How to describe motion of the wall of a liquid container?

[sceptic]

Hi, I wonder I cannot solve the following simple problem. I really don't know what kind of equations are relevant.

Imagine a rectangular tank, with vertical walls containing some water. The surface area is big. The wall of the tank is movable without friction, and its mass is negligible. All sides of the tank are fixed except one, and we push that movable wall perpendicular with force F. How can we describe the motion of the wall?

 

[Bystander]

You are raising or lowering water level in your tank. You can attack it from equilibrium with a given force. You can also attack it dynamically with waves, viscous dissipation, and all the other complications of CFD.

 

[haruspex]

First you need to create some unknown variables, e.g. density of liquid, width x (normal to the wall), height y of mass centre of fluid...
Consider the wall advancing some distance -dx. What work does the force do? What is the increase in KE+PE of the liquid?

 

[sceptic]

I think that energy and work is not useful in this case, since I would like to describe the motion in time. I have already tried. Maybe the horizontal momentum is more useful, however I do not know how to deal with the flow of the water, since the total negligence is not good, but the general solution is hopeless.

 

[sceptic]

You are raising or lowering water level in your tank. You can attack it from equilibrium with a given force. You can also attack it dynamically with waves, viscous dissipation, and all the other complications of CFD.

I would like to solve it dynamically (with some assumptions), but my liquid is not viscous!

 

[BvU]

Assume wall is moving slowly. No kinetice energy, no CFD. All that happens is that some liquid has to be moved up. Re-read Haru's advice and don't think energy considerations are for static situations only.

 

[haruspex]

Assume wall is moving slowly. No kinetice energy, no CFD. All that happens is that some liquid has to be moved up. Re-read Haru's advice and don't think energy considerations are for static situations only.

I agree that energy does indeed solve the problem. Actually it's a bit easier than what I posted. You don't have to think about small intervals of movement - just go for the full movement from starting point to wherever.
But I disagree about ignoring KE. There's no need for that, and it seriously distorts the answer.