 Now, we are getting into the application of work music theorem in the fluid dynamics. So, please, one knowledge theorem is nothing but application of work. Since we are talking about the application of work somewhere, right? So, rather than that, I have seen it. For past 10 years, I have seen it. If you don't fear it, you are not going to understand this work music theorem. Okay, then you have to memorize everything. Okay, understand how things work so that, you know, a cross-section of a bigger pipe, so I will be which it is coming from this side is V1 and velocity with which it is going out from there is V2. Same thing which is shown from this point of the fluid processing, right? In the initial position of the sphere to the final position of the work music theorem. Yes or no? That would be better. This is Uf minus Ui Kf minus Ai. Now, tell me, the entire fluid moving forward to things by using work music theorem. Is it clear now? Is there any force that is doing work on this entire fluid standard force on this entire fluid? It moves forward, distance which is, so force into this, into the displacement which is V1, Ve. This is the work that can work that something is wrong. So, the outside is wrong. The outside is here, both sides are outside. Something is wrong. See, you can say there is something wrong with WP2, whatever. So, total P2, A2, I can say that this is zone 1. This thing is zone 2 and that thing is zone 3. Was zone 1 present for 2 plus the potential of finally minus, I have divided the entire mass into zones. Potential is zone 1 plus potential of zone 3 finally, sorry, initial. Okay, here is the thing. This final potential is zone 2 and initial potential is zone 1, zone 2. Both are same. Zone 2's initial and final potential are same. Yes or no in final? Okay, initial is zone and finally zone 1 doesn't exist. That is also gone. Only zone 1 doesn't exist. What, what? So, finally zone 1 doesn't exist for sure. Finally? So, the one doesn't exist. Oh, I have taken this, sorry, sorry about that. So, finally and initially zone 3 doesn't exist. So, that is initial actually. Okay. So, this is equal to potentiality of zone 3 minus potential energy of zone 1. Now, tell me how we know volume, which is how much? This is mass. Mgh is the potential energy. So, that into g into what? H2. This is the potentiality of zone, it is potentiality of zone 1 which is how much mass. This mass move forward. There is nothing here now. That is replaced by some other mass. But that is not my system. My system is only this mass which has moved that. So, on the mass which was initially present in this much pipe. Yes. This is u2 minus u1. Okay. Find out now similarly, what is kf minus ki? Please find out yourself. You can again divide into zones. This is similarly in data. Equal to? I am saying much pressure. Okay. So, your h1 is equal to p2 plus 2 square plus low g hd. Keep on waiting, right? Okay. Now, tell me assumption that inner flow, not turbulent. Yes, several other losses are there, frictional losses. So, turbulent flow will not have just these energies. There will be energy losses that will happen. So, since you have ignored that inner flow. Okay. So, please write in any question until and unless stated others. Please pay attention. Few point here. That h1 is out of the pipe. And these two points can be anywhere in the pipe. Right? See, two points. I can say that constant throughout the pipe. Can I say it in a flowing water? Constant. Okay. Now, this is, Normal names. Volume is this much. It means that rho g h at that point is that. Fine? So, this one new kind of energy does some work. Energy. Alright?