All righty new clip here or a new version Well Oh cool Yeah, it's neat Okay, hold on there are a couple spots here this one is it's You can see the spacing here how it goes back back back And you have a bit of a bigger spacing here. I'm looking at the tip there and then suddenly it sticks And then we have a big move over here and then it goes straight up instead of continuing so those little Spacing irregularities just kind of kill the weight a little bit Since we're in the policy phase And then this one there's this is so heavy It's going to take a lot for this to suddenly change direction And you can see this here. We're starting a bit of an arc that way And then it kind of comes down straight and then suddenly over and it's this this move this way That I'm not quite buying and shoot right there So I think we can have that at the end, but I would continue that move Not this here. You might argue. Well, it's kind of maybe resting there But it'll be so heavy it would push that arm and that elbow down And then you can have that arc at the end and now the notice this thing to change like that That's the main thing I'm looking at is right now is a sword That's all cool This one is a bit light just a bit. I look at the spacing. Let's see here. It's that lift Give this Half the spacing and then a bit less and then we're getting more into it then you can start accelerating but Just at the beginning whoop has an ever so slight light feel And it's if you look at this corner here You can see how it moves over there over there over there over there And then whoa, it suddenly goes up. You can see that harsh Move there. So we wanted to make sure that all of these Points there are just a bit smoother In terms of the character let me see that leg is doing and I think that's okay Goes up. I think that's okay spacing wise Here you want to go. I mean it's it feels like it's kind of resting on that leg and then it's It's going through the wrists of how this is moving up I wonder if it might be more believable that It's resting on that leg and it's also the leg that pushes the whole thing up. So like by now that leg is up here and the knee is Did the the heavy lifting if that makes sense. I don't know if that's Too broad of a change at this point. I'm just looking at like how how is that character lifting? because there's just there's a pull back And then how does this realistically go up and because it's not more like this or straight arm into a swing This feels more like everything from this rotation up is coming through the wrist at the beginning And since you're already lifting the leg, you might as well push this and make it make it look like It's the leg that pushed this up and then you can rest here Into that. It's cool. Let me just see something on the knee. I think that's okay It's checking this knee here I think so. There's a moment right there where the knee locks Spacing wise it has forward lock and then continues a bit So just watch out for those spacing moments like that. It's not too bad. The rest you get some good rotating feet This feels a bit clunky here. What's going on? You got the back Oh here Check the spacing on the head kind of goes a little bit to the left and then whoa there We have a sudden pop to the right and then after that Locks right there. See that goes suddenly to the right. Boom. Suddenly to the left That stop is a bit better That one's okay here Wait fast I think it's okay. It's watching this leg how I think it's okay I do love this here Whoa That's all cool. Let me check the arms That's cool. I like that she goes and You might argue that this is a bit chest Headlocked where this feels like one unit.  I just want you so much you can do here It's a bit tricky with also the coloring, but I buy it and it's not too fast It's almost too even in timing how the elbow goes over there. You might have A slight variation in timing through there just a bit faster read and then lock But it's cool. Here gets tricky Because now we're starting to kind of break that wrist. I would go from this and then go And then that wrist is angled More aligned with the forearm and then the the pivot comes from the fingers So it's not such an IK wrist Especially here That feels just broken looking Even here you would have that angle more like aligned with the fingers Rotated and then at the end Definitely you want some ambient movement in the fingers and the wrists. See that there's a lot of movement there Where this feels very IK locked in a broken wrist there It's cool though. I still like that shot a lot. It's very cool Then This cracked me up. I like it It's just a bit chattery. If you look at this in the profile view It's very stroby and poppy Even this foot when it comes up feels very strong in terms of how we're here And then it pops back, but then straight up even if it would pop back, you would have a broader arc back But this feels just a bit A bit too sharp and then here we almost lock here See that there's nothing going on on this from this view So just watch out and if you can on something like this And then that compression to have maybe a bit more of a foot roll Or if that knee goes out this way, there will be maybe a banking of the foot pivoting off of here to feel that compression a bit more That's my main thing. It just feels Arc wise and spacing wise in the in the legs a bit odd. I feel like there's a bit of a pop in that elbow here You can see this here goes back Pop down and then pops forward and then locks And then the ears are a bit bit spliny slow And soft out and then this doesn't quite make sense how they They drag almost too late See that now suddenly go they suddenly go backwards on their own So if you kind of get a side this side like at one point Is it just to drag overlap and at one point? Do you want it to be like? Functioning ears where they listen they turn they might be Emotional thingies or like Star Trek and Dorian type stuff. Anyway, nerd Here's another one Visually like that. I don't change that color. I feel like those knees are Raw see how that goes down. It's almost like you're getting into intersections and weird stuff where I don't like it to me. It's a bit strong in the hips The loop doesn't quite work either if you look at that But it might just be just the overall clip where you have it Yeah, the main thing I'm feeling it's it's just a bit broad And if this goes down so far that it intersects and there's nothing really rotating here having A squish because if you're going that far, maybe maybe again, it would bank out this way To me it feels like I would lessen the hips by half So we don't have this much movement going forward And then your arc on the arms. I think okay It doesn't ever slide feeling of this versus continuing that arc a bit And there's some wobble in the head here. Whoop. See that goes forward or back So this feels I just like that that cost you right off. It's cool. I think I would Smooth out some of the left right and forward and back on the run just a bit. It's literally a frame It feels like we're hitting a few walls It's cute are the feet sliding sideways here It feels like you want to do a pivot off here, but we're sliding a bit too far to the left And this one's okay. I would potentially Get this one a bit more into the left instead of that straight down a bit more to the left So it's almost running like this. I'm exaggerating but instead of straight down So it's like the slower you walk the more outwards your legs are for balance and the faster you run the more inwards it can be It's not a Heart instead of rules for creatures. It's it's applicable for sure Not that you know, this is a humanoid thing. I'm saying this is a creature But I think in terms of running it just feels almost odd to have that kind of visual curve I will go more into Something like that And give it up there's so much movement in its and its arms her arms wherever it is I think we can have a little bit more side to side roll which will then in turn Roll the head a bit more. It feels a bit straight. I think we can have a little bit more. It's a fairly Static run. It's not like it's it's out of control panicky run But I think there's a bit of a stiffness in there because this is so long We can have a little bit more left and right just a bit So give this a bit less of an ica head or or or a world space head look to it But I see some heart stops and the rotations as well if you look at the backpack The breathing apparatus left right So some smoothing out in uh, and some of these spacing moments there super cute though. Love that rig All right, there's an email you can sign up You can start whenever you want you can submit whatever you want you get 16 submissions either way The like and subscribe would be awesome. All right. Thank you


