 నాసిసివాలూ సందా మ్మర్చతుతు మ్ర్చతీం. సాతోమ్వర్ స఑మిసాల్చిబి. మాదినా ఆందియా నోటంతెత్డ్చకా ద్థరిక్చవరిగా ఆవందిన్చికరందునిఌందెనందెచా ఇర్ర్చందెచ్చా గికనటోకా గాసిక్చనే అందిచారంనుకిచ థృప్వరన్నస్డతృదిిందరండినిమోమఌంద్సందాలూద్మాములొన్��ూన్సందాందాలొపర్యాన్టైధదిదాలునలకినందవరందియానుోనందాలేపరూత్రత్పయా� ధిత్రి ఎదిలు దారిలు నీ ఆదిలు ఆతోటేమా్చ కండించి నిచిత్నీింమం మాకైలినీకొచింటోకొటాత్ హాస్మ్ప్ కూట్చికొరికియంట్టొనీచిఋకో లాటాక్నం ప్గ్ పిక్క్ం చారందాట్ పికెంచిన్చిరందానం స్బికటిందిక్టితక్ స్టాతికులు పతిఖారందినం హిష్వందికారం. so what we are talking is what is the entry for the gas and exit for the gas entry is the sparger at the bottom and entry is on the top so L by D here also may be 1.52 okay in slurry reactor so simply it is coming out right so I am not saying whether you are right or wrong justify why do you say that it is mixed flow if there is no stirrer normally slurry reactor you have stirrer very rarely you have you cannot but you will also have the stirrer there if your catalyst is trying to sit in you know the catalyst is a solid it has got more density than gas and liquid okay nickel at least right so if you are taking large particles of nickel size wise and then they are trying to sit in if it is very fine dust of nickel it will move happily with the liquid right because gas is bubbling so the solids also are brought to the top again they may go back and again you see and that is why you have solids also in perfect mixing but it is batch generally we do not take solids as continuous in a slurry reactor you see now so gas without stirrer will be plug flow so the moment we say that we have plug flow then what are the non-idealities yeah channeling may be there and channeling will be there for gases when it is moving because sometimes you know gas will go in some other route very fast and some other route very slow so depending on which side you have more and more liquid because it is simply bubbling and bubbling creates khyas okay that khyas only creates good mixing in the liquid so I don't have to ask you know if you have a continuous liquid phase in slurry reactor we will happily take that one as the reason is that we have perfect mixing not by stirrer by gas itself it is create so like that every reactor you have to just imagine in the mind or draw and then try to find out okay where are you closest to which contacting pattern either plug flow that is one mixing and one extreme so we have we say that yes RTD equal to 0 for plug flow and RTD equal to 0 to infinity exponential decay is for mixed flow and what are the non-idealities when we say mixed flow mixed flow is liquid is in mixed flow in a slurry reactor what are the non-idealities by passing may be there dead zones in fact a lot in slurry reactor if the spargery is not properly distributed same thing yesterday we talked about fluidized bed fluidized bed also has a bottom at the bottom gas has to be distributed a perforated plate if that is not designed properly again you will have dead spaces that's why I said you know it is man made because we are only creating that if you are able to design those things very well at least some of them can be eliminated that is the advantage with non-ideal flow there are some parameters which you can eliminate there are some which you can never eliminate for example in plug flow particularly gas phase reactions and all that are liquid phase also single phase even single phase you can never avoid axial mixing but only thing is whether axial mixing is very serious or you can neglect when compared to the overall conversion that is what only you have to decide as an engineer that's all so any reactor for example rotary kill it will be moving like this you feed at this point okay and the solids will be coming like this and gas can be sent you know even in cement kills and any other non-catalytic reaction where even sorry even yesterday we have discussed about iron ore reduction right iron ore reduction in fluidized bed it is not only fluidized bed iron ore can also be reduced in rotary kill right so H2 may be sent either counter currently or co-currently right and then how the solids are moving how the gas is moving normally the length of the rotary kill is 20 meters 30 meters 40 meters that much is the rotary kill length diameters in industry will be 1.5 meters big pipe rotating slowly right so how the solids are moving because for each phase we have to find out how the solids are moving first ideal plug flow or mixed flow mixed flow we tell who's yeah I'm not saying right or wrong don't be afraid don't hide yeah who said mixed flow yeah I mean how do you define mixing because I think you know that's only trying to get some more information for you that's all okay how do you define mixing a particle should be anywhere at any instant of time can be anywhere at instant of time so when I have almost 30 meters or you know 20 meters of rotary kill slightly inclined slowly rotating what is you know rpm of your rotary kill by rpm will it create that kind of it will simply slide see it is slowly moving like this right and also please remember that you know I use this term hold up hold up means the amount of solids not only solids amount of gas gas hold up we call amount of solids solid hold up we call in salary reactor if you take amount of liquid liquid hold up we call all three is in that volume and fractions wise we will call epsilon s epsilon g epsilon l epsilon are the hold ups that is what you know most of my research a concerns that this hydrodynamics and then hold ups because unless you know how much is gas is there how much solids are there how much liquid is there you cannot design the reactor at all why if gas is only one bubble and liquid is may be 10 meter cube where is the reaction almost zero that means the gaseous reactant is not at all enough right so that is why that is very important information so that's why in the rotary kill how much you expect as solids hold up anyone anyone has idea let us say 10 meter cube total volume I have out of 10 meter cube how much do you expect the solids to be by 2 10 percent you agree with her she may not be right she is around 50 percent why why you don't fill up you can fill up happily and then rotate no as well as that nice movement for the solids that's why inside the rotary kill they will also have some kind of baffles the