Hydrostatic problem - Impossible integral!! Just studying hidrostatic over the internet and I saw the following problem: A U-Tube filled with water, initially at rest in a horizontal table, has A1=40cm2, A2 = 20cm2, A3=30cm2, h1 = 80cm, h2 = 20cm and L = 100cm (below piture). It is pressed in A1 by a constant vertical force F of 4N. Find the position x of the surface A1 in function of time (initial position is x=0). Given: g = 10m/s2, density of water is 1kg/L http://img191.imageshack.us/img191/2825/78925268.png [Broken] How can I solve this? I tried some stuff but it didn't worked. A1.dx1 = A2.dx2 = A3.dx3 (where dx is the infinitesimal variation of position for a infinitesimal variation of time). By energy conservation: F.dx1 = Δ(mechanic energy) Potential Energy -> Now imagine that the dx1.A1 volume of water has just raised and become the dx2.A2 volume. It raised dx1.(A1+A2)/(2A2) Ep = dx1.(A1+A2)/(2A2).dm.g But dm = A1.dx1.ρ Ep = dx12.(A1+A2)/(2A2).A1.ρ.g Kinetic Enegrgy -> Ek = ∫(dm.v.dv) dm = A1.v1.dt/ρ (v1 is the instantaneum velocity for the surface A1) v = A1.v1/A (A is the area of the surface considered) dv = A1.dv1/A Ek = ∫[(A13v12.dt.dv1)/(ρ.A2)] But I don't know how to solve this. I don't know even if it is right. Can anyone help me?