So, today as a part of this course IC102, we have two role plays scheduled. So the first one is from, I was going to say three idiots, but you will see some concepts being presented, play acted, and it should last about 20 minutes, but then we have the second one scheduled after that. So, let's get started. Jattu, go and plot a histogram using C++. Okay, sir. Welcome to C++. Sir. Sir, it's taking too long. Okay, then plot the histogram using Sylab. Okay, I'll try. Welcome to Sylab. H-I-S-G-P-L-O-T-X. Histogram. Sir, histogram. Very good, Jattu. You have plotted the histogram wonderfully. Now, get the mean of this data. M-E-A-N-X. It's 50 plus 85 plus 45 plus 60 plus 55 upon 5 and mean is equal to 59. Sir. Very good, Jattu. Now plot the median of the same data. M-E-D-I-A-N-X. Median. I'm going to arrange you in increasing order. You come here. And the median is 55. Sir. Very good, Jattu. Now, okay, now there are two data. There are two sets of data. Can you tell which has the highest variance of these two? Sir, I think V1 is greater than V2. Variance is a degree of spread of data around the mean which you can clearly see here. Very good. Jattu, you have made the right choice. Of these two data, can you tell which is the median and which is the mean? Let me try, sir. Sir, I think this is mean because mean is noise sensitive. Very intelligent, Jattu. You have done wonderfully. Hi, Jattu. Hi, Rancho. We will meet here after five years. In this place. Remember this date. And let's see which is the most successful. May I come in, sir? Yes, come in. You are from IIT, Bombay? Yes, sir. Very good.  Mood-eye CG? Yes, sir. 9 plus CPI? Yes, sir. Tech-fish manager? Thank you, sir. Congratulations. You have been selected for job. Thank you, sir. Thank you, sir. Hey, Rancho. What's the mean salary of a company? Minus 40,000. Minus 50,000. After five years. Hi, Jattu. What happened? Hi, Rancho. So you can clearly see that Chatur is still sad. Although the mean salary of Chatur was greater than the mean salary of Rancho. But actually the mean salary also accounts for the salary of the CEOs and the salaries of employees. In case of Chatur's company, the CEO was getting an extremely high salary which led to an increased mean. But the employees were still getting low salaries. But Rancho was smart enough. He decided that Mood is the best way here and to choose a measure of central tendency. I wish I would have understood the concepts instead of mugging them. All is well, all is well. I think Virat Kohli should be given a man of the best for this tournament. I think it should be Zangaka rather than Virat Kohli. After all, he has been more consistent according to me. No, Virat Kohli has scored more number of runs. Okay, just wait. Chatur, can I have the mean of the runs scored by these batsmen please? M, E, A, N, Zangakaara and Virat Kohli. We have the data here. Virat Kohli has scored more number of runs than Zangakaara. Yeah, Virat Kohli has scored more runs. But see, I don't think this is a correct judge for checking who is the man of the CEOs. Just look at their consistency. Let us have the data about the variance. Chatur, can I have the data about the variance of each batsman? Variance. Thank you, Chatur. See, the variance of Zangakaara is very low. He has been more consistent and he is a very reliable batsman. So I think he should be the man of the CEOs rather than Virat Kohli. Okay, I agree with you. Okay, so the man of the CEOs is Zangakaara. Zangakaara, can we have you on the stage? Here. You are the man of the CEOs. Thank you, sir. Thank you. Hi, Virat Kohli. No matter, man. All is well, all is well. I said I will do it, bachu. All is well, both are. Okay, whatever, whatever. Thank you. Thank you, audience. Hope you like it. Now I would like to introduce all our participants. Myself, bachudan. Himanshu Malhotra. My name is Anuj. I am Salih. I am Aman. Baljeet. Rupak. Himanshu. Shree. Tarun. Rishabh. Thank you all. All is well. So we are waiting for the other batch to come. In the meantime, if there are questions, there have been a lot of questions on my personal mail. I didn't reply to those. Are there questions that we should address before the quiz as they are getting ready? It will take about 5-10 minutes for them to set up. So there was one question on what is going to come in the quiz. Whatever we have covered in the class is included. Okay? And so about, there were questions about Sylab. Whatever was covered in the class and whatever is required to solve the assignment in the simplest possible manner. One can, of course, come up with a really complicated way to solve the problems, but I am not talking about that. Okay? So that is a portion. Are there still, are there any other questions regarding the portion? Whatever is covered in the class? And also, any questions, how many of you use the email address to which Moodle posts go? Either you use it or you should, or you have a dot forward. Because all my interaction is only through Moodle. Right? It is not possible for me to announce anything individually. Right? So I only go through Moodle and you should configure your system in such a way that either you access the email regularly or you put a dot forward. Is there anyone who doesn't do that? Are there people who think that this is not okay? Do you all check your Moodle account? Okay. All right. Is there any other questions? So some people had asked what kind of questions will come. So I could ask you to write, if you take Sylab for example, I could say, here is some data. Give the command for calculating mean or is plot or something like that. Or I could give a code that may be right or wrong and ask your comments. Planning to do most of them multiple choice, but possibly I will have two things to guess. So you will have set of some and another set so that unless you have both of them correct, you will not get the mark. So we could do something like this. I have not thought about, we are still in the process of deciding the exact nature of the paper. It is also likely that we will have different questions so that your neighbor will not have your paper. The other thing that I would want to point out is I would not allow borrowing of anything. No borrowing of pen, pencils, ruler, eraser, nothing. Okay, calculator.  Right? I will not borrow, I will not allow borrowing of anything. I don't want any excuse for talking to your neighbor. Okay? I will enforce it. If anybody is doing it, he will get a zero in that quiz. That's it. Is that clear? If you need something, if you think you need something, please bring it. I will not allow borrowing of anything. It may be just a pencil. It may just be a pen, but I will not allow it. You want something, you bring it. Okay? Any other question? I think Sylab and then the course, the theory portion. Theory portion also, we will whatever is covered in the class. So if it is a simple calculation, I could ask you for example to calculate the mean. I mean one is to say that how will you do this in Sylab? Then there you will give only the command. But I can actually ask you to do some calculation. Okay? And descriptive questions may not come because we will also have to think about grading. Now there was another question on marking. Okay? That was the other question that I have not answered. So we have, so end semester is 50 marks. Mid semester is 30 marks. That's already as per the institute rules. So we have 20 marks at our disposal. So what we are going to do is five marks are for general activities. It could be project, whatever. Seven marks for the first quiz. Eight marks for the second quiz. Okay? Five, seven and then eight. This is what I have thought about. Any question? Is that okay? Yes? So I think the second batch also has come. If there are any questions in the meantime, they will take another five minutes to get started. There is any other question you can ask me. So have I answered all your questions? Is there any other questions that I should answer? No? So how many