of momentum essentially is force balance and just as we wrote energy in, energy out, energy generated equal to energy stored. Similarly, we are going to write in this way also rate at which momentum is coming in, rate at which momentum is going out, rate at which momentum is generated is equal to rate of change of momentum associated with that control volume. But Newton's law tells me we will call it by a different name it is balanced by summation of all the forces. So, instead of me saying rate of change of momentum of the control volume Newton's law says F is equal to ma that is nothing but summation of all forces. So, a force balance is basically what we are doing we are doing a force balance and equating it to momentum coming in, momentum coming out and momentum generated. So, capital M in minus capital M out plus momentum generated equal to whatever is the balance of the forces.  What is so rho v dot n cap dA and there is a v here and this is integrated over the CS what is this integral when you look at this integral what do you understand is this a surface integral surface how do we know by this symbol and dA we know that it is a surface integral what is I will look at it this way rho v dot n cap dA what is rho v dot n cap dA? So, essentially what this is telling me is m mass flow what is v dot n vector. So, in fact the governing equation for mass conservation was just integral rho v dot n cap dA and that when it is evaluated over the surface becomes a negative sign for mass going in and positive sign for mass coming out because the velocity vector and the outward normal are in the same physical same direction outward for mass flow coming out and it is in the opposite direction for the dot product when mass is going in that is why this summation becomes a positive and a negative term which we write as m dot n minus m dot or whatever way you want to write equal to 0. So, same thing here the v times the associated mass flow rate. So, this quantity is the vector quantity. So, v times the mass flow rate associated with that direction. So, we are going to write this as what are the momentum which is going to come in go out for each of the control surfaces. So, this is the control volume control surfaces are these shaded I mean unshaded rectangles which are there. So, rho d y d z is the area of the surface u is the x component of the velocity v bar through the surface that is the mass flowing through that surface that mass carries a momentum in the x direction which is given by product with u. So, that is the momentum entering through the surface momentum leaving through the corresponding phase at a distance dx from it is nothing but what is given by our Taylor series expansion. So, u rho u delta x delta y delta z plus d by dx of this whole bracket which I am just going to write as rho u square for the derivative because delta x delta y delta z is just the volume. I will write the same terms for the y direction same terms for the z direction what am I doing here. How did I write this y perhaps you two are thinking same thing how did I write this term u into rho v delta x delta z is that right. What am I doing there momentum in the x direction. So, what am I multiplying with what mass flow rate in the in the y direction is multiplied with the velocity in the x direction because why are we doing this because we are deriving what are we deriving x momentum. So, we are book keeping the x momentum in all directions that is the reason why we are writing it like that these arrows are indicative of the mass flow rates direction the u which is multiplying each of these terms.  So, what this means I am going to ask himself ask. So, this is the mass flow through this control surface multiplied by the x component of the velocity which is contributing to the x momentum equation corresponding term of going out same thing for the z direction rho dx dy times w which represents the mass flow rate in the z direction multiplied by the u that is the x component of the velocity which is the momentum in the corresponding term for the upward. So, this when I write it is going to this become next slide. So, when I do this budget I would get the first term here here here will cancel off with these three terms and I would be left with d by dx of rho u square plus d by dy of rho u v plus d by dz of rho u w whole thing multiplied by delta x delta y delta z. So, what we have done is essentially we have opened that up this is what it is. So, this can now be expanded as u times d rho by dt plus d by dx of rho u I am keeping the product rho u in the second bracket in the third term I am taking u as one term and rho v as the second term and keeping that together.  So, rho u comes out. So, rho times u du by dx plus rho times v du by dy plus rho times w du by dz this essentially if you look at this is your continuity equation. So, this whole thing goes to 0 the first brick bracket goes to 0 and I am left with rho du by dt plus u du by dx plus v du by dy plus w du by dz everything has this delta x delta y delta z. So, we are divided through therefore, it is per unit volume basis. Now, one question I have what is this term sorry what is this term physically mean what is this term and what is this term I have four terms one is rho du by dt other is u du by dx v du by dy w du by dz what are these terms who said convective acceleration somebody said. So, u times du by dx plus v times du by dy plus w times du by dz if you just go back to your conservation of mass equation the concept of material derivative was introduced here if you look at the d rho terms. So, transport of density because of the x component of the velocity y component and the z component of the velocity. So, these first four terms became capital D by dt of rho same thing this will be your material derivative of the x component of the velocity du by dt is this clear any questions this is clear then y and z are the same we are not going now left hand side is taken care of right hand side summation of the forces what is summation of the forces what are the forces. So, for that we have to write the force balance properly we have to do with the appropriate side. So, this convention again is can get confusing to the students. So, we have to emphasize this again this sigma xx sigma xy and sigma xz first subscript denotes the direction of the normal to the plane on which the stress first subscript xxx here that denotes the direction of the normal. So, for this left phase the normal is in this direction which is the x x coordinate direction that is why the first subscript x and this is corresponding to the second subscript direction of the stress therefore this is the stress in the x direction this is the sigma in the y direction this is the sigma in the z direction acting on a surface whose normal is in the x direction. So, every phase has this. So, we have 18 such arrows which will have to be drawn all we are saying is each surface is having three stress components just to make life easy we are saying the first subscript represents the surface for first subscript represents the normal direction to the plane on which the stress acts the second subscript denotes the direction of that particular stress and the same convention will be followed for the others also. So, what we are saying is if this is the cuboid again we have sigma xx sigma yx and sigma zx it is we are not put it on anyway yeah it becomes messy. So, which of these is the normal stress which is the shear stress color color what is p delta y delta z how many say that is normal force it is a pressure force. So, pressure is compressive. So, pressure acting on the left surface is p times area and the corresponding term on the right face will be the Taylor series expansion of that normal stress acting on the left surface sigma xx times the area associated with that surface on the right hand side again it will be in the outward normal direction of sigma xx dA plus the first order term what is this violet color arrow here sigma yx why am I doing in the previous diagram I have shown sigma xz sigma xy sigma yz yy xz xy what happened to all those terms x momentum equation. So, we are concerned with the balance of forces only in the x direction. So, of these nine which are here this one this one and this one are the ones which are acting in the x direction. So, we are taking that only. So, this purple arrow is representing the shear stress in the direction like this. So, sigma yx dx dz why is the direction opposing we are writing for a velocity in the positive x direction this is going to be in the opposite direction. So, sigma yx that is the shear stress on this surface times the area associated with that surface and the corresponding Taylor series expansion of that. Why is it not in this not in this direction on top why is this why is the arrow direction reversed in all these this is outward this is outward this is inward pressure is inward whereas, here this is left direction this is right direction all this I have had a student terrible time what is that. You go to the name what is shear this motion it is when it is shear right scissor what does it do it is the opposite motion correct. So, shearing is essentially tearing apart like this so that is what acting on that solid surface on that fluid surface sorry. So, when I do the balance of these forces I will get dp by dx will come with a negative sign because it is in the negative x direction plus sigma xx which corresponds to the normal stress sigma yx which corresponds to the shear stress on this plane there will be a sigma zx which will correspond to the shear stress on the front and the back surface and then there will be a body force which would have to be multiplied by delta x