 in the last class we have derived the equations for design with elutriation right with elutriation and the last equations were 9, 10 and 11 where we have 1 minus x x b double bar is in terms of tau r i and t bar r i t bar r i okay or t m bar r i okay now we have to now really find out whether the t bar i how do you get it okay yeah and unless you know the t bar i you cannot calculate the conversions or given conversions you cannot calculate the volume of the reactor okay so these are the problems and if you notice those equations 9, 10 and 11 actually those are more general equations where you can simplify to the other two conditions what are the other two conditions for mixed flow yeah constant size single particles okay if tau bar i tau bar i equal to simply tau that means for all particles we have tau same and t bar i t bar of t bar r i is again t bar then you will have the first equation coming okay yeah the first equation in the sense that is you know first condition where we have only mixed flow and uniform size particles and if you take tau r i alone and t bar same as for all the particles then that condition becomes again the size distribution of particles but no elutriation with elutriation when you take then this is the more general expression where that means what I am trying to say is even if you are worrying about the examination you do not have to remember thrice okay it is the same equation what we have right but elutriation you have to do some more work to calculate what you will be the the mean residence time for each particle that is the only thing that is extra coming so that is why because most of the time till someone points out you may not recognize that the simplicity in the equations so that is why I am just trying to point out okay please take this equations 9 10 and 11 cannot be used to predict the conversions because t bar m of r i is not known and this depends on f 1 and f 2 of equation 6 let me write again equation 6 here for continuity t bar m of r i equal to f 1 w f 2 of r i w r i this is equation 6 yeah please take this also t bar m of r i can be calculated from elutriation data from fluidized beds elutriation itself is a separate research topic in gas solid fluidization okay next part I can write in a steady state multiparticle fluidized bed for particles of size r i the elutriation rate the elutriation rate can be written as can be written as rate of elutriation elutriation of particle size r i is proportional to is proportional to let me write here weight of such particles present in the bed or in other words f 2 of r i is proportional to w of r i okay or the proportionality constant yeah is k of r i w r i where k is elutriation rate constant k is not dependent k is a proportionality constant you have to find out that depends on what particle size you are telling in fact this is nothing but first order reaction the rate of reaction is directly proportional to the concentration of the particles in the bed okay and the k is the proportionality constant and that is it is it is not changing with this but it changes with for each particle okay that rate changes for each particle right so I will write here we will come back yeah k of r i is f 2 of r i divided by w of r i okay so this is equation last equation was 12 sorry 11 this is 12 okay nearly you understood no this is simply proportionality constant it is like first order reaction okay so more number of let us say 500 micron particles in the bed means okay more rate okay directly proportional to rate but this one as I told you that the fluidization in fluidization elutriation itself is a separate field there are lot of research papers published on elutriation on different conditions for different particles different flow rates all this and lot of correlations are available even now most of these correlations are not universal correlations that you know all put together can I generate one particular correlation no because I think still it is a difficult phenomena in a fluidized bed say karee you are asking something in the bed can we not relate it to the particles present in the feed itself would that not be more logical because unless they are in the feed they would not be in the bed no see you have in the bed the particles are falling here right so then here you have certain concentration of the particles here there is no concentration it is only simply flow rate so many kgs per hour but here I have so many particles per unit volume of the bed okay you have heard of hold up of the solids similarly we can also express this hold up either in grams or you can also express the hold up in terms of fractions you know for example we say that the voidage of the packed bed what is the voidage of the packed bed voidage of the packed bed not volume of the packed bed volume of a packed bed I think you know as chemical engineers you should be able to answer that very quickly yeah I asked you that what is the voidage in a packed bed I am asking a numerical value yeah why when it is 0.4 when it is 0.6 you cannot say 0.4 to 0.6 if you have sufficient information you could have questioned me what packing you are talking okay yeah so that means of course you cannot even visualize what is a packed bed that is the simplest system in a chemical engineering industry simplest okay so if you have spherical particles the voidage will be around 0.4 if you have some people use rashig rings or some people use bell strategies and all that then depending