of you think that we should do things like role play? Just raise your hand. Okay? All right. So we, during this semester, we also spent some time on, like, crossword. How many of you think it's a good idea? Once in a while to do that. Okay? We also played, thank you. We also played hangman. How many of you think it is a bad idea? How many of you think it's a bad idea? Hangman. Okay? Why? Why it is a bad idea? How many of you think it's a bad idea to have crossword? There are a few. Okay? So why it is a bad idea? Is it a waste of time? That's why it's a bad idea. Have you seen the survey? Yes, sir? Okay? So please fill that. I will ask Manas to add one more page to take feedback of the way this course was conducted till now. That will also be appointed to the other instructors. After this week, I will not be teaching your class. Professor Siddhartha Ghosh of Civil Engineering will. Thank you. I'll be finishing my portion, although I'll be the overall instructor for this course. So I would like to create that survey. One more page. I'll ask Manas to do that. So if you go to the same page, if you go to feedback for this course, then the feedback that you give in that will be useful for the other instructors. Right? If you have some questions to include, what questions to include, you can actually, in fact, I can create a thread and model. What possible questions we should have so that we get some idea of what should be done, what should not be done. Okay? I have not received many questions for the quiz from you. I received many answers that said zero. But questions, there are very few. So I think we have set 5 o'clock today or 12 o'clock midnight today. Otherwise, I'll set the paper. For, as far as the silab submission is concerned, I would only, we would only check whether your programs work. I will not really check. Some people said that they didn't use the formula for me, but they actually summed it up and divided. So that is okay. I have no problem with that. I didn't tell you that you should solve this program in a particular way. So any acceptable, any equivalent program code is okay. Okay? And some of you, how many of you have had difficulty accessing Moodle? There are some people who have, who could not register in time, whose Moodle page shows up and so on, didn't show up and so on. Is there anybody like that here? So there are some people, but I'm glad to say that 727 people submitted their assignments, silab assignments. So how many of you think that silab is reasonably easy to use? This is a story about how a stock market welcomes a layman. How can one survive the temptations of investment? We present you the story of Mini Dutta, who has inherited a fortune is 21 years old and is bored with her monotonous family business. So let's hear to the story of Mini Dutta, who follows a short shortcut. Oh, what should I do? Where should I invest? Which company should I invest in? You seem to have some problem in life. I'll help you. Oh, I'm so confused. I just don't know anything about these statistics. They confuse me so much. I'm just a beginner. Oh, beginner. Then you have met the right person. I'm a broker. Everyone knows me. Even the Tata's and the Ambani's have learned the ABC's of stock exchange from me. Come, I'll help you. Oh, wow. Then please tell me which company should I invest in. I think you should invest in this company. It has a positive correlation. What's that? See, if the stocks of some other company increase, then the stocks of this company are surely going to increase. So it will be profitable if you invest your money in this company. Okay, I'll do that then. The stocks of the company have fallen down. What do I do now? Broker, where are you? What happened? Why do you panic? The stocks of the company have fallen down. All my money has been wasted. Don't worry. I think you should invest your money in this company now. See, they have a negative correlation. You know that. Okay, I have nothing but to trust you. Thanks to the broker. Mini Dutta has invested in every possible company. And let's see what's happened now. This company has also fallen down. This broker has fooled me. Oh, no. Oh, no.  You don't know anything. I just can't help you now. With investment comes risk. And do not ever forget the conditions always apply. I'm the broker. I know everything. Even the Tata's and Ambani's have learned the ABC's of stock exchange from me. Come, I'll help you. Thank you. Now let me introduce our group. Deeksha as Mini Dutta. Sonam as the broker. Pratibha and Amrita as the banks. Myself, Pranosh. Thank you. I was thinking that we would be short of time, but we finished early. So you are, I had our associate dean, academic programs also has come. If you have any feedback for him, you can tell him either now or later. I want to introduce Dr. Sujata Jagannath, who has flown all the way from Bangalore to help organize this. She has a PhD in electrical engineering from the Indian Institute of Science, Bangalore. And she's into pedagogy, educational methodologies, how to increase student interest in courses, different ways of teaching and so on. When I was the head of CDP, we signed an MOU with Mission 10x. Mission 10x is a nonprofit trust established by Vipro. So we have been interacting with them closely. So I took the liberty to invite Dr. Sujata Jagannath. She came yesterday itself. In fact, she was here at 12 o'clock, 11.30 yesterday morning. Then she was in the lab throughout the afternoon till about 7 o'clock. Talked to everyone of the organizers, and then once again she came at 7.30. She came just for this. I would invite her, want her to say a few words. A very good morning. It's been a pleasure in IIT. So our interaction with Professor Kannan has been extremely learning aspect, as well as very nice and cordial experience for us. Mission 10x is the project for which I'm working on. And this focuses on enhancing teaching learning process in engineering classrooms. So in this context, we have been interacting with IIT and specifically Professor Kannan has been the key person with whom we have been interacting. And this was a very good opportunity for us to understand how do we enhance the teaching learning process. And what I appreciate a lot is, after I came yesterday and we started and all the Rishabh and the other group and Ayesha and the others, after meeting, after discussing, and they have put in a lot of effort and we could see the kind of output they gave today. So my whole heart rate thanks and appreciation to one and all here. I'm sure all of you enjoyed this as well as we have taken the learnings from that. Thanks a lot and I look forward to continuing working with IIT. Thank you very much. So, okay then, so please remember to, we are going to create, I'm going to request minus to add one page in which we want to get your feedback. Of course, some of these things are possible. See, we have always complained about large classes. There are some problems. For example, I cannot see the person who raised their hand. Don't even know who that is, okay? I cannot have face to eye contact unless you sit somewhere close. So there are some disadvantages, but there are some advantages too in that it is possible, you know, we have a very large spectrum of students with varying interests and hence it is possible to organize different kinds of activities which will cater to different population, different samples in the group. And it is also possible to, it is possible to concentrate our effort. In the sense, for example, if a faculty member, for example, we have four faculty members for this course. Now, if this is divided into, let's say, 200 student class, 200 into four, then each person will have to spend, will have to deliver the entire, all the lectures. So as a result, what happens is, as far as IIT's load calculation is concerned, teaching six hours for 750 students is considered equivalent to teaching, let's say, 25, 24, 26 classes for 200 people. It is considered equivalent to load. As a result, it is possible for a faculty member to put in a lot of effort to make those six lectures really count. So I know that some of you do not like large classes, but there are some benefits also. Whether I would have done the same thing if I had had 25 classes is not clear to me. I may or may not have had the time. I may not be able to spend so much time on every lecture. I did a lot of reading, mainly to identify interesting topics that will convey something useful in the class and that will also be relevant to the course in the rest of the things. So it may not be possible to put in so much effort for every lecture if there are going to be, let's say, 25. So anyway, this is something that we have to keep in mind. What we did was we made a conscious decision this semester to go through the feedback given by your seniors. How many of you have seen that feedback? Last year's student feedback. Is there anyone who has seen it? I'll see if I can upload it. So you will also know they may not have seen it. There is nothing confidential in that. It is an anonymous survey and they have talked about, for example, they said that do more computations. So we have done more computations. 