So I'm not OK with how some people derive this equation. These people consider a pipe whose endings have cross-sectional areas and heights which are different. They then use the conservation of energy principle by saying dW = dK + dU (Where W is work, K is kinetic energy, and U is potential energy). For this they consider that the work done on the system would be due to external pressure forces exerted on the whole system of water along the pipe. And here comes the part where I disagree: they use this Work (this value) calculated on the entire system of fluid to calculate the change in Potential and Kinetic energy for an infinitesimally small slab of water within the whole system. This is completely invalid isn't it? I mean you would have to consider the entire system, I think. My way of interpreting the derivation is if you consider just one slab the whole time. Is this a valid way of thinking? How would you derive this equation via conservation of E? Thanks! edit: In fact, in one video I saw, the person just says "the middle chunk of water stays the same the whole time, so we can just ignore it".