on even for reactors I am talking okay the catalyst can be made in terms of in the form of rashig rings so then it will be around 0.6 so that voidage is nothing but the fraction of volume which is vacant okay so similarly here the all the hold ups yeah then what we say is even in packed bed because I am telling you about packed bed the reason is that packed bed is the easiest one to imagine right so when you have for example two phase system that is solid as catalyst and fluid is going through this packed bed that means always I can look the look at the packed bed if I have spherical particles I have 60% of the fluid and 40% of solids no the otherwise the other way 60% of solids and 40% of fluid the fluid is within the voids okay yeah so these are the volume fraction similarly here I can have now volume fraction of the gas okay volume fraction of the solids but within that volume fraction of solids again I have yeah 500 distribution 500 particles 500 micron particles and maybe 1 mm particles or 100 micron particles all these things together inside the bed okay so that is why logically it will be the rate of reaction is proportional to the concentration concentration of solids okay so that is one of the simplest assumptions it is empiricism you assume that and then try to find out from the experiment whether what your assumption is right or wrong okay and in many cases in fluidized bed yes it is approximately tolling as directly proportional to the solids that are available in the bed not left it is all already in the bed okay that is why that is the meaning of minus r A equal to K into C A C A is the concentration left at any time right yeah so that this is similar to that and this is the equation for elutriation constant now if you observe that f 2 r i by w r i did you get that term anywhere in your t bar i yeah here you have so that means if I can estimate my elutriation constant from the experiments it is only experiments no theory there theory we have only for single particle elutriation that single particle what are the assumptions when you are deriving that single particle terminal velocity what are not spherical and okay other than that there are many assumptions in fact have you know any idea you heard of terminal velocity no sir I think it is creeping flow creeping flow you have creeping flow what will happen it only creeps so because there is no terminal velocity you know even at Reynolds number one if you have very fine particle it can fluidize it can go away yeah what are the assumptions when you for the derivation okay spherical particle and it is very very you know wild imagination when you are deriving because it is one particle in infinite medium why that is very important flow is there is only one particle in an infinite medium why should assume that yeah no interaction with the other particles and also no interaction with walls okay even if you have disturbance with the walls then your terminal velocities again the derivation is not valid okay yeah but in reality when do you use in chemical engineering factories only one particle okay never use okay so that is why multi particle systems are very very complicated that is the reason why we have lot of empirical equations that empiricism present day academicians very young academicians are not really appreciating that it is good but if you are break away this empiricism and then try to go for actual theory analytical expressions wonderful but in engineering not many systems are possible to analyze like that that is why we are still living with empiricism and even now you use heat transfer coefficients mass transfer coefficients from those correlations which have been developed in 40s 50s 30s okay but theory definitely help us to understand more and more the phenomena what is really happening so that is why these empirical equations we have to use from the experimental data and then if you are able to substitute that equation 12 in 6 equation 12 if you are able to substitute in 6 then we have t bar m of r i equal to 1 by f 1 w plus elitation constant yeah this equation is 13 yeah nice okay but still I am able to substitute for k r i from correlations available in the literature for this term right yeah first for example for 100 micron particles 500 micron particles 800 micron particles you can substitute but still I do not know what is f 1 okay so f 1 f 2 if I know f 1 we can calculate and then still you know so that is why what we have to do further is that these are all of course this equation is already known to you let us take this equation which has been already written f of r i plus f 2 of r i what is this equation number what was that equation number 2 okay yeah so now I will substitute here equation 12 here for f 2 so f of r i equal to f 1 r i for f 2 if I am substituting equation 12 then this will be k of r i into w of r i this is equation there is no equation I think at the end I will give that yeah so this w of r i also can be written in terms of we have another equation you can check this equation w of r i can be written as w by f 1 into correct f 1 of r i this is equation number 3 written slightly different that is all because w of r i also I do not know so that is why I just would like to substitute this one in terms of w and f 1 so that I will have f 1 everywhere then we can try to find out what is happening okay we can estimate what is f 1 so that is why substituting equation 3 in above okay that equation okay let me put 14 yeah