727 assignments have been received on Moodle. And the main objective of that is to make you use Sylab and see how easy it is to use. It is to convey that idea. So I'm heartened to see that many of you raised your hands when I asked the question how many of you like Sylab is easy to use. Is there anything else? Would somebody want to come and say something? Any of you, if you want to say something here, please come and say we have about five minutes. Okay, hi everyone. I'm Ayesha. I'm in the fourth year. So I'm your senior here. I just want to say we didn't have this course which you guys have. And we realized that how important this course is only when we are doing a BTP and we can't really use MATLAB but we don't know if we have to sit and learn that before we even start reaching any conclusions. So I think this is a very important course for all of you so that you understand basically how you're going to use this data because even once you get a job, since we are all IIT and we're expected to infer data, we're not going to be the ones who are going to be collecting all of this. So inference comes only when you understand what you're doing in courses such as this. So I think it's very important whether you get into any kind of job, you'll have to infer things, you'll have to make decisions and such kind of courses is what is going to come to your use. So I really think that please take this course seriously. I think that's why it's been got into your new curriculum in the first place so make the most out of it. And Professor Kanan has tried a lot to make this at least the first six lectures very interactive. I just hope you people appreciate that effort and try and work hard, that's it. Thank you. Is there anyone else who would want to say anything? So I would request you please come for all classes in large numbers. All of you please come because the faculty members are going to take a lot of effort because each one is going to teach only six classes, remember that. So please do come to the class, right? And please also come to the tutorial classes. There was some confusion about splitting you into numbers. Is there a class representative or a year representative? Academic representative? No? Okay. Yeah, it'll be good if there is somebody who will represent or a few people or ten people or one person per hostel, I understand. But it'll be good to have somebody so we can talk to. Of course Moodle is a great democratic institution. You put it then everybody gets to see it. Okay. So if there is no other question, see you all on Wednesday, on Friday. Friday same time 8.15. We'll start the quiz at 8.15. Thank you. Thank you all.


the flow assisted corrosion in details. We looked at the erosion corrosion of metals, we shall continue that erosion corrosion now and then we will go on tothe cavitation corrosion. In the erosion corrosion we looked at the importance of erosion corrosion. We also saw how erosion corrosion can be different from the flow assisted corrosion. In the flow assisted corrosion it is the diffusion of the corrosion product that is red determining step. If it diffuses faster then the flow assisted corrosion rate increases. And so, the formation of the film is is essentially governed by the dissolution of the metal ions. In the case of ion it is Fe 2 plus majorly and certain amount of Fe 3 plus and then they reform as a in a magnetic oxide. And the role of flow is to retard the formation of this magnetic oxide. And as the flow is higher the film becomes thinner and the film also becomes rough you can say to some extent. We saw that the the the factors that affect the flow assisted corrosion or material. In the case of steel you add chromium and it becomes strongly oxide forming chromium the flow assisted corrosion decreases. And the environment you know what are that? The pH is one one factor, the other factor is the velocity, other one is the temperature ok. Let me look at the oxygen content ok. More importantly that the the the flow assisted corrosion goes through a maxima. And the maximum temperature depend upon with single phase or the two phase flow irrespective of the velocity that happens. Velocity increase of course, the erosion I am not I am sorry this is flow assisted corrosion increases. So, that and so that is that is this interesting thing that high temperature they do not really happen, boilers they do not happen at all. The increase in oxygen content also lowers the flow assisted corrosion because it facilitates the oxide formation on the surface. So, that leads to the the what I call as new water treatment called as the oxygenated water treatment in some of the boilers. Oxygenated treatment may have some problem that we are not going to discuss now here. The other aspect is some is is a mechanical effect and flow and related to that actually ok. And the difference upon the factor like the velocity, the pressure and the the turbulence that they are going to be there. So, they are all going to contribute to the flow assisted corrosion and turbulent means design also plays an important role. In comes erosion corrosion we say the damage is really there is an impact and leading to film damage. And there is a film damage of course, the corrosion production falls. So, over year 2 increase in turbulence would increase the erosion corrosion. The erosion corrosion would get accelerated when you have solid particle suspensions actually. And so, that is a key issue in the erosion corrosion of metals. We saw the various factors that affect we listed rather the various factors affecting the erosion corrosion and they are film formation, the film stability, other is the velocity and the next was on the materials. We saw the film formation and film stability in terms of film characteristics right. What are the characteristics we talked about? We talked about the hardness, resilience, porosity and you know loss of porosity rather I think, absence of porosity, density ok. And the ability of the film to reform that probably we did not discuss ok. If the foreign film gets damaged how quickly the film can reform on the surface. The next aspect that we will be discussing now is on the velocity. One thing that you might look at is we can generally say that that when the velocity increases erosion corrosion increases. But we also know that there are other forms of corrosion like pitting corrosion and crevice corrosion they all drop when you have velocities right. We have seen when you discuss the pitting corrosion and crevice corrosion topics. It is also necessary to understand that there is a critical velocity above which the damage is become significant right. And this critical velocity that we talk about it is it is material dependent material and of course, the environment dependent. Now, if you want to just have a