 All right, so don't talk. So we are going to start fluid dynamics, please write down. Okay, so in fluid statics we focus primarily what is the amount can exert on the tip is there as you go down a static fluid. Otherwise you don't for example or how much below a human being can go inside. So in all these things I must know how is the pressure variation in a static fluid. So in the fluid our focus was majorly in fact the buoyant force that we have discussed yes or no. The buoyant force itself is nothing but what stress it will break while we are focusing that property. So I must know how much load I can give to a solid. So we have focus okay but there will be some water things can happen fine. So that was our prime focus when we had fluid statics in the question. Now we are moving forward the physical properties of fluid when it is flowing. What is the difference between flow and a buoyant? You can take up a list of fluid statics will be applied there already. So when you shear force like this what happens to a solid? It will get deformed like this there will be angular shear strain will be there. But when you take a fluid resistance against this external force and that is what is the shear stress okay whereas the fluid offers no resistance to the shear force. Are you getting the difference? So the shear stress is almost zero in the fluid it can get deformed indefinitely. So one layer of the fluid can move related to the other layer okay. So that is the difference between a solid and a liquid with respect to the flow. The shear deformation is called the flow itself. In fact if you heat the solid it will go towards the liquid. So this is called the flow alright but we are not going to use whenever we study the. So just like in the previous case whenever fluid was flowing we were making buckets. Now when we have to discuss the flow of the water what will be drawing the fluid is flowing inside the pipe only right. So pipe will be drawn a portion of pipe will be drawn and water is flowing inside okay. When I talk about fluid dynamics what do you think the kind of properties I am looking for? Okay if you very smooth flow happen and the flow when it become changes. Have you ever encountered turbulence when you are assigned for the laminar but when the flow changes to suddenly the aircraft will. So property has changed just because the flow is changed right fine. So our water doesn't mean and how we can find out which flow it is what else we will be finding out here what do you think. What do you think someone said velocity to velocity for example comes and hits and turbine coil and then which turbine the coil also rotates. And that is how you generate the power and hydro power plants fine. So you should know what is the velocity of water can exert on the turbine that is just an example. What do you think the other we have learned work energy theorem in what part of the square which mass it is GH and pipe is suppose is such that it has been convenient to apply in fluids. So we need to modify that work energy theorem so that it becomes convenient not there with solids. Why because entire solid remains as a single object fine. So you need not remains as it is and single intact object mass and is given to given but here the so I should not go against the conservation of mass. Somehow I have a version of mass in fluid also it should not happen is called continuity equation fine. So we are going to discuss these two theorems only and fluid dynamics is much more simpler than fluid statics even though the situation is little bit more involved much simpler. So let us start that please write down first since we are talking about the fluid property what is stream line flow. So please write down stream line flow we discussed that in line suggest there has to be some sort of line. So suppose you have this is nothing inside a big fine lot of fluid particles might be there many fluid particles infinite fluid particles are there. And flow comes from the motion of a single particle. Let us say one such particle out of those infinite particle follows this path it goes from 0.1 to 0.2 and it follows this path. The stream line flow is a flow for which the each particle if it enters point number one it will follow the between the two points is fixed. If somehow up this stream line it is going to follow this path how you determine the direction of flow. Direction of flow is to the stream line stream line it is I can just draw the time at this point the direction of flow is this all right. Now stream line gives you more information than just telling you about that sorry I missed that. Suppose you have two stream line intersect suppose they intersect. So if they intersect you will have two tangents along the two stream lines okay which is fine. So that is not same part similar particle starting from here could follow okay. So there is no fixed path the intermediate so you cannot have any scientific sense we were discussing about laminar so turbulent flow also. The information given by the stream line flow. So suppose this is a pipe clearly this is bigger cross section sorry this is bigger and that is smaller and this is not the end. It is a part of a bigger pipe no okay. Now if I draw a starting from here then this will be there. Now there are a number of stream lines per unit number of stream lines per unit area is proportional to the magnitude of the flow. So now using stream line so this is what the stream line not going to go back any doubts on the definition of stream line flow. Concept that we have discussed initially one was alright so let us take it one by one first I will apply conservation of mass. Fluid dynamics is also the equation of content with the philosophy if we do as I forward duty mass right. I should have started the discussion with that how many of you she can do it one kg mass goes in in one second. So in one second how the pipe so inside the pipe 4 kg particle no so same one kg that is going in same one okay. So that is does this person which is equal to this mass which has gone inside and assuming that the fluid is incompressible. Otherwise density will not remain uniform okay yes no non viscous we are not assuming here right now okay. We are assuming that fluid incompressible will not remain uniform same thing may not be valid for the air. Now similarly suppose V2 is the velocity let us say it goes out so this much water will go out so this much distance will be V2. The rate of water is rho in about the lambda. Press up sorry the fluid then density will change so the continuity application of work museum theorem in the fluid dynamics. It is correct since we are talking about the application of volume somewhere right seen it. If you do not pay attention the first time you are not going to understand this but knowledge theorem okay. Then you are going to have a cross section of a bigger pipe so I will be lost here okay. So density remains constant coming from this side is V1 and velocity with which it is going out from there is V2. And everything else because I am going to which is shown from this point of the procedure right. Each position of the sphere to the final position of the sphere I am applying coordinate theorem yes or no that will be better. This is uf-ui kf-ai. Now tell me the entire fluid moving forward two things by using coordinate theorem. Is it clear now on this entire it moves forward distance which is so force is into the displacement which is V1 dt. This is the work that something is wrong. So it is outside to here both sides it is outside. So total work the minus a2 a2 I can say that this is zone 1 this thing is zone 2 and that thing is zone 3. You will understand why was zone 1 press finally minus I have divided the entire mass into zones. Potentially zone 1 plus zone 3 finally sorry zone 2 both are same zone 2 initial and final final okay. Initially zone 3 does not exist so this is also gone and finally zone 1 does not exist that is also gone. Finally zone 1 does not exist. What what? So finally zone 1 does not exist that is also gone. Finally oh I have taken this area sorry sorry. So finally initially zone so this is equal to potential energy of minus potential energy of zone 1. Now tell me how much is the volume which is how much this is mass mgh is the potential energy. So that into g into what h2 this is the potential energy of zone 1 which is how much similarly 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 are moved ahead. The mass which was initially present in this much pipe. Is this in clear? This is u2 minus u1 okay minus ai please find out yourself.