right there I am not writing that at least you have to write you know substituting equation 3 in 14 what you get and rearranging I am just jumping the steps and rearranging what you get is f not f 1 of r i equal to f not of r i divided by 1 plus k of r i to w by f 1 can you please check this this equation yeah it is very simple only so this is equation number yeah okay I will write here instead of that 14 a and I will write here 14 b okay that is good now yes so now this one is f 1 of 1 particle size so if I want to get total f 1 I should take the summation of all that okay f 1 for example again I am telling f 1 sigma if I say you will immediately confuse so I have to say that this is f 1 for 100 particle 100 micron particles may be 500 micron particles and 800 micron particles if I have that distribution okay so I can write f 1 equal to sigma of f of r i which is also equal to sigma of all particles f of r i f not r i 1 plus w by f 1 so this is the one this is equation number 15 whatever procedure is now using that equation we have to solve f 1 f 1 is present on both sides now okay so that means you have to guess you have to guess a value calculate this and that must be equal to your guess value and the data what you get is f not r i d rho yeah that is the feed so you know and w hold up will be given for a already existing reactor it should be given otherwise you have to calculate w for a given conversion okay one of them okay so and now f 1 I do not know k r i you know it is empirical correlation so you know in this equation everything except f 1 so you guess f 1 and then l h s must be equal to r h s under those conditions you just stop when both are same then you will have that f 1 so using that f 1 what you do you have to calculate t bar of t bar of yeah of a particular size so then I know w I know f 1 I know k r i I can calculate and from this I will go to now equations 9 10 and level correct yeah what are the things you have in equation 9 10 11 what are the parameters you do not know that is all only 2 okay do you know tau you said okay yeah you do not know tau what is tau tau tau tau tau tau tau tau tau tau tau tau tau for a single particle where from kinetics you already get that tau is for single particle okay single particle kinetics already you know whether it is following shrinking core model film control or diffusion control or ash control that is why you have those equations already so tau is already known to you right and t bar m you are calculating for given size if you know what is f 1 and what is w and what is k r i so then you can substitute these two and calculate x bar okay good yeah so that is why what we do here is how to calculate f 1 step 1 is very simple only you will love it then choose f 1 that is guess okay guess f 1 value and substitute in 15 in equation 15 yeah and step 2 is match LHS and RHS if it is not then again you have to guess another value and again do that till you get both are equal and then of course you can calculate the yeah you can you can choose that f 1 from that f 1 you go to 13 okay yeah I think probably you have to write that I think there is one problem which I have given like this in the assignment which I have given stars you have put know at the end somewhere elutriation and all that also is given so they think you please try that they are very beautiful problems particularly non catalytic reaction design is wonderful design it is very very good and in fact I do not have much time you know because I now have to go to catalytic reactions from there you have to go to catalytic reactor design and then you have to go to fluidized bed reactor design then you have to go to slurry reactor so I am not able to take some more complicated cases like you know of course packet bed you know is a system is equivalent to your plug flow okay yeah so but I think it is a beautifully you know is a transient problem I can put for example the non catalytic reaction the iron ore in packet bed and then send hydrogen but I can give those problems as an analytical thinking problem now really if you are able to solve that that will be beautiful what what I may be asking is that I have a packet bed batch solids iron ore and then I send hydrogen draw the concentration profiles of gas as well as solids solids means x b okay and x a or c a how the concentration changes in the bed if it is co-current or it can be counter current okay so the particles are reacting with time that is the transient phase it is not steady phase whereas gas is in continuous phase steady flow but both the profiles you should be able to draw okay that gives beautiful analytical thinking I tell you beautiful that means unless you understand the whole packet bed and then the phenomena that is going on inside the packet bed you cannot draw I think I have been telling you last semester also I was telling you the simplest problem which you can imagine is okay I have put a iron ore ball spherical may be 5 centimeters or 2 inches or 5 inches or 6 inches ball in a furnace where I have the hydrogen continuously filled up okay so now can you draw the temperature initially when it is just because the reaction has to have sufficient temperature so I just took the ball and then put inside the furnace has 500 degree centigrade let us say the furnace has 500 degree centigrade then how the first of all temperature profiles are changing inside the particle once it attains 500 degrees then the reaction may start after reaction