feel of it ok, I just give some data here ok. How the the the corrosion rate the erosion corrosion rate will change depending upon the on the on the materials ok. Suppose, you take say material let us take copper admiralty brass and you can take let us say C 706 and this is copper nickel right. This is copper technical right and you also have C 715 of course, we need to put some 0s here ok. This is a copper I think 30 nickel. We also have C 722 and this consists of some alloying elements like you may have some iron maybe some nickel you know not nickel iron some titanium and things like that. If you look at copper in fact, it is it is very interesting low velocity right. If it is going to be less than 30 feet per second all are a problem. You know why? You take a pipeline you take an heat exchanger where the flow velocity is low and they are not the right material to use. Any idea about it? What do you think? Low velocity is also a problem. See most of the process fluids might have some kind of some kind of particles you know second particles you know dispersed particles. Sometimes in heat exchangers if you see water may be some fowlent and the velocity is very low then what I mean they start depositing on the surfaces. It is not erosion corrosion problem it is another kind of problem they are going to get and so, you normally have a problems in these cases. So, you can if you if you want to rank it in terms of the the properties I say this is this is poor I mean in terms of the erosion corrosion resistance I would say this copper is and of course, you can also go for stainless steels or titanium. So, maybe you see what? See if you increase the velocity you would find that stainless steels are good titanium are good this I would say I would say moderate levels ok and they could be moderate levels and it could be moderate levels ok. This this can be even you ok. So, these all you know all these copper based alloys the velocities may be around about I see probably about you know you can go up to maybe yeah about 6 to 9 feet per second velocity that you can go for it this is higher ok. So, beyond that the copper based alloys would have a problem. So, higher velocity means stainless steels and titanium alloys these are the ways that that you can use you can use it. But titanium alloys cannot be used I mean titanium alloys can be used, but the stainless steels of all categories cannot be used in seawater application right there are some problem. What is the problem there? We use a stainless steel in seawater application what is the problem? Yeah it could be pitting corrosion, cavities corrosion. So, you can only use a highly alloyed stainless steels like super duplex or hyper duplex stainless steels or go for super austenitic grade stainless steels. Now, if you look at the copper based alloys compared to the stainless steel stainless steel is much harder and copper based alloys are reasonably softer. So, the utility of these materials are you know restricted based on the flow rate applications. The flow rate is increasing and I think the choices are going to be much limited ok, you go for stainless steel or titanium based alloys. But the same logic if you look at if you look at a cast iron and steel. So, which one do you think will be better from the erosion corrosion point of view ok. So, this is this is better this is inferior compared to that. Sometimes the velocity can have beneficial effect right. This they have reported for 347 stainless steels in red fuming nitric acid. The formed corrosion rate it drops like this may be thin about let us say 12 feet per second it drops like this. In the case of the case of aluminum alloys slightly different corrosion rate versus velocity the reason being in aluminum alloy what happens is. So, aluminum alloy that you have it forms two kinds of films aluminum nitrate and the other film is AL2O3 film. You know some nitric acid. The aluminum nitrate nitrate is is a salt film and if you increase the velocity the salt film just gets disturbed and goes away. Aluminum oxide is quite intact. So, the so initially the corrosion rate increases because of the removal of aluminum nitrate salt product. After this what happens the aluminum oxide remains on the surface and subsequent velocity it does not disrupt AL2O3 stable. So, the corrosion rate does not change after this. So, here so this means here removal of of ALNO3 rice salt. The mechanism here is different. The mechanism here stated mechanism is that the corrosion of steel in nitric acid leads to the formation of nitrous acid and the nitrous acid is corrosive corrosive. Now, what happens the flow when there is a flow what happens now? The nitrous acid is removed from the surface. So, subsequent corrosion by nitrous acid is avoided. So, increase in velocity decreases the corrosion rate because the accumulation of nitrous acid does not occur because of the flow velocity. The next thing that we will talk about is the turbulence. Now, the turbulence can happen if the surface is not smooth, if there is a change of direction or if there is reduction in the diameter of the pipeline can happen. So, higher the turbulence higher is the erosion corrosion. This is very predominant in the heat exchangers. We have seen the heat exchanger overall when you discussed I think galvanic corrosion some of you might recollite right. What is that if you recollite? So, you will have lots of tubes right I think. So, the liquid you know enters through the header right the shed and there is almost a 90 degree turn and it enters. The maximum turbulence they occur at the inlet and as it travels towards inside the degree of turbulence decreases. So, the maximum damage in the heat exchanger it occurs at the inlet right. So, that is why it is called as inlet corrosion. Now, how do you really avoid this? One way people avoid is they go for inserts they are called as ferrules right. So, this is a tube for example, this is the it is not necessary they do not protrude they just go inside you know I think ok. I have just shown it for convenience. Now, this ferrule the advantage of this ferrule is that the ferrule can undergo erosion corrosion and when it gets damaged you can replace it and put another ferrule. So, the light of life of the heat exchanger significantly increases. But there is still a problem what is the problem? When the fluid or liquid enters here there is going to a small step this is a small step. So, there can be erosion corrosion here. So, so you need to smoothen out you need to make it like a feathery kind of you know tappering off as to be done in order to reduce this erosion corrosion. But use of ferrules are being done. So, it is industrious accepted practice to minimize the inlet corrosion of heat exchangers impingement is there ok. Impingement is a direct impact. So, the impact can be high here. So, more erosion corrosion can take place this is impingement attack where impact takes place and if you are going to have soil particles then the extent of impingement attack becomes quite significant. And these are common it can happen in gas turbines, it can happen in cyclones, it can happen actually right. So, some of the units they really feel you know in gas turbines where where do they happen? It can happen in the turbine blades right, it can happen in aircrafts external part it you know it moves at a very high velocity it can happen. Some cases you can change the design and you can improve upon, but there are cases where you cannot cannot change the design everywhere right, but where there is a possible we can change the design. For example, here you do not make it you know you increase the one way to do is that increase this radius. When increase the radius what happens now you you will have less impact, less turbulence can can occur. The other way of course, to visualize this is that you take this part little heavier right, you make it as thicker where you know for sure that you are going to have impingement taking place. See it can