baffles lift the particles and then fall lift the particles fall lift fall there are many and only solids are sliding so every time it is going up and down falling up and down fine that is where you have the good contact with the gas so it is only around 10 percent and the rotational speed can be only 3 pm for 3 rpm or 5 rpm or 7 rpm like that very very small angle gain it is 2 to 3 degrees may be 5 degrees also okay but not 30 degrees 40 degrees 40 degrees means everything will come very fast okay so all these things are there so now tell me Pooja which one the solids will have what kind of contact that means you know whether distribution RT device or PF is it PF or mixed flow or you convinced why it is not mixed flow or you are not convinced so how do you imagine this you tell me how do you imagine that the solids will move in a mixed flow that is not rotary kill please yeah that's why I said diameter is 1 meter and then length is 20-30 meters now you ask your building people to use this kind of thing as mixer nothing will mix there okay yeah I think she is imagining that because on the road we see most of the time only those things you know what is L by D of that now your condition is still not convinced still you are with building people area solids will beautifully slide like this overall you have good plug flow but action because when the solids are raised falling sometimes it may go back and forth okay and again that will move further fall a little bit back and forth so if you look at the entire one the little bit of back and forth movement will be there axial mixing that is a non-ideality okay and the radially uniformity we don't take it there mainly it is taken as you know the axial mixing part so that is what for gas push a gas is right so yes anyone and it's going and when it's going to the kill so naturally it will touch the solids contact then you will have the conversion okay so like that any equipment this non-ideality this back mixing that happens a little this actually helps the any bad mixing will not help the reaction the in protocol if there will be only ready mixing what why you should have mixing at all mixing is bad for reactions we have been telling all the time because concentration will decrease so rate of reaction will decrease so even when the particles are moving this way that way the particle which has already converted a little bit more than the earlier particles again and coming with mixing with other particles I mean it is not solid solid reaction but even then it is unnecessarily going back and coming forward so what we design is okay for one inch particle just for easy imagination or one centimeter particle you need one hour residence time for getting converted to complete iron so okay so anything less than that more than less than that will give you less conversion more than that is there is no use for us okay so that is the reason why you know actual mixing also is bad for even in road taking okay any non-ideality okay the way we imagine our plug flow so like that any reactor you bring you give me one choice one choice of the reactor apart from what we have discussed what other reactors you have come across okay moving but is the easiest one that is why I did not say slightly complicated one okay moving but what what will be the patterns moving but you know the solid if it is take counter current solids will be coming from the top slowly moving moving but I told you moving but is nothing but a packed bed moving okay that entire thing will be simply sliding down so wonderfully we can imagine this one as because those particles you know we can never get exactly same size in reality so that is why some particles will slide more some particles will get stuck somewhere so that is why on the whole it is plug flow but nearest non-ideality there also is actual mixing okay and radial uniformity may not be there sometimes depending on the size so like that any reactor like for example FCC what kind of reactor they use FCC fluid catalytic reactor it is fluidized bed but it is not conventional fluidized bed where you have large diameter and height is small l by d equal to 1 and all that so it is fluidized bed actually it is called fast fluidized bed the solids will be moving with the gas and then they get separated in the cyclone and the solids are nothing but you know catalyst so that will get regenerated and again it comes back so solids are moving in plug flow and also gas also is moving in plug flow like that that is why the first statement which I made long time back that any reactor you bring you can beautifully classify only into these two categories instead that all the reactors can be classified into two categories and ideally you can imagine what kind of flow and we know that in reality there is no ideal flow right but closest to ideal flow what you were imagining the moment someone says that I have plug flow in this reactor your mind has to go there if you are very very fussy about exact conversions then okay let me also see what is the non-ideality how much we are losing because you are assuming ideal plug flow and calculating conversion but in reality you may not have when you do not have in reality how much you are deviating from that plug flow that comes through non-ideal parameters okay so that means definitely if I want 90 percent conversion for a in a tubular reactor in a plug flow reactor and ideal plug flow gives me 1 meter and because of the axial mixing to get the same conversion I may have to put 1 point 1 meters or 1 point 2 meters that extra length that anyway we do not care as engineers because by factor of safety that is given up by God to us okay factor of safety okay so that is why I calculate 1 meter cube and then add okay I am not very sure I put 1 point 2 meter that is why always you know even I think even digital cameras will have factor of safety because you know always when you say I think anyone any photographer did you see only one shot taking and going away you will first a smile and then you will smile you will take photo and you are about to leave no no no no one more smile please again because second because he is not confident that the original one would have come properly so that is why they are also factor of safety only in the examination same examination you cannot write twice okay