starting how again the concentration profiles are changing that means of course we are assuming the hydrogen is constant throughout that is not a problem but around that you may have filling right so now you have to draw the concentration profile of the gas and also concentration profile of the solid concentration profile means conversion profile so these are wonderful problems I think you know instead of going to google and then searching all nonsense things you can just sit down in your room if you do not have anything just take a pen and paper okay now let me draw the concentration profiles in its distillation column or in a heat exchanger or for example in a pipe okay velocity profiles that is the simplest one you know so if you are able to think about that then it is really you know that only shows that you have passion in your chosen field I know you may be laughing at me this fellow does not have any work so that is why he is telling all the time yeah and I am not able to change their faces I think B Tech faces till now I think you know they are stunned absolutely I think may be stores may smile sometime but I think no I do not know what is happening in our B Tech system my God they have that skepticism all through that you know looking at the teacher that this idiot will be talking something and we will be just sitting and then doing whatever we want Prabhu how did you develop that not you personally I am talking in general now because I want to learn that I want to know why people are so skeptical about any subject mechanical engineers complain the same way civil engineers complain the same way of course chemical engineering you know yeah so any system I think you know computer science earlier supposed to be very good okay and computer science and what is that other one electrical and electronics now they also become stones and we are not talking about 100% there may be always 4 or 5 out of 100 that is nothing statistically 0 correct no I mean when I have 100 people in the class 90 people of 95 people are just heckling at me only 5 people are listening I do not even see them I do not even see them know that is one drop of good water in the ocean how do I see that good water where I have to go and take okay yeah this is what I think why I have you know what is the reason and it pains me a lot and and they are I mean most of you also I don't only blame them don't love you are also like that okay you are also like that from the you know but you are not getting this exam some other exam you are writing okay so I don't know except school education beyond that we are not learning anything I can guarantee that even if you are learning that will be delta x but if you have passion definitely those people are learning Prabhu got 99.99999 I do not know how many nights we have there okay why because his passion is not engineering his passion is something else no like that many they can do wonderful work after getting something you should put your heart and soul into that particular field so that is why whatever you get I think you should be able to put your heart and soul and then do it because I don't get something I cannot go to every day and then drink what is the use by the way okay yeah so then what is the use I say you have come here with a purpose and I think I can tell you seventy eighty percent of these two faculty members are really enthusiastic to tell you something because all this enthusiasm was killed by the by seeing the faces where you know stone faces or wooden faces okay yeah so I think that life in this in the face is totally go out the moment they enter the class and of course when the class is over very happy just go and start laughing right the reason is that everywhere every minute every second you are guided by someone or other either your brother sister or mother or father nowadays I think this idiotic cell phones are there so the moment they think that you are not doing what they want they will send SMS do this so that is why every field and every field has thrills in in that particular field but only thing is you are not able to see and sometimes as teachers we are not able to exit you also that is also there but nowadays I think you know I feel it is 50 50 but that 50 50 you know if it is 60 60 percent for students and 40 percent faculty when it is going beyond that then you know the enthusiastic people also will die enthusiasm of the faculty members also is killed I told you know five people may be listening 95 people may be sleeping mentally okay so then you cannot you cannot talk to I think you know that is very easy to talk to empty chairs rather than people sitting and lot listening to really that is easy for us once you have the you know forced marriage is only forced marriage because you may not like chemical engineering in the beginning okay but once you came to chemical engineering you are supposed to love that again otherwise you only feel very bad you feel very bad at the end if someone asking you you are a chemical engineer do you know this you may not show because we are all actors from you know birth to death we have only act in between only two stages where you do not act is before birth after death okay because my god I think we have a degree but we are not able to answer this man like simple question like in our village some people used to ask me what do you do as a chemical engineer we do not know because no one told us so then only vaguely we used to tell that no no we