delta y delta z because body force per unit volume times the total volume of the qubit. So, we take everything divide through by delta x delta y delta z yeah a function f f of x plus h is equal to what is what does calculus tell me that that is definition of limit we can write here it is what he told. So, that it is the first term of the Taylor series expansion that we are using right from mass conservation we have used this even in differential equation for heat diffusion. So, when I do the balance I am left with the left hand side which is rho du by dt which is the material derivative and the right hand side which is nothing but these things. So, everything has dx dy dz which gets cancelled off this is called as the Cauchy's equation. How do I explain body forces pressure force normal now these forces we understood reasonably well because we can feel the stresses because we know that they are gradients but how do I understand body forces one is gravity okay that is because of which centrifugal force you have you get yes electromagnetic force Coriolis force what is Coriolis force for example, if I have a pipe in which fluid is taking place like that at the same time this pipe is rotating. So, there is a linear motion and the same time rotary motion. So, the fluid particle whichever is there here it is going to have what is called from right hand from rule. So, this is the flow direction this is the Coriolis this is the direction of rotation this is the Coriolis acceleration Coriolis force would be in the opposite direction okay. So, when this body force is there all our things are going to go everywhere whatever future factor everything what we have derived they are all for no body force you take one of the body forces it will be one phd it will be one phd for any configuration because everything will change if you just take Coriolis force friction factor will change heat transfer coefficient if you take centrifugal force everything will change if you take electromagnetic force the way he said that is a phd by itself okay you just take one and its influence is significantly different I mean its influence is significantly high which is what makes my velocity distribution pressure distribution and my integral parameters friction factor and if I take temperature energy everything subsequently will change. So, that is what we need to understand. So, body force generally we are not taking when we are deriving in our regular thing but if we take every complete nature of the problem will change that is true body force by definition is per unit to volume per unit to volume this one there is a error there both are enters exit exit one is one is one is that the last one is exit rate of increase minus rate at which it enters plus rate at which it exists I will correct and actually I do not personally I do not think it matters because it is a budget see we are getting back to our if I put E out and E in still the equation is valid that should preserve a say it is a convention q coming in in thermodynamics the people have broken their heads over its q coming in is positive q going out is positive how does it matter if you follow the same convention throughout in a given problem you will always be right within the problem do not change the convention that is all okay. So, now what are we doing complete thing is over we have to just substitute for sigma xx sigma xy sigma xz we have to substitute the terms they are all in terms of velocity gradient yes here I am stating without deriving especially normal stresses shear stresses at least I think I can feel what it is but this derivation is again a lengthy one which we do not intend to do it at all here but basically one thing I can tell how we arrive at these equations what we do here is we assume that stresses are proportional to strains stresses are proportional to strains and we get set of equations if we solve those equations I will get stress in terms of what is del u by del x that is a strain that is a normal strain what is a del u by del y that is a shear strain. So, if I take stresses as proportional to strains then I will be able to relate my stresses that is sigma xx sigma xy sigma xz in terms of in terms of gradients in terms of gradients okay I am not deriving consciously I am well aware of that that will be again 3 to 4 transparencies I do not intend to do that but this I need to keep in the back of my mind that stresses are proportional to strain I am taking and taking and going ahead okay fine is that is that the right way of doing that is how I introduce viscosity you know how is viscosity introduced that is how I introduce you know so that is that is basically so this I can easily do for Newtonian fluid so stresses are proportional to strain so I get these values for normal stress shear stress and again shear stress I substitute that what was this sigma xx sigma xy sigma xz I substitute that if I substitute that I will be if I expand that I will be getting rho du dt minus del p del x plus mu del squared u okay plus del by del x of mu by 3 del dot v plus fx what is this equation called or all put together what are these 3 equations called Navier Stokes equations okay so we can write very nicely vectorial form although I do not like vectorial or tensorial I would like to expand it so that I can feel each term easily okay so but then people try to write that in vectorial form this is vectorial form but all that I want to emphasize here is this these were the equations how many equations I have and how many unknowns I have these were found by Navier and Stokes independently Navier from France and Stokes from English England so they were they found independently these equations that is why we tend to call them as Navier Stokes equations how many unknowns are there and how many equations are but then only problem is that I cannot get closed form solutions all the time why because why why can I not get the closed form solutions that easily for few restricted cases for flow through a pipe fully developed flow flow between two parallel plates all that we can get closed form solutions why not generally I solve once and keep it and use it for any situation because my equation is nonlinear my equations are nonlinear so they are not mathematically tractable they are not mathematically tractable that is that is that is what makes my life difficult okay so with this I think we are through with momentum equation but now what I would do is instead of starting energy equation I will spend time on morning what professor broached up that is turbulence we left one question if you remember rho u prime v prime now that we have Navier Stokes equation in our hand I am going to go to this is my fluid mechanics notes so I have not put this yet now that in the morning discussion it was logically leading to that so I thought it is okay that we thought that we should introduce you this so now how did we handle turbulence someone said random the moment the word random comes which mathematics comes into picture what is the recourse of maths which maths I take into account yes statistics so I take recourse of statistics and that is what I am doing so I take an average value u bar and u prime is the velocity at any instant minus u bar okay so now what is u bar what is u bar I am integrating it for for some time t here in this case I am starting from time t0 to t0 plus t that is all the difference morning professor derived it for 0 to t here I am showing it between t0 to t0 plus t but now how do I decide this capital T how do I decide this capital T can I take half a second now let us say I have an imaginary sensor hot wire anemometer is the typical sensor what we use for measuring velocity as a function of time mungage is used with this you can feel it you can discuss with him left and right in the guest house what is hot wire and all you bug him and get to know what is hot wire is a small wire which is 5 times thinner than my hair diameter 15 micrometer I will try to keep that with a wheat try to keep that wire at a constant temperature okay and that wire is one arm of a wheat stone bridge now when the flow takes place what will happen to my temperature of the wire it will dip when it dips again I will apply certain amount of power to bring it back to the same constant temperature which I had said earlier so that measure of change of power is the measure of velocity that is very simplistic very simplistic way of telling okay so the point is if I have such a thin wire whose thermal inertia is so less you can understand what I mean by thermal inertia what I mean by thermal inertia here rho vcp is very less so time constant it can respond very fast so then only I can get this velocity distribution no no no no no no no no no I am not going to take a question I have not answered my question yet so how long should I integrate this I will that hot wire will give me the velocity as a function of time how will I decide this capital T one minute because I can integrate for long time half a minute one minute two minutes three minutes four minutes five minutes six minutes how do I decide while doing experiments I will not allow mangas to answer others anyone can answer should professor said in the morning should average velocity