically in general you know if you look at a practical situation where this nozzle is going to get used it is exactly the opposite that the back pressure is normally going to be a constant but the stagnation pressure usually keeps changing so it is just a matter of convenience that we choose to describe the operation with the help of a constant stagnation pressure and a reducing back pressure you can do that practically but typically only in a laboratory setting in fact what I can suggest is there are videos available on on youtube as well as the Massachusetts institute of technology open courseware website where they are showing these kinds of experiments done in the 1960s and 70s and it is very useful to go and see some of those experiments that are now available on the net where you will see that they are actually in a in a laboratory setting able to control the back pressure using a vacuum pump sort of arrangement that they have implemented so it is possible but it is possible only in a lab setting thank you. The profile, internal profile at any point at all points between the upstream and back stream yes see yes so the question is about the profile the conversion nozzle whether it is standardized or not my understanding is that it is not really a standardized profile and in fact if you if you go back to our discussion and the discussions typically available in the text books and so on we hardly ever talk about the profile of the the nozzle all we talk about is that you can choose any profile as long as that profile is sufficiently conforming to a quasi one-dimensional type situation you can utilize this theory to at least estimate what sort of a performance you can you can obtain but my understanding is that there is no standardized profile for for you know neither the conversion nozzle nor for a CD nozzle for a CD nozzle though there is a standard procedure which is called a method of characteristics using which you can actually design a particular profile but even then that is not a very standardized profile thank you sir can there be any separation taking place inside a nozzle so the question is can there be any separation taking place in the nozzle and it is possible if you if you have very large angles in the divergent section so for example in case of a convergent nozzle it is not going to happen but if you are dealing with a convergent divergent nozzle in the divergent section especially if you for any chance if you are working in the subsonic condition and if the divergent section angles are sufficiently large then it is quite likely that the flow there gets affected by the adverse pressure gradient and you may get into a back flow for a reverse flow thank you hello sir my question is that how back pressure practically controlled in a nozzle in order to achieve the maximum efficiency so the question is how is back pressure controlled in a practical situation to achieve maximum efficiency the answer is actually that typically you are not in a situation to control the back pressure the controlling of the back pressure and the resultant operation characteristics as we described today in the class is just from a description point of view that we use when we discuss the characteristics of these nozzles however when they are utilized in any practical situation normally you do not have any control over the back pressure and what ends up happening typically is that you may have designed a nozzle for a certain pressure ratio but what ends up happening is that the stagnation pressure on the upstream keeps on changing a little bit and usually the nozzle is going to operate slightly off design one way or the other so the short answer is that in practice you cannot really control the back pressure you can control the back pressure in a controlled laboratory setting sort of a situation where you are maybe testing the performance of such nozzle but in a practical end application it is nearly impossible to control the back pressure thank you hello sir my second question is that in case of convergent-divergent nozzle at throat we consider the Mach number is one can you explain how that is yeah so in case of a convergent-divergent nozzle the situation is not too different than what it is for a purely convergent nozzle so you can imagine that you have a CD nozzle where there is an upstream stagnation pressure P0 let us assume that that is constant and then we are again able to control the back pressure and in particular we are able to reduce it continuously starting from a value of P0 so as you keep reducing it there is more and more driving potential in terms of the difference between P0 and Pb that is available to drive the flow through the nozzle and as you keep reducing the back pressure at some point the pressure at the throat will reduce to a value equal to P star or the critical pressure corresponding to which you will reach the Mach number of one at the throat and further if you keep on increasing sorry decreasing the back pressure what will happen is that because the nozzle is going to choke once the throat pressure becomes equal to P star or the critical pressure even if you keep on reducing the back pressure to whatever value you want the Mach number at the throat is not going to change from value of one thank you one to one zero go to institute please go ahead good evening sir this question is to Puranik sir this question is to Puranik sir in case of converging diverging type of nozzle how much does the surface finish of the equipment plays important role in defining the supersonic and sonic condition over to you so the question is about the aspect of surface finish on the performance of a convergent divergent nozzle this question was answered to some extent earlier also so the surface finish is indeed important and if the surface of the nozzle is extremely rough then what is going to happen is it is going to enhance the friction that the flow is going to experience so that way what is going to happen is the performance of the nozzle is going to start deviating from an ideal situation that we discussed today of what we call an isentropic situation because the fluid friction will make things irreversible and you will start going away from the isentropic situation that we discussed the second aspect that comes into picture because of surface imperfections in particular if the surface imperfections are in the divergent section is that there will be creation of oblique shocks within the divergent section because of these imperfections and because of the shock generation there is further increase in the irreversibilities and again the performance of the nozzle will decrease so ideally one would want to keep the the surface finish as good as possible that is what my understanding is thank you thank you over and over 1286 U V Patel College of Engineering please go ahead I wanted to ask what is the significance of wet bulb temperature and why it is required so I did answer this question yesterday that the wet bulb temperature basically what you really need is the specific humidity to carry out all your calculations and the relative humidity just to tell you how moist or dry the air is so since some things are not very easily measurable like the specific humidity we use some other quantities like the wet bulb temperature or the viewpoint temperature so from a practical point of view the wet bulb temperature is primarily used to get the vapor pressure at that particular point so that we can get the specific humidity so that is the primary aim to get the wet bulb temperature otherwise on its own there is nothing else that you would rather look at the wet bulb temperature next question is on the psychrometric chart the cooling and humidification are these processes possible simultaneously cooling and humidification so for example if I draw the psychrometric chart so what you want to do is you want to go towards the cooler side and you also want to go higher in specific humidity so you know the question is now you know what do you want to do with this see as long as you can put in moisture into the system at the cooler temperature you can try to attempt this so for example cooling and humidification is always done in a regular desert cooler you know you throw in moisture into the air and you cool the system and also humidify it so this is a very standard procedure if you want to you know cool the room using a desert cooler thank you there is a term chemical humidification can you please throw some light on it can you repeat what what is the term you talked about there is a term chemical humidification okay I am not very familiar with this but probably it is to do with the use of silica gel to dehumidify so for example rather than passing the air over some cold coils if I use some chemical which will absorb moisture you can actually dehumidify the room and probably this is what is meant by chemical dehumidification but I am not pretty confident if this is the correct answer I would rather ask someone and tell you but probably this is what it should be thank you okay thank you sir over and out