How does the standard derivation of Bernoulli's Equation work? So, the derivation itself (the work energy theorem one) is pretty simple, but the work-energy theorem is supposed to be applied to particles, not systems of particles. And even if I did that, shouldn't we include the potential energy related to the arrangement of different particles in the liquid also be included? Or is there any reason it remains unchanged? Why do we only use the change in kinetic energy and gravitational potential energy?
Another thing that bugs me is how the net work done is calculated $$p_1A_1v_1\cdot dt - p_2A_2v_2\cdot dt$$ In the end, we're just multiplying the force on each end of the flow tube with the distance traveled by the ends of the flow tube, not the displacement of the system, so it technically isn't the work done on the system (at least that's how I see it), the work done should be the product of the force and the displacement of the center of mass, I believe, which this clearly is not. Can someone explain to me how this actually is true then?