same time so that is only problem there okay good so like that we have factor of safety we are taking care of it now believing that this non-idealities are creating different distribution than ideal distribution ideal distribution we have exponential decay it goes beautifully but if I have channeling sorry bypassing for example bypassing it will not be exactly like exponential decay or if I have this one I have already told you plug flow when I have right when I have plug flow what kind of response I have shown you there in the outlet if I have step 1 pulse input so that means imagine disk disk is pulse input how the disk is moving exactly like that comes out if I have the non-ideality what kind of what will happen to distribution it goes like this that is what is non-ideality that is the effect of non-ideality so your flat velocity you know not that flat concentration curve which is simply one line direct delta function that is now distributed that is because of non-ideality in this case axial mixing so if I have dead space for example in same plug flow what should it should come how the how the actual mixing is there and over axial mixing I also have dead space another disease like diabetes and heart attack material in the dead space will come after some time it may not come but it will come dead space is not really dead slowly coming that is what what we say dead space okay slowly somehow you know there will be mixing a little bit and then it is what coming it will have a long tail as Savita said so you will have like this that is spread and then it goes long tail see now that means your ideal distribution has been totally spoiled by these non-idealities ideal distribution ideal distribution is simple direct delta function you can imagine direct delta function know arrow okay so that one has been spoiled by like this by axial mixing and now by tail another one there that is dead space right if you have channeling then what Rahul said is one peak for the channel another peak for the main so the channel one will come first with the axial mixing because axial mixing you can never avoid in plug flow right and other peak you see how simple it is you have to imagine okay in the brain and once you imagined all this in the brain now you have to go for actual mathematical representation okay good so now we believe that residence time distribution is really spoiling the ideal ideal distribution so that is why we have to find out RTD how do you how do you estimate RTD for any column okay so how do you estimate RTD how do you estimate Ghana or determine that is the question what is the technique used okay so the ideal one is okay if I know if I can reach each and every particle or like that you know earlier also I told that if each and every molecule is attached with a timer and collect all these timings at the outlet and then plot those timings that means number of molecules and the corresponding timings so I mean I am sending thousand molecules out of that may be some 10 would have come in the first second so may be another may be 20 would have come in the next second so all that number okay if I plot then we will get normally this kind of distribution for a general vessel we are not talking about ideal plug flow or ideal mixed flow this is what what we get so but actually that is not possible you cannot even put timers right and also reaching molecules is impossible so that is why what we try to do is we will try to find out the behavior through some tracer techniques so that technique generally is called stimulus response technique stimulus response technique what is the stimulus response technique I will give you one simple example so that you will not forget about what is stimulus response technique okay same example which normally I give okay so this is what is the one which you have to find out you know response technique okay now please take this because you will forget anyway right so that is why let me record okay this you have written how do you estimate RTD and it is through stimulus response technique okay good I will just to estimate RTD the ideal situation is to measure or obtain information on each and every molecule in the bracket you write information like concentration temperature velocity C capital T and U so that one can calculate the conversions in the reactor once you know concentration profile at every point so then automatically you know what is the conversion okay pull stop this is impossible at molecular level pull stop hence we should resort to at least getting information on a group of molecules or a packet of molecules using tracer techniques or more precisely stimulus response technique okay good so what we do normally is that I have a general reactor may be I think just I will draw like this okay I will just draw like this only otherwise you may be thinking that only that kind of reactors you have to design okay this is real vessel we are not saying whether it is plug flow or mixed flow okay so then here under steady static under steady state conditions you have the flow volumetric flow rate volumetric flow rate there is no reaction okay and most of the time we do RTD without reaction just to find out the hydrodynamic information and RTD is one of the hydrodynamic and afterwards we will see how do we couple this information with the reactions okay good so this is what time t equal to 0 the pulse input means suddenly I will add some amount of tracer at t equal to 0 and then here I will put a probe or otherwise you have to collect samples and then get this is probe of course this probe should be taking concentrations along the cross section uniformly okay good now we have to record yeah we have to measure with respect to time what is the concentration of this tracer for example if I put the color may be red color this is normal water and I suddenly introduce some kind of red color may be 10 ml of the tracer and then that 10 ml depending on the kind of flow that is inside you will see at the end for example all this 10 ml 10 ml if it is ideal plug flow I will see only after this is V and t bar and also tau because we are talking about only no reaction and all that so volume by volumetric flow rate so if this 10 ml is only ideal I mean if it is if this one is plug flow that 10 ml will come exactly after this t bar or tau right if