# Hydrostatic Force Problem

1. Mar 11, 2008

### the7joker7

1. The problem statement, all variables and given/known data

An aquarium 8 m long, 4 m wide, and 4 m deep is full of water. Find the following: the hydrostatic force on one end of the aquarium.

2. Relevant equations

3. The attempt at a solution

I already found the pressure and force on the bottom of the aquarium...now, my main issue understanding what the question means when it says 'end.' Do they mean one of the side walls? One half of the aquarium? If anyone happens to know what that likely means, that'd be awesome.

What I've tried so far is Density*gravity*L/2*W, which was wrong.

1000*9.8*4*4 = 156800.

Is it just the force on the bottom of the aquarium divided by 2? That almost seems too easy...

2. Mar 12, 2008

### HallsofIvy

Staff Emeritus
IF the force is a constant, then the pressure on a surface is just that force times the area of the surface. That, I presume, was how you found the force on the bottom. However, the force, at each point on a wall, is not a constant. It varies with depth. Imagine a thin horizontal line, of width "dx", at depth "x". What is the force at depth x meters below the surface of the water? What is the pressure on that line? (For a very thin horizontal line you may assume the force is (approximately) a constant.) The total pressure on the wall is the sum of the pressure on all those lines. Doesn't that look like a "Riemann sum" to you? You can make it exact by converting the sum into an integral. (I have this suspicion that this problem is in a section on "applications of integrals".)