# Fluid Statics - net upward force

1. Nov 29, 2014

### Roodles01

1. The problem statement, all variables and given/known data
Find magnitude of net upward force on a cube in terms of l, ρ (rho), g and h. then show that h = m/ρl2

A solid cube, mass m, side length l, is placed in a liquid of uniform density, ρ(rho), at a depth h0 below the surface of the liquid, which is open to the air.
The upper and lower faces of the cube are horizontal.

(this is from previous question https://www.physicsforums.com/threads/force-exerted-by-fluid.784711/)

2. Relevant equations
pressure, p = ρ g h
mass = ρ x volume of liquid displaced

3. The attempt at a solution
Net force, Fn = (pbottom x area of cube face) - (ptop x area of cube face)
p at top face = (pT) x ρliquid x h x g
p at bottom face = (pB) x ρliquid x (h+l) x g
so
Fn = (ρgh + ρlg - ρgh)
Fn = ρlg

Net force - fine.
Er! how do I show that h = m/ρl2
I know m = ρ x v . . .

2. Nov 29, 2014

### haruspex

I can only make sense of the question if h is different from h0. (Your working all has h, but the question used h0.)
A reasonable meaning for h would be that the block is released and floats level with depth h immersed.

3. Nov 29, 2014

### Roodles01

I have looked at the question and unscrewed the bits of paper I attempted my answers on and the h0 seems to be a complete typo, it all says just plain h. I will try to work through with that in mind, as you say.