it is mixed flow it starts from zero onwards right but in general what you record here is this kind of concentration versus time because normally what we expect is you know the meaning of this curve is most of the time we expect that this is t bar or tau we expect that most of it will come around that but with that variations and all that you may have this kind of thing or you may have sometimes long tail or you may have two peaks all kinds of things may come but in general this is what we show that is why even in the first examination when I gave you started only this one when I asked what are the what is the ET ET only I asked I think ET for ideal reactors most of the people have drawn this for ideal reactors we have two right so you should have drawn exponential decay that is for mixed flow or there are delta function one of them but many people have not written that I think almost nil written that okay good so this is the kind of thing so you have to take some kind of proper care when you are doing this experiment because this flow should be steady first of all otherwise your tracer will be different okay I mean because unsteady flow unsteady flow also can be done but we do not do normally yes okay and afterwards you have to very carefully add this right and also we know that this tracer should be identified at this point how do you identify you can measure color you can measure conductivity you can measure pH so some property which you can very accurate measure and then that property is converted into concentration concentration of tracer okay so I mean in reality it is not required but still you know we have to only use this concentration versus time diagram otherwise if you become expert you do not have to I think say the same property whatever you need to measuring that also can be used because in the actual utilization of this curve you are normalizing this curve for the area under under that under that curve to be 1 okay and why do you do that and all that I will tell you now good so this is what is the experimental technique to find out and it is very easy for me to tell on the board but when you do the experiment it seems next semester they are asking me to take your lab okay so I will also give open-ended labs you design everything and then you design you conduct the experiment then definitely you learn a lot right so this kind of experiment also I am planning one where you cannot you have done this kind of experiment probably in your BTEC right at least one of one or few people right so in your BTEC you had no CRI lab RTD lab also was there yeah so but on your own I think if you are able to do how much you have to add and all that then I will observe you how you are doing it right okay so that is why doing is very very difficult you know but that means you can make a lot of errors first of all you don't know when to collect the samples what time you have to collect samples that question is also will come anyway next semester you will see all this right if mean residence time is 10 minutes how much time you take the sample and what is the sample frequency right and particularly it is all this will come when you don't have instrumentation automatic recording means without understanding you are recording it okay but I don't give automatic recording you have to do with your own hands first learning is you know doing is learning right yeah okay so that is how you know there will be lot of difficulty in doing this accurately and inaccurately there will be thousand ways of doing not doing also okay good anyway so this is the one what we have and with this information how do you define now this ETFT and all that now okay so now if you come to the definitions definitions what we do after getting this one is that we first try to find out area under this car as Q area okay right how do I find out area under this car this Q equal to simple calculus zero to infinity because I don't know the boundary and you don't never you never go to infinity anyway okay C into C into DT DT so then we get the exit as distribution ET as C by Q where Q is that but why should we draw like this I will explain I think you know we will also derive that why should we draw I mean why should we calculate in this and then say it is ET but by the way what is ET exit as distribution what is exit as distribution I think I have not I told you know what that exit as distribution okay good yeah so that is the one and now we the definitions why okay we will just stop here because this is what is experimentally done this procedure adding running this at steady state and also measuring anyone can do because I mean just with a slight training anyone can do without much a brain thinking right so now this will stop it and afterwards we now try to find out what is that we have to do here information that is required in terms of definitions we define our car this residence time distribution car as okay okay now it is ET and this is T normally we may expect a general car something like this I mean any shape I can draw okay any shape I can draw and now if I take this is 0 this time also 0 and this is ET the units of this is minutes inverse is it correct minutes inverse yeah this is C this is integral 0 to infinity C D T C C units will get cancelled only time units will be the inverse time units so this is the one so if I have to take yeah so this area let us say this is time this is fourth minute so this is sixth minute so this value this is point one that is point one now what is the area of that particular strip point right so this area equal to what is the formula it is ET delta T where delta T equal to 2 okay so that is why this is equal to point 2 what are the units okay this is how we want to define this distribution yeah anyway finally it has to go to 0 that means all the material should come all the material should come out definitely right so that is why good so this area under this strip it is 20 percent now why we are defining in this way and what is the total area this is what actually you do in your particle size analysis also you know particle size analysis also exactly you do the same thing right yeah now this gives me an idea now that 20 percent of the material is spending a time between 4 to 6 on the average 5 what is the use of this information for me what is the use of this