be a function of time should average velocity be a function of time no then that means whether I take five minutes six minutes seven minutes it should not matter but if I take two shorted time two shorted time my average velocity might be erroneous I should take five minutes six minutes seven minutes fifth minute average velocity should be same as sixth minute that should be same as seventh minute that should be same as eighth minute if they are different I should integrate still longer duration what is your question okay that is not in the purview of this but still no if you have a single wire you cannot if I have a wire now this is my wire let us say this is my wire and flow is in this direction it is going to measure velocity in this direction now if I orient this in this direction it will give me it will give me what why velocity similarly if I orient normal to z direction I will get the z velocity but I need to orient all the time with single wire but there are cross wires there are triple wires all sorts of things are there let us not get into that telling is easier than doing okay fine so but in principle yes we can do now coming back average velocity is this now u is equal to u bar plus u prime what is u prime now u prime also u prime bar I am saying u prime is u minus u bar u prime bar what will happen if I integrate this fluctuating component without doing statistics let us see this and see let us not have to do integration we will do that integration anyways but if I average only the fluctuating components for long time what will happen sometimes it is plus sometimes it is minus sometimes it is plus sometimes it is minus what should happen it should get cancelled out so ultimately I should be ending up with zero that is what happens that is what happens if I integrate that you can go through this integration u bar minus u bar so u bar so if you integrate this you get again u bar and you get yeah one analogy which I just was thinking how to tell it you think of any of these prices of of course everything is increasing now price but you think of a stock price yeah base price and then it fluctuates ok so if you are a smart fellow you will not sell it immediately or you know you are lazy fellow you might just keep it for several years or months on end at the end of the day net value will be the same as what you have purchased by and large talking of normal thing of course if you look at gold or something right now it is always increasing we are not taking such a case but by and large a stable thing which minor fluctuations up and down integrated over a long period of time it will average out to be the base value so these fluctuations essentially die out with time they are not dying out the magnitudes of the fluctuations are such that the positive and negative almost cancel off to give you almost zero value that is what you before I flash the next transparency I am now going to ask you a question now will my u prime v prime bar is it going to be zero u prime v prime bar we now saw that little while ago u prime bar is it is not visible no problem this is a different okay sorry so u prime bar we saw that this is so now will u prime v prime bar be zero what does u prime means fluctuating component in the x velocity now similarly as he asked hot wire I will orient and measure the v velocity and get v prime so at every instant I am going to get u prime and also v prime if I multiply that and then average over a period of time will it become zero need not be it need not get zero okay so that is what is the what is this what was this what is this this was my what did we tell in the morning this is turbulent shears see physically also we can think like this u prime is what random motion in the x direction v prime is what random motion in the y direction if I have both of them only I can have some mixing happening some mixing happening otherwise mixing cannot happen is that right is that right that is how physically I have to understand this minus rho u prime v prime but you can always ask how how on earth I should know that I should be defining this normal stresses and all that it is like a religion professor that is terms we have one professor by name aw that a with whom I have learned all this in fact what y plus and all I taught you in the morning it is so ingrained in my mind because of professor that because he has learnt it from folding that k epsilon model itself has come from launder and spalding okay the one which I was answering in the morning so he taught us so that is why it is so universal velocity profile I do not have to remember at all because he has taught us it so well so well because he has learnt it from the originator laundering spalding himself okay so point is this shear stress is because of u prime this is shear stress now normal stresses if I take normal stresses again u prime squared bar u prime whole squared bar can it become 0 u prime whole squared bar u prime can be plus or minus why am I squaring it to make it nonzero okay so it cannot become 0 if I average so this is minus rho u prime squared bar is my normal stress so how do I understand this I think this is all fine I will leave it there so we understood no we understood what is the normal stress I mean what will happen to my u prime if I average u prime for long time what will happen u prime if I average for long time it becomes 0 but u prime v prime bar if I average u prime v prime if I average it is nonzero so similarly if I average u prime squared for long time it is nonzero okay now let me take the neighbor stokes equation okay and now what are we going to do is that what did we do by telling what what did we do in turbulent flow we divided the flow into two domains what was that one was no no no no no no no no no that is why I wanted to tell I have I have I have I have divided into two domains one is mean motion another one is fluctuating motion it is like mean motion on mean motion I have superimposed the fluctuating motion so there are two motions so one is mean motion another one is fluctuating motion okay whatever I measure with the pitot probe what is it going to measure mean motion u bar is it is going to capture it cannot capture u prime okay so now now let us take the momentum equation instead of taking continuity equation we will just take the momentum equation now why do not you put the mean component and the fluctuating component for each term come on I want all of you to derive because many of you are sleeping I want all of you to derive because I cannot derive it but I want you to derive come on let us take the first term that is let us say del u what is that yeah before doing that I have to do the small trick I will take the x momentum equation left hand side okay please write this in this form that is you have rho del u by del t plus u del u by del x plus v del u by del y plus w del u by del z let me rewrite this as del u squared by del x is that okay how how is this equal to this can anyone tell me how is the left hand side of the second equation same as the left hand side of the first equation you expand this now what do I get continuity equation you will get if you expand that and that will that will become okay please I have not put that here because it becomes too lengthy if I go on putting so that I have not put that so you get this now you average this you average the first term now you just take del u squared bar u squared upon del x now you do the Reynolds averaging that is what is this I am going to put u squared I have to replace u by u bar and u prime for you I am replacing that is my yeah for you I just said a little while ago that I am having two components one is the mean motion another one is the fluctuating so if I put u bar and u prime and I have to square it know I have to square it so if I square it and expand it what do I get del u prime squared bar by del x plus del u bar squared by del x what happened to my u prime u bar bar that is I get two three terms I have put two terms only what happens to my u prime u bar bar it is 0 it is 0 can you see that I think I have done that yeah I have done that here u prime u bar if I expand that blindly if I expand that see u prime that is u bar I can pull out pull out of the integration and I know that this integration is already 0 so u prime u bar bar has to be 0 agreed so now that is the reason I have only two terms two terms so that is del u prime squared bar by del x plus 2 u bar del u bar by del x now this is only for the first term what am I doing what am I doing I am doing what is called as famously Reynolds averaging apparently Reynolds did it so that is why it is called as Reynolds averaging okay so similarly let me just go ahead and do it for me u v the previous term was next term is del u v by del y if I do that what will I get u has to be replaced by u bar plus u prime next one is v bar plus v prime if I take the product of that u bar u bar u prime u prime bar u bar v prime bar what should happen to that 0 similarly v prime v bar u prime bar also has to become 0 so I end up with only two terms you see here I had one term extra and here I am getting one term extra because u bar v bar anyway is there so u v bar I get similarly I can do it for del u v bar so you get