happen in heat exchangers you know the you know you in in in heat exchangers you have baffles you know sometimes they hit right. So, it is possible that that you can increase the thickness of that you know more for that life of the overall component can be increased significantly. So, when you look at this one thing becomes clear that the design plays a very important role in minimizing the erosion corrosion right. When I say design all that reduces the impact impingement, all that reduces the turbulence can increase the erosion corrosion resistance of the system. So, it is it is a design parameter as much as material parameter as well as the the environmental conditions that are operating a given system. Let us go to materials. What should be the material property you think that would give you a better erosion corrosion resistance should be hard. So, it should be a mechanic from mechanical properties point of view it has to be hard. Is sufficient to have only hard thing? What else? The operation resistance comes from hardness I mean you increase the hardness generally they are resistant to that. Is the sufficient to be just hard? Yeah. So, it should be also having corrosion resistance of course, that is that is involved in the corrosion resistance package right. See corrosion resistance how can you how can you improve the corrosion resistance? Either the material can be noble material or it can be pass waiting material these are the criteria right. Let me give an example martensitic steel I have given some four examples here. I can give if you want I can give you even aluminum I can give you in lead if you want. Now, let us take for simplicity only the stainless steels steel family. Can you just compare and what will be your view about just erosion that damage resistance and erosion corrosion resistance damage please you know listen to my question you have four different type of steel you can have two types of damage mechanism one is erosion other is a erosion corrosion. So, what will be your view? Suppose I take a I take for example, simply erosion right how do you rank this one? Nobody yeah you are right then. So, when it comes to erosion of course, assuming that the hardness is same I mean I am I am not really going to vary too many things right assume that the hardness of martensitic steel and stainless steel are going to be the same ok. So, if you look at erosion both martensitic steel and martensitic stainless steel will be almost the same when it comes to erosion corrosion martensitic stainless steel will be better compared to martensitic steel. In fact, it might so happen the ferritic stainless steel may be better than even martensitic martensitic steel depending upon the corrosive nature of the environment. The environment is very corrosive it is possible that erosion corrosion resistance of a ferritic stainless steel could be better than erosion corrosion resistance of a martensitic steel right because martensitic steel generally are more prone to corrosion compared to the ferritic steel here. But the most vulnerable among all this among all this from the erosion point of view which is the most vulnerable here 1, 2, 3, 4. Ferritic. Ferritic could be more right next better would be ferritic stainless steel of course, martensitic steel and martensitic stainless steel would be almost similar. So, I wanted to understand ok the concept of our development how it is it has been done. Aluminum and lead of course, if there are low velocities and we have less problems when velocity is increased then it is a problem. See this is very interesting thing it is not necessary that you can extrapolate at all velocity. At a normal velocity it is possible that the lead in lead you know lead for example, in sulphuric acid dilute sulphuric acid at static conditions at very low flow conditions lead may be good ok. Whereas, with a high velocity lead is softer so that fellow will not even withstand that actually. So, it is not possible to extrapolate you know at given velocities to higher because at higher velocities the mechanism of damage may be different is more mechanical damage dominated corrosion problems than the corrosion dominated problems. At low velocities what is the dominating mechanism? Low velocities is corrosion at higher velocities the dominating mechanism will be mechanical factor actually. So, it is not possible to just make extrapolations the way you want it actually ok. I would like to give an example of how these things really happen in practice. See there is one of the industries in India was making what is called as hydrogen generation unit. It was it was you know they had a license it is able to have engineering you know capacity. This unit was I think you know commission somewhere in the Eastern Europe. The hydrogen was generated from hydrocarbon. When it when it generated from hydrocarbon it consisted of hydrogen plus water. Of course, there will be some amount of some amount of carbon dioxide, some amount of formic acid or kind of stops, but these are very low quantities. If I want to give hydrogen to the user what I should do? I should I should strip the hydrogen from water carbon dioxide and formic acid. The carbon dioxide and formic acid they dissolve in water. So, when you remove water automatically this go away right. How do I remove water from from the gas? Yeah you hear it? Do you think gas will remain there? How do you do that? You are talking about industry unit they are going to produce a few tons of you know hydrogen right. You cannot use chemicals and all kind of stuff. Any other method you can do? No? Simple. Yeah. First of all you pressurize not sufficient lower the temperatures. You pressurize and lower the temperature what happens to water? Water will condense right water condenses and the air will be free from a gas will be free from water. So, that is what done people do in the industries. Now, when you pressurize it you lower the temperature water is getting separated this is a good water right. So, this is now pumped and they call this as process condensate in the industry. It is a nice water no chlorides and all, but what what does it have? What what does it have? It it it has carbon dioxide has got a formic acid. So, it is pure water almost like distilled water. So, what do you think is property? What will be its pH you think? It will be alkaline, neutral and what do you think yeah. So, it should be slightly acidic. Now, the whole line is under under a higher pressure right. So, you compress it you pump and then. So, there is a pump here it is a pump. So, there is a compressor here ok. So, this is called as a pump ok say condensate pump and this water is pumped to you can pump it to a to a water treatment unit and then to boiler you can do that ok. Now, the interest comes over here this is the pump. In the pump the fluid goes at a very high velocity right. So, what are the process parameters? These are some of the process parameters. You can see that the flow rate is is 15 meter cube per hour and linear velocity is what matters for us it is about 2.1 meters per second that is the velocity water goes. And other parameters like you know suction pressure and discharge pressure are given from the point of your corrosion these are interesting. Now, impurities of carbon dioxide, formic acid all the stuffs. So, the pH is between 5 to 6. The temperature is between 30 the Celsius and maximum of course, you can go to 40 degree Celsius atmospheric temperatures. So, they initially thought that in in the design they thought that that the pump should be made up of martensitic grade stainless steel. They were planning to have martensitic grade stainless steel, but somewhere something happened. Finally, when they just about to start the unit they formed as a typo problem instead of martensitic stainless steel they went for martensitic steel ok. So, they realized just one day before that this is the problem. Now, the whole unit hydrocarbon unit is a part of the refinerized system you