information for me yeah to calculate the conversions so that means now in a non-ideal reactor where I do not know what kind of pattern it has ideal plug flow means I have equation ideal mixture flow means I have equation but somewhere in between I do not have so that is why I conduct this RTD test and find out and then draw the information in this in this format and now I know that 20 percent of the material is spending a time between yeah 4 and 4 and 6 that means on the average 5 and I imagine that that group moving as a batch reactor which has spent a time average time 5 minutes now if I have a first order equation I mean first order reaction then I will have conversion from that that is what is the original idea of residence time distribution how do we calculate the conversions for a non-ideal reactor where I do not have to have a design expression but conduct this RTD test and then try to find out what will be the conversion that was the original but it was not successful because that was only successful for first order reaction other than first order it was only for linear processes for non-linear processes that was not possible and why it was not possible I will tell you you know after some classes right but right now this was the idea and once they had this idea and then did it and then try to calculate what is happening thinking that for all reactions we can do this they found that for except for first order reactions other reactions we cannot do that so for second order reaction some more information is required or half order reaction some other information is required okay so we call what is called micro mixing macro mixing so this kind of information is required right that what is micro mixing macro mixing I have to tell you later so that is why this is how it is defined so now what is the and ET is called the exit H distribution function now we have a definition from this figure itself what is the exit H distribution function because ET is a function ET is not a fraction fraction is only ET delta t ET delta t is the fraction right so that is why please remember that is where normally my students make the error right ET ET itself they think that ET has an equation that ET also what we will derive for all systems we can derive equations for ET so that I can predict the you know material coming out between any time t and t plus delta t right okay please take these definitions now yeah so ET exit H distribution definitions we are writing exit H distribution ET distribution function actually ET yeah so this is defined as the fraction of material because we are measuring at the outlet the fraction of material which has spent a time between t and t plus delta t is ET delta t next sentence is ET is called the exit H distribution function then next one is you have cumulative H distribution function very widely used these two distribution that is called FT see why we are telling ET and FT is ET is a function of time and FT also is a function of time so once you understand this FT is very easy to understand what is that it is cumulative that means I am not talking about between 4 and 6 yeah from 0 to 6 so that means what this area under the correct to yeah till this area okay all this area so this will be FT so we know 0 to t ET DT that is the one and where FT is called cumulative H distribution function so that also please take for cumulative H distribution function below that the fraction of material in the exit stream which has been in the system for a time less than t is FT what are the units of FT which has been in the system for a time less than t is FT less than t means you know till 6 minutes that is less than t yeah till 6 minutes what is the fraction even in this example if I am telling so we can also write the same thing as 1 minus FT is what yeah I think 1 minus FT will be the fraction which is ET has come out yeah more than 6 minutes I think from 6 to infinite time okay so these are the definitions what we have and we also have another definition called internal H distribution internal H distribution this is not very widely used internal H distribution function normally represented as IT this one is the fraction of material which has a time t and t plus delta t inside the reactor the other two are exit please remember that exit this is internal right so I mean yeah okay please write that the fraction of material which has a residence time between t and t plus delta t inside the reactor t and t plus delta t inside the reactor is IT delta t again that fraction is only IT delta t okay now then full stop you have to write IT is called internal H distribution function internal H distribution function so yeah the internal H distribution function IT is similar to you know in our IIT if you assume that may be thousand people every year entering thousand people every year going out in the communication right so then all the programs we know I think you know how many people are their total hold up that is total so inside how many people have spent a time one to two years or maybe one to one and a half years all programs together and less than one year you cannot go maximum minimum time to go out of IIT is minimum two years and maximum is infinity now really infinity we have also given a degree for one person of 17.5 years yeah and I think some of the b-techs are taking I mean maybe eight years nine years 12 years something like that okay yeah anyway there are special cases you know that is one or two molecules will be there always like that we should not worry we should not worry okay if I take you know the m-tech program okay how the people are moving is it plug flow or is it mixed flow Pooja why plug flow for m-tech they join in July and after two years July they will all of them will go again there may be one particle by some reason that we are not talking but many people many people will get huh that is not you can ignore one person okay there are many then we have to worry as you said you know why this dead space okay yeah good so then if you take MS Phd program you know yeah then only you rememberize otherwise concepts you will forget right okay in fact you know when I plot this information yeah every time we plot for senate after convocation is over now you zero time you know when they enter it is zero time and maximum may be seven years