How Much Friction Is Needed to Prevent Leakage in a Cubical Water Tank?

[burningnachos]

Homework Statement

A water tank is formed by sliding four identical cubical blocks together. All edges are watertight. Each block has mass M and is L meters on each side. You wish to fill the tank to its brim, i.e. to depth L.

What is the minimum coefficient of static friction between the blocks and the ground so that the blocks do not spread apart and cause the tank to leak? Water has a density ρw and the atmosphere pressure at the tank's location is Po.

Homework Equations

The Attempt at a Solution

I assumed we were talking about the blocks "sliding" apart as opposed to tipping over as in torque. If we're trying to find the coefficient of static friction, that means the water is exerting a force on each block (equal for each block). I'm not sure how to begin finding this force. Teacher said water pressure on a dam acts at a point 1/3 way up, but that doesn't seem to help.

Help would be appreciated, thanks.

 

[paisiello2]

F=∫P(y)dA

where P(y) is the water pressure at any depth y.

 

[haruspex]

As paisiello2 notes, you can get the total force by integrating the pressure over the area, and using the fact that the pressure depends linearly on the depth.
This is analogous to finding the area of a triangle on a horizontal base by integrating the width wrt the height. Again, the width depends linearly on the distance from the top.
I agree your teacher's comment does seem irrelevant. It would be relevant if the blocks were instead walls and we were concerned about the walls falling over. In that case we would want to know the torque about the base exerted by the water, not the total force.