cannot stop this you stop it everything will be stopped and they start running the system now. The good point was they were having standby pump because to know you know these are the you know units that can can go bad and so they do not want the system to be you know shut down unplanned shut down. So, they had a standby pump then they thought ok they probably knew that martensitic steel is not same as martensitic stainless steel. Then it is how they started operating one pump for about 3 hours then moved to another one for another 3 hours they keep on struggling between these two things actually happening at all. So, they were little worried. So, why they were worried was that if you want to order another one it will take another 9 months it is just not possible it is not just of the self it takes about 9 months to get the to get the new one actually is ok. This is about 27 its slide is 9 right ok. So, look at these comparison of these materials now between the martensitic grade ASTM A216 grade is a martensitic steel and ASTM A743 it is a martensitic grade I think stainless steels. The chromium is between 8.5 and 14 percent, nickel is about 3.5 to 4.5 percent ok. You know molybdenum is is range now. Now, they are worried because martensitic steel is is really you know corrosive and compared to carbon steels actually ok. So, what will happen? So, they started working alternatively and then they start called called one day and they said well this is a problem. It was indeed a problem. The issue here was different. Suppose you have pump 1 and pump 2, one pump operates other pump is standby and you keep a standby if this environment the pH about 5 is there stored the corrosion is not going to stop. Only erosion corrosion of course, is is reduced because there is no flow, but corrosion will not be stopping right. So, it is it is not prudent to keep the corrosive liquid getting stored. They might think that there is no erosion corrosion, but there is a corrosion at all right. So, one thing one of the thing that they can at least look at is monitor the thickness of the pump and see what happens. So, one thing you can do that right. Other thing that you can do is that I do not start alternatively at least start one for one week and keep everyone dry. So, that the flow does not corrode at all right. Otherwise what happens you are simply corroding both of them and you are not really happening. So, what was done was there advice that ok please do not start alternatively at least keep for about a week time and keep other one dry happens. So, then what happens then subsequently what we do is then you can make a calculations actually ok. You can make a calculation because you know what is the normal pH and all of course, it is very difficult to make exact calculation we can make some kind of comparison for this particular pH what what what is effective to happen at all. It is so happened they are I mean the pump was safe for 6 months by the time they can get a another unit. The point I want to emphasize here is that it looks simple between the martensitic steel and martensitic stainless steel, but a small error can land into a problem and can lead to unexpected failure can happen at all. So, that is something you do see happening in this. This is not very old this probably about 2 years yeah about 2 years back this incident happened and it was a one multinational company it is not that it is some spurious company dealing with this system at all. So, the point that we need to be looking at is look at the corrosion plus the mechanical the hardness properties are both are important. This is the passive current if I damage here current will rise it can go like that or it can go like this alloy 1 is going to your which is better alloy 2 is better. So, the alloy development program will take care of both the electrochemical and the the metallurgical aspect of of corrosion ok. So, that we we do not have erosion corrosion problems. So, let us give an example now. Now, you have iron chromium nickel chromium alloy let us take an example here assuming that the hardness properties are same which of the two will have better erosion corrosion assistance. You got my question? I am not giving other elements present here I am just giving the base alloy is iron based it is a nickel based I have chromium here and chromium here assuming that the hardness is same which of these two will have better erosion corrosion assistance and why what do you think? Certainly one will be better than other one do not you think so? So, what do you think? Chromium. Yeah. Nickel chromium may be you you guessed it right or you or you figured out the science of it ok. So, let us look at the science of it why do you think nickel chromium is better than iron chromium? So, relatively nickel is more noble compared to iron it is as simple as that ok. So, you have you you find that this is certainly it is it is better. So, those cast ions which are having more nickel or will be better than the one with nickel free cast ions ok. So, broadly that you can say the same is true in this case also right you take copper zinc and copper nickel right this will be better. Now, if you are going to add let us say copper zinc and aluminum suppose add to this. So, this is better than now if you take let us take the case of alpha brass and alpha plus beta brass which you do not do you think will be better in terms of erosion corrosion damage yeah. Alpha plus beta brass alpha beta will be better. So, so this is what you have to look at. So, I mean alpha beta brass as you metallic guys would know right this is a two phase one right the two phase will have a better toughness just hard compared to that actually right. So, if you look at here it is a very interesting thing that can happen in the limited extent dealloying erosion corrosion resistance. So, I do not call resistance here I say erosion corrosion both scales are going say manner ok can you plot how this will happen. So, there is a dealloy is concerned this guy will go like that corresponds to this right. So, what will happen for erosion corrosion something I will go right. Now, depending upon which is the dominant mechanism right if there is no flow very low velocities probably you choose alloys of this this this here right, but the high velocities you choose try to choose alloys somewhere here otherwise instead of dealloying they will fail by erosion corrosion damage. The other example is is iron silicon actually you are going to have 14.5 weight percent silicon excellent material for handling sulphuric acid is very used for impellers you cannot use for a pipeline there right you can use a for a pipeline iron silicon alloy of this one can you make a pipe out of this you cannot it is only cast product you know this is also brittle you cannot make. So, it is ok for the impeller pump you can do that no problem pump also you can no problem ok. So, the silicon forms a very hard silicon dioxide protective oxide hard oxide. So, it is it is certainly better you can also give an example let us say durimit is an alloy durimit 20 it is it is it is made only for the sulphuric acid applications actually consists of 30 nickel 20 chromium 3.5 copper and 2 moly. Take this versus a stainless steel like let us say type 316 stainless steel this is a 8 nickel 18 chromium it is not 8 nickel it says 10 nickel actually ok 10 nickel and you have about 2 moly durimit is far better from the erosion corrosion resistance point of view it gives nitric acid it gives in the sea water applications or going to be there actually. So, it is a combination of the hardness plus this is what required in order to have better erosion corrosion resistance that is a point to try to dry home in the discussion. So, we have almost come to the end of the discussion related to erosion corrosion and having understood the mechanism understood the factors affecting the erosion corrosion you should be able to tell how we can prevent or you can control erosion corrosion yeah and you just what is the what are the ways that you can do that. Material selection. One is a material select a better material that has good erosion corrosion resistance that that you know how it comes out it comes out from the hardness plus the corrosion resistance properties ok. Then what is the other important thing? Structure the turns the design. The design is is second most important thing you can have a design to avoid turbulence you may not avoid completely, but you can minimize it actually ok.  