theoretically speaking okay over the time given by senate but occasionally we are also allowing in cases where they go beyond eight years nine years and all that now peak is going like this not able to follow okay this is zero time this is ten years let us say okay so number this is number yeah it goes like this zero zero the average is 5.5 this is what phd right no that is what is happening that is true if you want you can go and check our websites and all that you know we will have this data you know maybe you are not allowed to see senate minutes but I think you know senate minutes we can show that so this that is the distribution this is exit a distribution because after convocation only we are plotting this it is not inside please remember that it is not inside it is so that means you know all this time till here what you call anyway time and the real time lag which is given by senate is only two years for phd and one and a half years for two years only you know within two years you can complete and just after two years you can complete phd and within a eighteen just after eighteen months or one and a half years you can submit for a message beyond that it is not allowed even though I allowed one or two people because I think as dean because they have done extraordinary work I think three months before or two months before also we allowed them that means even in sixteen months or fifteen months but there was also reason because that guy was a project earlier he has done lot of work so special permission given by senate and then we allowed that right so this is what is happening so this is the average 5.5 years now and you know this is not for the people who are doing external registration and all that external registration they work outside so it may be difficult you know for them to do but this is only our brothers and sisters who are on the campus full time full time always okay yeah so they are there full time not doing the work so that is what is happening unfortunately so that is why you know we are trying to call them to director dean we used to call them and then talk to them why you are taking time and all that so because most of MSPHH scholars should know because MSPHH scholars we know only entry time exit time is not known whereas M tech they cannot stay beyond 24 months they will be thrown out that is plug flow this is axial dispersion with 10 the 10 years 16 years I told you that is 10 now bypass is not there bypass means you know that person I told you what is that if you within minimum time at least you should be one and a half years so that fellow has submitted even 15 months that is bypass okay you see everything is there within us all RTD also can be explained nicely so that is the definitions of all this right so IT we do not use usually except for material balance there is one equation where we have to use that this is T bar IT equal to 1 minus FT okay you I mean you do not have to worry about how that equation has come can anyone tell what is the meaning of that equation very simple FT is the fraction which has come out okay atleast spend that much time and we are exit so 1 minus FT of that must be internal so that is why T bar IT because we are taking the overall balance there will not be delta T there will be T bar that is all see that physics of the meaning you know of the equations meaning of the equation is also very simple if provided you start thinking you know thinking and trying to understand very good beautiful so this one and here the tracer when we were talking about so there are also some properties for the tracer okay properties for the tracer that also let me write that properties of tracer here yeah what are the do you know any very good first one may be non reactive but I think I will write here if you are this itself is enough for everything same physical properties properties as original fluid or flowing fluid okay that is one and next one is it should be missable sometimes you may have the same physical properties it may not be missable okay the tracer should be missable oh my god many things I have to do I say number 3 yeah not reactive should not be reactive number 4 should be easily analysable should be identified by some technique okay these are the properties but there is another thing it is not a property but again it is man made okay so how much quantity you have to add how much quantity I have let us say 5 liter vessel yeah it should be measure that's all but you should not add because it is 5 liters use the tracer volume should not be 10 liters okay so that is like like this world boxing champion trying to find out who is good who is bad on the road correct no if you use our pulsing foot one slab is heavy weight boxer correct no even if it touches who will fall that's all over so there is a system destroyed system destroyed there is no response there only one response dead so that is why we should not add so much where it disturbs the system okay so the best thing is as what he said it should be as with less quantity recognizable as less as possible but recognizable right that is the kind of tracer amount what we have to add and you know this miscibility like you know I can easily tell you imagine that is a simply water is flowing and then you added without knowing mercury as tracer what will happen water is flowing and you don't know okay how to contact it as you took a mercury one day in the laboratory and you bought the mercury it will happily go and sit there permanently dead space and you will be waiting waiting waiting nothing will come okay so that is why that miscibility and all that should be perfect instantaneously miscible okay good so these are the properties and now why should we plot in this way let us discuss okay that is mathematical description of e t and f t first let us take f t so and you know that f t okay pulse input will give you always e t and step input will always give you f t and I think here I have told you about pulse input but step input will be how do you conduct experiment with step input yeah now go on adding means you cannot go on adding but what we do is you have here a normal parallel line this is tracer okay and a time t equal to 0 you switch off this and then start this okay and then start that so now what will happen if you are imagining that you have a red color red