make medicines okay so we make fertilizers we make cement that kind of thing they are very polite I think you know they have not asked how do you make cement okay so if they have asked how do you make cement gone because chemical technology course long time forgotten okay so that is why yeah shaker comes from two aspects one is understanding the second is visualization both go always hand in hand unless you have a visualization you cannot understand the subject when you say fluidized bed on the on the board it is very difficult to visualize what a fluidized bed is unless and until someone has physically seen it you say elutriation elutriation is easy to understand as a word but not as a concept when unless you do experiments on your own unless you see the setup it's very difficult to visualize yeah but I think you would have simplified things but you know can't you imagine a particle just going out of the bed but I think you know see if you are not able to even imagine that I think absolutely we don't have any imagination so from the first day itself you if you are asking the person to visualize a single particle he may not be able to visualize some everyone has their own speed sir if someone from day one you start that person to visualize that he may not be able to visualize that and after a few point if he is still not able to visualize somewhere it will shatter his confidence also that I am not visually able to visualize such a simple thing how will I visualize the bigger things which which are coming my bigger things will no one ask you to visualize because very difficult you know for example three three dimensional diagrams is very very difficult to understand we are not going to that level of visualization it is simple you know particles floating in water you cannot visualize particles floating in air you cannot visualize okay and then one particle are you know few particles just going out because every day also you are seeing I think when you have a lot of wind don't you see particles just flying off dust and all that okay that is what is the elutriation and that is why I give you so many simple examples so that your visualization is simple simple examples for all my complicated problems I will try to tell you know particularly in my teaching I do all that all the time like plug flow no one can visualize so easily then why should I tell Tirupati Q sorry even Tirupati Q I cannot visualize means what can I do and not only Tirupati Q okay you would have not gone to many people may would have not gone to Tirupati okay but I have told you even road traffic okay every car going exactly at same speed every vehicle moving exactly same speed and I told you also another example you know conveyer belt so many examples if I gave you also if you are not able to visualize no sir you have to show me how the molecule is moving inside the tube yeah that is why as a teacher as a teacher we give you very simple examples where you are capable of visualizing I don't know I think in every class also any teacher will try to tell some examples I say in any class examples are part of the teaching so that is why so many examples I bring movies I bring so many things to use so that you know what you know because I think the one simplest definition of teaching is taking student from known to unknown okay traffic is known to you okay so I am taking from traffic to unknown plug flow reactor so like that many examples which I give plug flow where did you visualize only mixed flow only mixed flow you should have visualized oh Q yeah exactly that is before entering brochures that is true and mixed flow where did you see inside that yeah so then you see very simple you never forget again mixed flow that means a guy can be anywhere inside YIT any instant of time any instant of time so that is what is mixed flow so that is the kind of simple examples we give so that you can easily imagine very good so like that only I say like that only slowly you have to because all the disease with the students is that if the if they are not getting marks they think that you know they don't like the subject and marks and liking subject is totally different okay but anyway I think nice I think I could talk to you this one I think it is bothering me a lot really bothering me a lot I think as you told me maybe in 95 people are not listening to me means I definitely would have exaggerated may but I can add only another 10 that is all 15 no this is what what we observe in particularly 100 classes because earlier I used to be teaching only beta classes I think really enjoyed those classes wonderful students out of 30 may be just one or two students who are not attentive that is all but other I think you can get 28 students beautifully attentive all the time I am not exaggerating out of 30 at that time because even though they don't like it there are also people who have been pushed by parents even at that time but once they have taken they were at least doing that minimum thing but now the even that minimum things are not there that is why DNIC has always again plug flow Q for the people coming sir I have completed only two credits this semester so how many say semesters I will take to complete you will take 100 semesters because 200 200 credits they have to finish approximately 165 of course yeah so like that okay anyway I think I will stop here tomorrow we will do multi-stage fluidized bed you know tanks in series mode using the same thing okay you run now