In fact, people talk about 20 to 30 degree is what is the radius I mean is the is the angle between the between the the turn you can talk about ok. What else you can you can look at? Filters may be we can use. Yes you can use some filters even even in the design also you can talk about using what you can use you can use you can use extra like baffles you can use ok to to see that it is not going to impact directly right. Again how how do you see this is not ok ok right. So, you see that you know the fluid you know. So, the branching the way how we want to make the branches there are there are there are only examples they are not exhaustive by itself. Look at over design you know place place over design where the critical parts we talked about the ferrules heat exchangers. So, wherever the other way of looking at is this it is going to damage impinge it should be readily replaceable you can able to replace it right quickly. So, that is also it is acceptable yeah you are talking about something yeah. What what is other alternative thing? Use of filters to remove solids. Yes use the filters to remove solids you can also talk about altering the environment right pH control, inhibitors all these stuffs you can do that. You can talk about hard coatings you can look at the time tested one what is called cathodic protection where possible. But not of course, everywhere you can apply all these methods and where possible. But what is the bottom line? The bottom line is the bring down the cast right and the bottom line is safety where safety is involved right. So, so these are the few available methods to control the erosion corrosion you want you can discuss more on this later. Let me just finish off this cavitation damage and I know this here we are already spend about close to 1 hour 20 minutes night I think. Let us cover this topic of cavitation damage.  There are several persons with a mechanical engineering background right you should say quickly what is cavitation damage? So, what have cavitation the pressure is different at different stages and this causes bubbles as pressure changes these bubbles can implode when they implode it can damage the surface layers of the turbine or the blades and other equipments. Is very correct ok. So, the cavitation damage essentially happens because of implosion of bubbles on the surface structure and this transfers huge amount of energy on the structures. This happens as you said in impellers in propellers in turbines turbines also you compress right you compress it ok happens. So, understand how these clings can happen in a in an impeller ok. You can consider a situation I am just giving a brief account given in the fontana book I will not go much details actually ok. You can consider a cylinder having water right. So, it is in contact with the tight piston right. So, your water and I have tight piston when you move this piston up what happens the pressure reduces right. Now, we know that the water can be boiled even at ambient temperature by lowering the pressure. So, it is possible that you can you can boil the water at ambient temperature if you are going to lower the pressure. So, as you lower the if you as you rise it up it lowers the pressure here then what happens now water evaporates when again it reverse this direction then there is going to be compression then lead to condensation. The bubble will start shrinking, but beyond certain level it cannot shrink then what happens then it is going to be implosion it implores and implores then it is a it is a shock right. It exerts a pressure as much as 60,000 pound where is less 60 psi something like that we can say and this pressure exerted can lead to plastic deformation. How can you verify there is a plastic deformation or not yeah fine, but it seems a small bubble you know it will not change the shape so much it could be a dent yeah it could happen, but but dent can happen you know you could simply corrosion also can have a you know a dip. But with the plastic deformation how can you do it metallurgists should tell what do you see you will see a slip step you are going to look at this in the microscope and you see nice deformed layers right you see slip steps that is indication of the plastic deformation of metal. To summarize that to cavitation to occur it must have a region of low pressure where the liquid will evaporate and then the evaporated you know vapor will be subjected to a higher pressure. The pressure is sufficient enough to condense and lead to implosion and that leads to the plastic deformation of the material. If you look at the mechanistic point of view we want to draw draw some kind of schematic diagram of what happens in the material all the metals are covered with some oxides right like this it form a bubble here when you increase the pressure what happens bubble implores this gets damaged when the area is dating damaged then it gets corroded again right. Now what happens is very interesting now the formation of the bubble over here is much easier right because it gives you additional surface. So, the bubble can go and rest on this then what happens then again implosion film damage and what happens then there is going to be again corrosion film formation then again again starts right again bubble will come and form on surfaces starts continuing process. So, the the pit grows primarily because the surface becomes rougher it becomes easier for the bubble to sit on surface. Please notice that the very implosion by itself is not a problem if it happens within the liquid I have no problem it happens only in the surface it causes the damage. So, the cavitation damage that is occurring here more of a mechanical damage and corrosion is a consequence of the removal of the film exposure of the bare metal to that and again the further damage comes by the mechanical process implosion of the bubbles. Of course, corrosion occurs why because the environment interacts and then forms a film and so on so forth. Now this also you know there are of course, several examples it can happen is this also depends on the design. Suppose I have a pipeline like this they want to join on to this pipe actually they reduced like this. Now look at this design here is a pipe the larger diameter smaller diameter you welder like this where do you think the cavitation damage will occur yeah just at the reduction area this is the reduction area right because the pressure is increasing. So, such kind of design you know mistakes it should be avoiding the impeller you cannot do anything right is the impeller works on that principle only there is a suction there is other pressure is increasing you cannot do anything, but these designs are you can be avoiding it actually. I talk to this many people will do this, but surely this is the place where you have problems for sure. So, how do I control the control of this? One of course, is hard materials coatings no you know of stellate coating cobalt containing coatings you can do that you can also have resilient coating see the resilient coating what does it do it it it just does not lead to plastic deformation right and you can also have it also means like rubber lining for example, you can have smooth surface what is the advantage of smooth surface it does not allow the bubble to stick on surface and use inhibitors the fact that inhibitors reduce cavitation damage means there is a corrosion taking place simply not a mechanical damage per se ok. So, that should come to the end of discussion.