color now is continuously entering right and till what time you have to conduct the conduct the experiment yeah that is why it reaches here this is finally the concentration what you have added here C0 that is C0 okay so this is step input and this is pulse input so by looking at the curve or data if data given to you shows that initially it is increasing increasing increasing and then staying some 2 3 values constant so that means I do not have to tell you which input is that that is step input and the other hand this pulse input data is first may be 0 or very small value goes up and then comes down and finally goes to almost 0 it should go to 0 that means otherwise it is not going to 0 meaning is that still there is some tracer inside so material balance wise is not correct it is not correct that is why you have to conduct the test till all the concentration comes out right okay so this f t will give the step input f t step input let me draw here that okay this is the one okay yeah here I have C0 this is coming out V V and a time t equals 0 C equal to C0 that is my tracer and this is cut off okay both are connected like this so when this is closed this is opened or this is open this is closed okay so what kind of walls you use for one one opening one closed one will open the other one signal goes that other one should be closed okay yeah so that is the kind of walls you will have here then you have to conduct here then this goes like this this is C0 finally this is time good so now what we do here is to write the balance we focus at any particular time here at the outlet at the outlet we focus and outlet is only here even though I have shown so much doesn't mean that you are measuring here you are only measuring here okay you are only measuring here that is a time after sometime t after I switched over from normal fluid to my tracer C0 after sometime t I will just imagine here at the outlet okay what is that imagination what kind of fluids I have I have old fluid that means a time t equal to 0 that was there inside you are switching off you know white fluid switched off red fluid started so now at this point after sometime t you cannot I mean analyze that after infinite time infinite time there will be only red nothing will be there right yeah so after sometime logical time you look at this and then look at the streams okay a stream and then imagine that in your mind you have separated both what is that separated both white fluid separately red fluid separated okay now as per our definition of ft the red fluid is the fraction of material which has spent a time less than t because that t is I have decided that is ft what is the concentration in that what is the concentration of red material C0 correct no C0 only what is the concentration of red material in the white fluid the other stream 0 that is the balance only we are just making right and here yeah okay that balance is you understood no V plus I am sorry V into ft C0 plus V into in fact the other one is 1 minus ft you remember this see at this point of time I think do not get confused Volga you already confused look looks like that correct no yeah so what is that you are not understood here at time t equal to 0 I am sending red fluid right and white fluid is stopped so that means the entire thing at time t equal to 0 at that instant is only red fluid so a white fluid red fluid just entered then depending on a kind of mixing and whatever we do not know what is happening inside depending on conditions there you will get mixture of red fluid and white fluid at this point various times I am talking about okay after 5 minutes what has happened at 50 minute I have taken some sample and then looked at that right so that contains white and red now I separated those two mentally right so the separated one red one is the material which has spent a time less than t that for 5 minutes because red fluid started coming only 5 minutes back correct no till then I think only white fluid was coming right yeah so then that is ft what is the concentration in that C not and total flow will be yeah I think you can calculate and tell me I mean sorry you can put the dimensions and tell me what are the units of this what is the concentration units yeah moles or grams you know in tracer we will say grams okay yeah grams per later and what is the overall flow rate that is all this is tracer most balance tracer m b that is what what you are writing right okay that is one and the other fraction Olga what is the other fraction this is for red what is the other fraction white so that means this white would have entered t minutes before correct no because at time t equal to 0 or 5 minutes before there was no red fluid only white fluid what is the concentration of red fluid in that in that particular 1 minus ft 0 so this will be 0 concentration equal to 0 because we are writing only balance for tracer tracer is red right okay so now this entire thing equal to what we see here V into C correct no it may not be the initial concentration I separated what is the whole picture is that that stream I have separated red fluid separately and white fluid because red fluid entered only exactly 5 minutes before and that means when you are measuring at the outlet 5 minutes I mean at the time of fifth minute all that fraction what you collected till 5 minutes would have entered only 5 minutes before or would have spent only 5 minutes that is the definition of ft that is the definition of ft so that is why yeah this balance this is white fluid yeah so this total equal to V into C what are the units of V into C V is again moles per second and concentration is sorry V is later per second and concentration is so again you will get most balance right are you okay yeah so this is the one this entire thing is 0 so V will get cancelled then what is ft C by C not so you conduct step input experiment and then plot C by C not because you are measuring every time C continuously if it is a probe continuously that gives you C otherwise you have to take samples and then measure C you know right C not you know and if you do that one you will get a curve something like this sorry what is this value very good that value will be 1 and what I have shown here is only only C C this is C and that maximum value will be only C not so C by C not will be 1 C C how