u bar del u bar by del z plus w bar del u bar by del z plus del u prime w prime by del z is that okay are you all with me okay now let me do it for pressure same thing for pressure pressure is I have to replace it by p bar plus p prime p prime bar has to p prime bar has to vanish so I get only del p bar by del x so if I write complete equation complete equation what I wrote earlier I have u prime bar squared by del x 2 u bar del u bar by del x plus u bar del v bar by del y plus v bar del u bar by del y this is the additional term and this is the additional term is that okay yeah which one so p prime bar is getting no problem no problem no problem first time when you are doing it will happen so when I rearrange that I am coming back to my momentum equation what were we doing to remind you this was my momentum equation I was trying to replace each term with mean motion component and the fluctuating component so that is what is called Reynolds averaging when I do that I get you see what is that I get if you just see only this this this what are what are these three terms they are what they are what first three terms left hand side del p bar by del x and this they look similar to my old momentum equation but this is representing mean motion mean motion you see every term is having what what is called bar now you see on the right hand side with minus rho what are the other additional terms which are there which were not there earlier fluctuating those are what are called as Reynolds stresses okay so the first term this is contributing for the normal stresses this is contributing for the shear stress and this is also contributing for the shear stress this was done for which equation x momentum equation I can do similarly for y and z now you see when I do that here in u and v let us take x as this y as this z as this so u v means it is going to be u prime in this direction and v prime in this direction so mixing in this plane okay so u w means this plane so u prime is in this plane in this direction and w prime is in this so that is mixing in see it is so physically it is very easy to see if I imagine this picture u prime v prime means mixing has to occur in this plane u prime w prime means mixing has to occur in this plane is that okay so that is how you can imagine now v prime w prime v prime u prime all sorts of combinations you can yes now now if I put these in complete x y and z completely if I do that what are the additional stresses I get these are what first three terms in all of these equations or what name is tox equations applied for mean flow additional terms which are coming is r sigma xx prime tau xy prime that is minus rho u prime squared minus rho u prime v prime minus rho u prime v prime w prime bar okay I am not going to answer you one question now but I am going to ask you none of you asked me which I was waiting that you will ask me but none of you asked why I write always minus rho u prime v prime does that mean that it is negative sign tau wall I wrote lamp today morning tau laminar plus tau turbulent and I wrote for tau laminar it is mu del u by del y plus tau turbulent is minus rho u prime v prime does that make my shear stress negative compared to laminar I am not going to answer this question please cook this in your minds overnight and give me the answer tomorrow morning okay you can check wikipedia whatever whatever no problems but if you as long as you can come up with the answer you come up it does not matter okay so these are these three are what are these three normal stresses in x y and z direction and these are additional shear stresses in x y z direction is that okay yeah so these are called Reynolds stresses so now you see already in laminar flow my life was so difficult for laminar flow I had four equations four unknowns at least number of unknowns were equal to number of equations so but then we said okay we cannot solve it because it is non-linear but now I have same number of equations but number of unknowns have gone terribly high so rho u I mean rho u prime squared v prime square w prime they are all very high how do I solve no solution you have to measure them morning professor was saying how do I get them these shear stresses these fluctuating components how do I get them no way I will have to measure them measure them and use in the form of models that is what has been done in k epsilon turbulence model and that is why it does not work for all class of problems some reason for flat plate and internal flows these stresses have a definite pattern so if I have to come up with a turbulence model properly for a impinging flows I have to take proper these measured stresses is that okay that is the only way I can get closure in my problem what do I mean by closure number of equations should be equal to number of unknowns the unknowns are additional how many I have got into how many I have got into 6 unknown stresses I have to only way out is I have to take hot wire animometer or laser Doppler velocimetry or particle image velocimetry and measure so that is why I keep saying experiments and numerical work go together they are not separate they are complementary to each other so they have to complement one has to feed to other okay fine so this was done what we are studying today and trying to understand today was done more than a century back okay we are studying nothing nothing nothing absolutely nothing new there is a saying also if you want a new idea read an old book it only means that there is nothing new in this world everything someone has thought it is just that we are trying to understand again okay anyway so this is Reynolds stresses in 1895 Reynolds has done all this okay I think that is what we went up to laminar shear laminar shear stress turbulent shear stress and that is how we got into this viscous layer overlap layer and all that is that okay okay I think I think I think that is about turbulent stresses so coming back now okay so now okay before doing the non-dimensionalization now I have written can I if I take a flow over a flat plate flow over a flat plate what is my conservation of mass equation let us write I want all of you to write along with me so what do I what is my momentum equation yes you can flip your pages we have derived in the morning just before lunch d rho by dt plus rho of del dot v that is del u by del x plus del v by del y plus del w by del z is equal to 0 what does this mean what does this fellow mean to us what does this physically mean stretching in x direction stretching in y direction stretching in z direction this is dilation volumetric dilation it is getting swollen or maybe compression but people call it as volumetric dilation if it is incompressible if it is incompressible it cannot it cannot it cannot dilate it cannot expand okay so only it can dilate when it is compressible that is what it means so nice isn't it so now let us take momentum equation what is my momentum x momentum equation rho rho come on one of you should tell I will have to catch someone to yes du by dt this is total derivative remember equal to minus del p by del x plus mu del squared u by del x squared plus del squared u by del y squared plus del squared u by del z squared plus mu by 3 is that right mu by 3 del of let me go back I cannot also remember yeah del by del x of it is there del by del x of if I assume property is a constant I can pull this mu by 3 out but let us not do that del by del x of mu by 3 into del dot v del dot v I don't think I need to expand that because I can write this as del dot v so that you know what is what it is del dot v plus fx equal to 0 what is this x momentum equation so similarly let me write for y momentum equation no problem d by dt is equal to minus del p by del y plus mu into del squared u by del squared sorry del squared v by del x squared plus del squared v by del y squared plus del squared v by del z squared plus del by del y of mu by 3 del dot v plus f y is equal to 0 now is that okay no I have not told sorry 0 is not right oh sorry you see I am also sleeping okay so so it is it is it is 0 has to be it has no meaning if I write it as 0 absolute nonsense okay so now if I take my fluid as incompressible if I take my fluid as incompressible what will happen what all terms will vanish what will this equation reduce to del dot v is equal to 0 is that right now what will this equation reduce to let us say there are no body forces this term is 0 because del dot v is 0 and this term is 0 and I am neglecting this I am neglecting this is that okay and if it is steady flow if it is steady flow what will happen to this term I will have to with u del u by del x plus v del u by del y plus w del u by del z I will ask you a question let us say I say that viscosity is 0 when do I say that viscosity is 0 inviscid flow okay ideal flow where there is no viscosity so what will happen to my equation what is that equation what is that equation I do not know whether I have kept it here or not but anyway what is that equation yeah what is that equation what is much used abused whatever yeah yeah yes Euler's equation you will get because that is how historically hydrodynamics came into picture where viscosity was not considered that is why D L M birds paradox what is D