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Current time:0:00Total duration:5:19

More on finding fluid speed from hole

Video transcript

before we move on I just wanted to make sure you understood that last point I made at the end of that list last video we said that the pressure kind of inputting into this you could we could view this this Cup with a hole in it is essentially a pipe where the opening on the top of the cup is the input to the pipe and this little mini hole is the output to the pipe and we say that this is a vacuum let's say there's a vacuum all around I don't want to do it last time I closed it but maybe a but we have a vacuum everywhere and since there's a vacuum everywhere the pressure at this point p1 is equal to zero and the point I wanted to make is because we have a hole here the pressure at that point at p2 is also equal to zero you can almost view it as maybe the the atmospheric pressure at that point but since we're in a vacuum that pressure is zero and that might have been a little confusing to you because you said well wait I thought at depth at depth if I had a point let's say it that same height that I would actually have a pressure at that point of Rho gh and that's true that's completely true you do have an innate pressure in the liquid at that point of Rho gh and actually that's what's causing the liquid to come out but that's actually taken care of in in the potential and the in the potential energy part of the equation so let me rewrite Bernoulli's equation the input pressure plus Rho G H 1 plus Rho v1 squared over 2 is equal to the output pressure plus Rho G H 2 plus P v2 squared over 2 and I think you understand that this term is pretty close to 0 if this the the rate at which the surface moves is very slow if the surface area is much bigger than this hole so it's like if you poked a hole in hoover dam that whole lake is going to move down very very slowly like 1 trillion of the speed of which the water is coming out at the other end so you could ignore this term and then we also define that the hole was at zero so aged to the height of H two is zero and so it's simplified down to the input pressure the pressure at the top of the pipe or at the left side of the pipe plus Rho gh one and this was kind of this isn't potential energy this is but it was this was kind of the potential energy term when we when we derive Bernoulli's equation and that equals the output pressure or the pressure at the output of the hole at the right side of the hole plus the kinetic energy PV to the kinetic energy term because this actually doesn't add up completely the kinetic energy because we manipulated it and I just wanted to really make the point that well that this is this is definitely zero I don't I think that is clear to you because we have a vacuum up here so the pressure at that point is zero so we could ignore that and so the question is what is the pressure here and I said well this pressure is zero because we have a vacuum here if I were to say that the pressure over here at this hole is equal to P gh let's say that I said that the pressure at that hole is actually equal to P gh where this is H then I would have the situation where P gh is equal to P gh plus P V squared over 2 - and what does that mean that when I say that that that pressure at the output of the pipe is P G H that means that I'm applying some pressure into that hole and essentially that pressure I'm applying into the hole is exactly just enough offset to pressure the to enough offset to offset the the pressure at this depth and because of that none of the water will move you could imagine if this is the hole let's say that's the opening of the hole and I have some and I have some water particles or some fluid particles let's say that these are the atoms these are the atoms we're saying innately at any point let's say that this sure there is a pressure at this point that's equal to Rho gh but this is p2 how much pressure I'm exerting on this end of the hole this is p2 and if I exert Rho gh this at this end if I exert Rho gh at this end then this these molecules that are just about to exit the hole aren't going to exit because they're going to get the same pressure from every direction so what we said in the last video and I really want it because this is a subtle point is that the outside pressure being on the outside part of the hole is zero and because of that we end up this term is zero and we essentially end up with the that d the change in the potential energy all becomes kinetic energy which is something we're familiar with from just our our kinematic Center and our energy equations well anyway with that out of the way let me do another problem and actually I will do that next problem in the next video just we have a clean cut between videos see you soon