simple that is ft so that is why when you conduct step input automatically you will get ft very simple balance but only thing is in your mind that clarity should come right so red fluid white fluid white fluid was flowing originally I switched over to red fluid at time t equal to 0 after switching over at time t equal to 0 5 minutes later I collected the samples okay sample then I imagined that you know that sample separately what is the white fluid and what is the red fluid white fluid would have sorry red fluid would have entered only 5 minutes back and our definition of ft is that the fraction of material which has total fraction which has entered a time less than okay which which has spent a time less than t that 5 minutes is the t what is the concentration in that C not because only red fluid only red fluid I have taken and other white fluid is 1 minus ft that fellow would have entered earlier right what is the concentration of red fluid in that 0 so that is why this entire thing will get cancelled and this is the mass balance and finally you will have grams per second correct no or gram moles per second I think that is okay right molecular weight we will give you that so this is what is for ft now let us see for et et pulse input okay here also we do the similar experiment similar experiment okay volumetric flow rate volumetric flow rate and concentration and here we introduce this is direct delta function delta function this is at time t equal to 0 so saying that you know direct delta function is always I told you know we should not take kgs and kgs of material and volume if I know density if I know I can calculate what is mass also so let us say 10 grams of tracer I am using which can be identifiable without disturbing that is very important when you are adding it should not disturb the flow when it disturbs the flow your steady state will disturb under steady state conditions only so that is why what we do is we take a injection in the laboratory and then so I am telling next semester you have to imagine yourself okay next semester you have to somehow inject without any disturbance okay good so you will somehow introduce this material into the reactor or into the vessel and then that is all stop and also direct delta function definition you you know know the width of the pulse will be 0 height equal to infinity area equal to most lausiest description where we never get any idea what do you mean by width 0 height infinity area 1 okay yeah but that is a mathematical description great mathematician said it is possible we also say yes okay yeah but you know that is impulse very quickly that means that that pulse is very very small right that is the meaning there so that is the kind of input I give so the way I am telling is you take the syringe and then often over if you inject that is not pulse because the entire experiment time may be 1 hour and often over you are injecting that so that you cannot treat as pulse input okay so that is the reason why I am telling that okay good so this is the one now here we would like to find out E t I mean write the material balance again here okay so the amount of the amount of tracer coming out amount of tracer coming out out of the reactor out of the reactor between t and t plus delta t I am not asking fraction I am only talking about amount of tracer that is coming that means after introducing what I collect here is between like that you know fourth minute and fifth minute what is the tracer I am getting right yeah what is the tracer amount total amount how do I calculate this let me call this one as delta m okay so this delta m yeah equal to and what is this one how much is coming here v into c okay and I am asking for what is the amount of tracer that means amount grams amount means grams or moles okay grams how do I calculate that at this point v c into delta t that is all that is grams so that means between fourth fifth minute and sixth minute that one minute that is delta t how much mass has come right so that is the volumetric flow rate multiplied by concentration that gives me grams per time multiplied by that interval time delta t okay that will give me the total amount okay so what is the total amount you know completely all the tracer if m is the mass okay m is the mass which is added there okay sigma of all these or otherwise total total mass equal to m which is nothing but 0 to infinity v c correct no I mean as Sushmila said I can put sigma sigma is again for discrete but I think continuously when you can write this one now the definition okay this is the total mass that is the amount of mass coming between t and t plus delta t what is the definition of et what is the definition of et fraction of material which has spent a time between t and t plus delta t can you get from these two equations et equal to delta m by x l delta m by m which is nothing but v c delta t divided by 0 to infinity v c dt v is constant volumetric flow rate I told you know constant density system okay yeah and also no reaction there so now what is the equation now c oh no that is right only but here it is not this is only fraction of material with r t residence time t and t plus delta t I have swallowed some words here r t r is a residence time this is the fraction only what we know it is not et please remember that okay correct no it is not it okay so now here I have c delta t c delta t divided by integral 0 to infinity c dt and what is this one okay so okay so this is c by 0 to infinity c dt that is what is et that is et but not to remove that yeah this is nothing but et that is what is the definition very simple definitions and original allowance payal book you know not original means second edition all these derivations are not there but in the last one he has added but I have been teaching this earlier also because I think carberry and some other people have given this one this is because it gives you a feeling otherwise blindly we are asking them to plot I removed that I have plotted no integral 0 to q q yeah here this is q q equal to 0 to infinity c dt that is the area under the curve and et equal to c by q that is nothing that is et only so if I add delta t delta t both sides that will be fraction very good very better huh break this program is without any break says what does makes in between okay so okay I think break