L M birds paradox D L M birds suffered from this paradox that is why it is called D L M birds paradox D L M birds tried to calculate force around a cylinder what is the net pressure force around a cylinder pressure net force around a cylinder he got 0 all the time he calculates he gets 0 but he knows that there is some resistance because viscous some if not viscosity was not defined that time he knew that there is a resistance for the flow but he is getting 0 so that is why it is called as D L M birds paradox because in his derivation always he neglected viscosity okay so now this equation if I neglect viscosity I will get Euler's equation which can be reduced to Bernoulli's equation okay so this is in fact we can introduce back we can relate in the class we can relate if you are teaching fluid mechanics you have you have you can relate back to Euler's and Bernoulli's equation from this okay so I think we will stop here it is time that we stop here I think I will not even go to non-dimensionalization because it was good that we took a recap so but one thing as a teacher I would believe that as a teacher I should be able to write continuity equation momentum equation energy equation in the middle of the night if I am open up also yeah yeah now let us ask ourselves now before we wind up we have three more minutes that is a good question how do I feel each of these here I did d rho by d rho by dt means what density variation with time and space because by virtue of velocity by virtue of velocity now similarly what is this this is coming from pressure force you go to its mother who is the originator this is the pressure force what about this you can call diffusion term but this is actually viscous forces this is actually viscous forces when I take viscid flow in viscid flow I make it as 0 so what are these terms yeah but if I have to write Reynolds number in Reynolds number I always use one force upon another force inertia force by viscous force inertia upon viscous force so what is this inertia force mass into acceleration no so it is inertia force what was this this was mass into acceleration no it is mass into acceleration so we should be able to see the picture what the equation is in fact if I have to recollect surely I am joking in Feynman you know Feynman Feynman was the scientist who got Nobel Prize on something I do not know on what I got but he was involved in diagnosing why challenger Shetl failed okay he what he tells in that is each term I should be imagining as a picture he tells so that is what everyone says you know if I can think through pictures I have understood that yeah actually fluid mechanics is a wonderfully visual subject unfortunately it is taught in such a boring way that the whole beauty of the subject is lost in fact I had the opportunity to take compressible flow that is where you have density changes that gas dynamics under one very famous person who had so many pictures in his lectures every lecture would have some 5 to 6 pictures and the it was probably the most enjoyable course and doing compressible fluid mechanics through the pictures lot of this incompressible fluid mechanics became clear actually I mean at that point oh this is like this how foolish we are we could not understand because we could not understand because there was no feel for those terms so we should try to make it as visual as possible and unfortunately we we are behind completing the syllabus getting the exam in time this that that but it is just teaching we are not educating you had some question how do I feel it total acceleration all that I can see it is having both convictive term and the transient I do not think I can tell anything other than that inertia I understand always everyone has inertia now we have inertia to get up to go to coffee so we have inertia in the morning to get up so that is how fluid particle is also having inertia to move so that is what is this inertia I think every term as I mean it is having a meaning okay so I think here we will stop and get started tomorrow morning but I want you fresh in the morning because we are going to start on a fresh note the energy equation okay which is going to be involved in what we have derived so far.


Hello. Thanks for rejoining us. It's the breakfast on Plus TV and we are being joined by a member of the independent Petroleum Marketers Association of Nigeria, Ipman and the person of Chief Uqadike to talk to us on the NNPCL's issue of oil marketers with fresh directive on refund and new prizes. Good morning and welcome to the program, Chief. My friend and good morning Nigeria. Okay. Nigerian National Petroleum Company Limited NNPCL has issued a fresh directive to oil marketers on how to go about getting their refund and the new prizes of petroleum products. Work us through what this really means because we do not understand how this impacts on the oil marketers and what the story is all about. Let's get on the inside first. Okay. Well, it's been a very, very trying time for us because independent marketers, our only source of petroleum product is NNPCL because they are the only people that supplies petroleum products and they are also supplied to the Dakman members. So we normally get our supplies from NNPCL and sometimes we also source from Dakman members when NNPCL run out of stock. We always look towards having the best price from NNPCL. So during this time of deregulation, our tickets were already in the system, we paid 8,100,000 for 45,000 liters of petroleum on them. But it had a price of 118,000. You know, the benchmark then was to sell at 195,194. Unfortunately, during this period on that review, Mr. President came in and made that policy statement. So and immediately NNPCL stopped supplying us. Most of us who have spent 1.8 million, 8,100,000 for a product since past three months have not yet received because NNPCL gave us directives that we should augment it. And augmenting it would cost us almost $30 million there, $30.8 million, approximately $40 million. You know what it takes in the Nigerian economy now and the banking system with this high interest rates. So it's probably very difficult for NNPCL, for independent marketers to cope in with this new directive. A lot of y'all go ahead. Well, a lot of your marketers are already lamenting, your colleagues are already lamenting that they will not be able to meet up. Does this mean that most of your members in the smaller downstream members of your group are going to go under? Yes, there have been protests. A handful of protests here and there and also an entire membrane by our members. They have besieged our offices at our national headquarters. And our national president has engaged them, a large number, has engaged NNPCL. Although what they were able to resolve from the meeting was the issue of margin tickets, since some of us have more than five tickets in the system, that it can be matched so that it can make up the phone. But we have issue of funding. Funding is our problem. Look at the huge amount of money we are going to invest on this product. 21.7 million, 21.870 thousand. And your profit is not up to even one million. You might take two, three months to sell one truck off, depending on the size of your station. And Nigeria's now minimizing buying petroleum products. Before, in a philly station, a philly station can sell up to 10,000 litres. 11,000, 15,000, 2,000 litres per day. And now most of those philly stations are struggling to even sell 500 litres a day. And it is the same diesel. We are buying diesel plus the same amount of 15 litres, 800 litres. And we are running the station, the same staff. So business is not good for independent marketers. And it is not easy because we are already paying back in interest. Some of our tickets have been there for more than four months. And then business have not given us supply.  So most of our members we are cheating. You know, that why don't you give us the ones who have paid already so that we will go and sell them because the money has been there for more than three, four, five months. Here in interest. And some of our trucks have immobilized to NNPC to be able to pick these products. And NNPC did not supply us. So is it our own problem that you didn't supply us as we went to? So why are we not doing the fresh up? But the management came out and said, no, that before you do any differential, that was that memo you are talking about.  