Dear students, let me put forth to you the following question. Where would the mean of a symmetric distribution lie? I think many of you will have answered the question. You must have said that it will be in the middle. Yes, it is correct. If it is a symmetric distribution, the mean is actually in the middle of the distribution. But let us try to prove this algebraically. Let us do a proper formal proof so that it is established. Alright, question kya hai? Let a random variable x of the continuous type have a pdf f of x whose graph is symmetric with respect to x is equal to c. I am not saying that the origin of 0 is symmetric. In fact, I have said that the origin of 0 is symmetric that value is equal to c, that point is equal to c. So now this is the situation and what we have to show is that the expected value of x, the mean of x is equal to c. That is the point of symmetry. The mean of this variable also lies there. So how will we proceed? Let me give you a few hints to answer this question. We just said that we want to show that e of x is equal to c. So we can modify that and write it in a way that we may show that e of x minus c is equal to 0. I am giving you a hint that you should show that expected value of x minus c is equal to 0. That is the same thing as expected value of x is equal to c. And the next hint is that the expected value that you will get, obviously we are talking about continuous variable, so we will integrate the formula of our expected value. If we put that, then the integral will come. So you should break it. Break it into two parts. Write that integral as the sum of two integrals. The first one going from minus infinity to c and the second one going from c to plus infinity. After this, the next hint is that we will apply some transformation which will solve this easily. The first integral is let y be equal to c minus x. And the second integral is let z be equal to x minus x. x minus c. And apart from that, very importantly, use symmetry condition. And what is the symmetry condition? If a curve is symmetric around the value c, then the symmetry condition is given by f of c minus y is equal to f of c plus y. That is y. If the variable is being called y, then the algebraic version is f of c minus y will be equal to f of c plus y if it is symmetric around the value c. This is the first integral in which you have substituted y equal to c minus x. Then you apply symmetry condition. Now that I have given you all the hints, let us try to implement them one by one. First of all, let us write that integral the expected value of x minus c is equal to the integral from minus infinity to infinity of what, of which expression? The expression x minus c multiplied by f of x. Now, we are going to break it into two parts. So it will be equal to the integral from minus infinity to c of x minus c into f of x plus the integral from c to infinity of x minus c into f of x. Of course, it is necessary to write dx in front of it because the integral is not complete unless you write dx with it. But when you say it, all you don't have to say it. It is understood that if you are taking the integral, then you are writing dx at the end. All right. Now, as I gave you the next hint, that now these two integrals are here, so first of all, let us substitute it. Let y be equal to c minus x. So as soon as we substitute or transformation is a better word, as soon as we apply transformation, you know that we have to see the change of limits and we have to see the conversion of dx. Obviously, if y is equal to c minus x, then dy by dx will be equal to 0 minus 1, or not minus 1. And that means that dy is equal to minus dx. This is the first thing. The second thing is the change of limits, as x tends to minus infinity, y will tend to c minus infinity, i.e. c plus infinity, i.e. infinity. Let me say it again. If x is tending to minus infinity, y is tending to plus infinity. And the second limit of the integral was the lower limit, what was the upper limit? The first integral was c. So as x tends to c, y will tend to c minus c, i.e. y will tend to 0. So this situation has come, as far as the first integral is concerned. Now the transformation applied on the second integral, you can do that too. What is the transformation applied on the second integral? Let z or z be equal to x minus c. So then dz by dx will be equal to 1 minus 0, i.e. 1. So that means dz is equal to dx. And the change of limits, as x tends to c, z tends to 0. You can do it, it works out very simply. And as x tends to infinity, z also tends to infinity. Okay, now we are ready. Now we will put this in it. The transformation we have done, now apply the two integrals. So when we do that, then as you can see on the screen, first its converted version is minus infinity to 0. Note that I did not say 0 to infinity. Infinity to 0, and then what is inside it? Minus y into f of c minus y dy. And then the second plus, what is its situation? 0 to infinity z into f of c plus z dz. Now solve it for the first one. You know that if you want to interchange the limits of the integral, you want to make the lower limit upper and upper. So what happens? If the sign is first applied to it, then it will be over. If it was first plus, then it will be minus. And if it was first minus, then it will be plus. So let's apply that. By doing all that, what is the final answer? The expected value of x minus c is equal to minus 0 to infinity. That minus is over, but there was another minus inside it. So we are still having a minus. We reversed the limits. Infinity to 0. Now 0 to infinity is over, which is what we need and which is correct. So minus 0 to infinity y into f of c minus y dy plus 0 to infinity z into f of c plus z dz. Okay. Now last tip that I gave you, let us leave the second integral as it is. Just now let us focus on this first integral. The first integral is, we apply this symmetry condition inside it. Because we know from the start that our f function, that is a symmetric function, symmetric around the point c, then apply that algebraic condition in the first integral. And what was that condition? f of c minus y is equal to f of c plus y. So now put this first integral in it and it is in front of you on the screen and what does it come out to be equal to? Minus 0 to infinity y into f of c plus y. We wrote a plus instead of minus. Now after that, this expression for my dear students, you can also write this way that it is equal to minus 0 to infinity z into f of c plus z dz. That is why I called it z instead of y. Why? Because I am applying the concept of the dummy variable. Whenever your integral is a definite integral, it is not an indefinite integral, then the variable inside it, whether you call it y or z, or x or w, or whatever you call it, my dear students, it does not matter. Because the upper limit has to be applied, the lower limit has to be applied later. That variable has to disappear from the middle. So that is what is the concept of the dummy variable. Apply that here. Put z instead of y where it is written. After that, what is the final expression that we now have? The expected value of x minus c is equal to minus 0 to infinity z into f of c plus z dz plus 0 to infinity z into f of c plus z dz. If we are doing minus and plus one thing, then obviously the answer is equal to 0. So what we wanted to prove is that it has been proved. Expected value of x minus c is equal to 0, implying that expected value of x is equal to c. If our function c is symmetric, then the mean value of that variable, expected value of x is also equal to the same value. Expected value of x is equal to c.


Have you ever pondered the intricate mystery of the Holy Spirit? How does this divine entity play a role in our lives and what is its connection to Jesus Christ? Welcome to an enlightening journey into the pages of the Bible as we seek to understand the Holy Spirit. The Bible in ancient text provides profound insights into this subject. According to the Bible, the Holy Spirit is a part of the Holy Trinity, God the Father, Jesus the Son and the Holy Spirit. This concept is derived from scriptures such as Matthew 28 verse 19, where Jesus commands his disciples to baptize in the name of the Father, the Son and the Holy Spirit. The Holy Spirit is not just an abstract concept or a force, it is a person with emotions and intellect. Ephesians 4 verse 30 cautions believers not to grieve the Holy Spirit, implying that the Holy Spirit has feelings. Additionally, Corinthians 2 verse 11 shows that the Holy Spirit has the mind of God indicating intelligence. Now let's delve deeper into the relationship between Jesus and the Holy Spirit. The Gospel of John chapter 1 verse 1 states that in the beginning was the word and the word was with God and the word was God. The word here refers to Jesus. Moreover, John chapter 1 verse 14 explains that the word became flesh and made his dwelling among us. This means that Jesus the Word of God took on human form. This is a profound mystery that signifies the divine nature of Jesus as well as his human nature. The Holy Spirit played a significant role in the life of Jesus, right from his birth. According to Luke chapter 1 verse 35, the Holy Spirit was involved in the conception of Jesus. Furthermore, the Holy Spirit was present during Jesus' baptism, as seen in Matthew chapter 3 verse 16. The Holy Spirit also led Jesus into the wilderness to be tempted by the devil, as recorded in Matthew chapter 4 verse 1.  The Holy Spirit played a significant role in the life of Jesus, who is the Word of God made flesh. Understanding the Holy Spirit and Jesus is a journey of faith, guided by the wisdom found in the sacred scriptures. It is a journey that enriches our spiritual lives and deepens our understanding of the divine. Thank you for joining us on this enlightening journey. Stay curious, stay enlightened, and continue to explore the profound mysteries of our faith.