And if they give you your refund, I also want to let you know that the sources of petroleum products in Nigeria has not been multiple. It is still, it is still mono. NNPC is still supplying. Even when this regression policy is being implemented, we are still at the mercy of NNPC. If are they doing that, or are they giving licenses to import all the reputation of petroleum products from other sources? We will not have, in many markets, we will not have authority. For us, I'm talking to you now. Our records, we don't have authority. Okay. But is this even legal? Because are you exploring any legal steps to recollecting this, your money, getting your refunds? Not even refunds, getting the products for which you paid. Because if you paid four months ago, except maybe you pay and say, whenever the product is ready, I can get it. But if you paid four months ago, expecting to have these products, that shouldn't be a cost that you should carry. So are you exploring any legal ways to address this issue, or are you just going to collect your money back or add the 13. something millionaire to get new products? We have constantly, in so many ways, approached NNPC. We have called them. We have discussed with them. We have also used our lawyer to write them. At that place, they should be able to revisit that template. Or even give us a discount based on incurring interest on the money we borrowed from back. But they are very, very adamant on this. And because we know, like I said, that the source of petroleum products is still monopolistic. And they still have NNPCs that supply everybody in this country. So we don't have any option. Then we have written them with our lawyer. They have not yet to reply. I want to continue to tie down there. Most of this, because of this increment, most independent marketers are going out of business. Because it's not even easy for us to raise 8.17 millionaire for the first place. We are now coming to raise to 1.17 millionaire to buy 45,000 liters of PMS. They are at the present rate of 494aire per liter. So it's a very, very trying time for independent marketers. We are almost out of business. And it's very decisive. We have been pulling the government and also other agencies to intervene in this issue. To see how they can be able to appeal to the empty of NNPCs to give us a discount. Even if it starts in NNPCs, it can also give us a discount. We are able to take our tickets. As I was talking to you now, some other private depots that have products and have tickets of our members also give them a discount. Some of them pay for NNPCs. I am able to pick up the product. So we have to push on the face of interest ruled from bank. Because by the time we are at the present rate of 1.17 millionaire, who also is selling at the loss because interest have already taken our profits. And you find out the marketer will be struggling to be able to recover his capital. Well, NNPC, our petrol import monopoly is the big thorn on the back or the flesh of marketers as you have repeated listed this morning. And there is this headline that says that marketers are moving to end NNPCL petrol import monopoly. Bring us up to speed on this move by marketers to end this monopoly that has been a major problem to you. Well, because we are not actually expecting the deregulation policy to be removed abruptly. That is why we were caught up in the web. But as I know, by last week when we had our national working committee meeting, we discussed that I also have applied to NNPCL for a license to import a product. I was also talking with some of our foreign partners to see the best way we can be able to import a petrol product and distribute. Like I keep on saying it, that independent marketer is the only channel that petrol products can be displayed in the new synchronization of this country. And we are holding the nation's 90% of the distribution and retail unless in Nigeria. With the highest storage facility. So it is where we are starting to go into importation. Like I said, we can have a lot of milliliters. We can have a lot of it. What we need is comparatively competition in this market to be able to reduce price. Because as I said, demand of supply determines price. And when we will have upon that supply of petrol products, I also want to bet you that the cost of petrol products will come due. Since our consumption has been cut off by the price and some neighboring countries are no longer sucking from Nigeria and reaping the dividends of subsidy. We were just wondering, just like Maureen asks, when we will get something definite. Because if NNPC is still in charge at this time after the subsidy has been removed, it is a worrisome thing. But how far have you gone? How close are you to the point where licenses will start to be issued? They will begin to issue licenses to independent people that might want to import fuel into the country. What have you done about that? How much is the level of engagement with the people that matter in that regard? Well, I still want to let you know that all this depends on government pedestals. We are able to issue those licenses and you cannot start importing petrol products without getting license from NDPR. So it is not on our own making or we can be able to determine when license will be issued to us. But we also ask the federal government to ensure that the process of issuing licenses for importation will be very risky because of the period we are finding ourselves. We are just trying to figure out of this trying time because the federal government wants Nigeria to face the reality. And also I believe that NNDPR will ensure that some of these licenses will be issued as per the last person. It is not only independent marketers. Major marketers are also sourcing their licenses to import petrol products. Even Thaipan Mephas also have gone to source licenses to import petrol products. Well, previously we independent marketers were having imported petrol products who are the imported AGU and all the rest of them. But we are having some challenges, little bit of back end challenges of recouping this forest pack to where we got the petrol products. Which is one of the slacks that we have. But I know that by now government will not find out the seamless way in whereby people can be able to recoup their money and transform it to forest so that they can be able to go back and import again. Well, smaller fuel stations will definitely fold up from what we are seeing with the kind of challenges that you and your people are having independent marketers. Tell us, will that also affect the availability of fuel? Well, definitely it will. But it will not be as significant as it used to be before. Because with this removal of this regulation, you will find out that the agurais are not protesting. Neighborhood countries who are using that opportunity to siphon products from Nigeria and now the borders are protesting. You will find out that anybody has cut down his movement, even using fuel in the aguraitos and all the rest of them. And the movement, Tupuna prefer to do some meeting than meeting in Udeni. So in Nigeria, we are trying to adjust. So in Nigeria, we are happy people. So we are trying as much as possible to be able to be happy with the kind of conditions we are finding ourselves. And I also believe at the end of the day, it will turn out very, very good. And it will also moderate the lives and way being of people. But I don't know how it's going to stop smuggling into other countries. Because obviously, whatever we sell in Nigeria, it is almost like double or more in neighboring countries when the petroleum products are taken there. And I'm sure that's why people smuggle these things to that place. So you now saying that our consumption has reduced because of what is happening now. What if these licenses are given to the independent marketers and they import this fuel into the country. And then they decide also to sell in the countries that will have more value, will give them more value for their products. How are you going to prevent that? Is it possible? Well, I will not say that if an product is being sold at 195 Naira, it just is very, very simple arithmetic. April is being sold at about 95 Naira. And in a neighboring country like Kemeru, Dogan or Resounden, it's being sold at 400 Naira and Nigeria. And now it's sold in Nigeria at 400 Naira, 500 Naira. I don't think business will be a solution. The rate of consumption there, if they increase the rate of consumption there, it will moderate the consumption there too. So it will also reduce the consumption at that particular place. So when you have excessive things, you use excessively. When the product is more 18 Naira, you can decide to burn your generator for four days without stopping. But now it's 500 Naira or a little bit less than 500 Naira. I don't think in Nigeria that is receiving money the way I'm receiving. We'll be able to lavishly use all these kinds of ACPs and all the rest of them. So you will see that the consumption rate, even NNPCL has also said they're going to adjust their importation in the person volume because demand have reduced. So it's simple arithmetic. It's there. It's not something that somebody will say I'm permutating it. We are not permutating it. People want to buy 10 liters and they use it for three days knowing fully whether they don't just go to grab some for them without calling out the person. So you'll find out the behavior attitude and characters of people have changed towards fair consumption. Okay. Well, this means that of course, you know, before now we were told by NNPC that Nigeria consumes 66 million liters of fuel daily. Now that will drastically drop apart from dropping. We wouldn't have that controversy anymore because the customs had also said it gave us a different figure. We wouldn't have that controversy anymore with regards to what Nigeria actually consumes on a daily. Did you hear me, Chief? Hello, Chief. We seem to have lost connection with Chief Ukadike Chinedu, a member of Ipman. Hello, Chief. Yes, I was saying that with this whole development, the controversies over the quantity of petrol consumed daily in Nigeria will no longer be there. Hidato NNPC has said we consume 66 million liters daily. Customs had given a different figure. So this will take away all of that controversies from the narrative. Yes, I'm aware that the statement created by NNPC that they are going to reduce their importation of petrol in Koro to 30 million liters a day for Nigeria. And I think the statistic is very realistic within a short period of time. If we were able to articulate and also know that NNNDPR has also issued a statement to be able to see how they can be able to track products that have been supplied, to be able to determine actually the quantity of petrol in products that has been distributed and consumed by Nigeria. I think all the whole sectors, the administration is all about policy. And policy is all about the person who issues it. I think some processors and institutions, who they are like aesthetic attitude towards some of these things, I think they are pressed up maybe because they know that with the coming of this year, the new president, and initially fit down that if you don't perform well, the job is online. I'm just worried about the future. From what is happening right now, what kind of hope do we have in the coming days? Let's say in the next three months, what are we looking at from your experience with the NNPC, with policymakers and everybody? What are Nigerians looking at in the coming days? Okay, like I said before, we have an interaction with Mr. President during his campaign period and he frankly told us that the corruption in subsidy is so much that Nigeria will kill Nigeria and it's going to remove subsidy and that he has, what he takes to do, he has the apparatus and the purchase to also implement it. And although we are thinking that some of those modalities would have come before the policy statement, but because the policy statement has been done and maybe there is an internal meeting, NNPC went ahead as full of Nigerians, so they want to say that they are working in line with the director of Mr. President. And it got to everybody from the web, so I also believe that we will also have our trust because the most important thing is that you must put trust in leadership, no matter what. You must also put trust in leadership. We have to trust in leadership and be able to comply and support them and to find out actually the best way since we will work out. So although it is very, very difficult for us in twenty marketers because I'm telling you that the cost of fund is so very, we don't have a petroleum bank, we don't have an energy bank, like they have back of it and all the rest of them, wherever you can take full fund and be able to do our business because our business is also essential. We are also in the categories as essential workers because petrol is forever essential to all the households because Nigeria is driven by domestic distribution of petroleum products. So I also believe that we must have faith in this leadership and see what they can bring to the front burner. And by the next three months maybe we will also have a chat like this to be able to have a phrase where we are and where we are coming from to know where we will go back to where we are coming from or to know where we will forge ahead. Before the deregulation, the marketers too were fingered with regards to making things difficult, taking advantage of Nigerians and making things a bit difficult for Nigerians even including this taking of our field to neighboring countries to sell. You do recall that the minute the president said fell subsidy was gone, marketers took advantage of it and began to sell at crazy prices before the price template was given. How do you respond to that? No, no, no, no, marketers are not taking any advantage, even Nigerians took advantage. Even when they said that deregulation and you see Nigeria scooped the filling station, you see thousands of fire crews with the agricultural and cattle to buy at the same price and the rest of them. But when the price was adjusted, you see the whole queue will disappear. So who is taking the turn on each other? Marketers don't even have enough money to be able to buy at a new price. And you also want somebody to sell off what he has, the furniture he has and which he knows that that furniture is almost someone's rent, maybe he'll take it for $300 and he wants it to say $300. So how will you be able to replace that furniture? How will you be able to replace that product? So Nigerians also want to take advantage of the... The explanation that was given that time, chief, because Nigerians were asking if they feel the bought was bought when subsidy was paid because it was supposed to have ended by the end of June. And the announcement was made in May. And then they began to sell to us at a price that seemed to suggest that it wasn't subsidized, when it was subsidized. The explanation given was, well, so that you marketers will be able to buy again when you buy without subsidy. Now, you marketers are still crying that it takes... What about the money you made from the sale? No, my sister, my sister, let's do this thing. We started this conversation with a very simple question. Our tickets are in the system we bought at the old regime price, which is 188. The system has this ticket that's still there. And then we say it has not flooded us. And they have reported to the new price. So how do we sell the one who have in our business, the old price? When even our tickets, we have over 4,500 tickets at the old regime price, in NNPC of us, as I'm talking to you now. And we are not insisting that NNPC, you are asking me a question. One in NNPC, I said they said they will not sell to us at the old price we bought. I bought something in your supermarket. At the old price, it did not supply me. When I said it should supply me, it said no, it should tap money. But the market has increased. I also now advise independent marketers to sell the little one they have in their business. At the old price, the one who come here will get the money. I will get the money now to talk and collect this one to come and sell to you. How do you know that we need to service you? I will not profit to rent it. Even now that we are sitting at the loss, this is our business now. We are administrating at the loss. We are paying our workers, we are paying our drivers, we are paying our drivers, government assist here and there. And you use to 1.13 million Naira to do business. You cannot get up to 1 million Naira as profit in one month. So the major problem is the NNPC. How do we recover our investment? The major problem is the NNPC delaying in the supply of the goods that you already paid for. Yes, that's what I'm saying. And that was in May. We're talking about what happened in May. I'm making reference to what happened in May. We paid in January. It has not even yet supplied. I can forward it to you. Because you're understanding we had. I'm talking about products we paid in February. Yes. Chivo Kadike, we understand what is happening. We're just asking. We understand what is happening. That's why among the very first questions I asked you was whether you're exploring legal means because normally like you alluded to, you don't pay for a product in a supermarket and they collect the money. Months ago they do not supply and then now they're asking you to pay the new price. It's not done anyway. I really wish that you would explore legal means so that the interpretation would be given to Nigerians. It might happen in another sector and we need to know what the outcome is likely to be. But as we sympathize with you as it were. Now that we have a clear understanding because Nigerians were really miffed when that inauguration statement was given and suddenly the prices went up. When we were told that the budget was in the budget, the subsidy lasted up to 31st of June. So Nigerians began to wonder why are the marketers ripping us off when they bought during subsidy. So now we have a clearer picture. Here immediately that statement was done. They stopped supplying. No, they sold any one liter of product for 48 hours. No, they sold any one liter of product for 48 hours. And one way I came back to say okay give us our product. They said no. We should go and bring that 10.17 million there. Even though who pays for a vessel? Who pays 2.17 billion? We're not asked to make up 9.17 billion. It's a way of telling us that this business is no longer for the poor. It's no longer for the middle class like us. People like us. That we should leave. And we may return our finishes to farms. Well thank you so much. It's an investment we have put all our life or everything we have to build up these finishes to ensure that we can be able to feed. Thank you so much Chief. Who can do Kachinedu of Ipman for your time and insight and all the explanations you've given with all that's happening. Especially regarding NNPCL issuing oil marketers fresh directive on refund and new price. Thank you for coming Chief. Thank you. Thank you very much. Alright. I appreciate it. Alright you're still watching The Breakfast on Plus TV Africa. We'll take a break now and bring you sports. Stay with us.