Maximizing Fluid Storage in a Rectangular Tank with Given Force Limit

[liberty/death]

Homework Statement

This is just a general question.

The questions I can't get go something like this:

You're given a liquid you plan to store, in a tank, say for this example, a rectangular one with square sides. You're given the max fluid force that the interior walls can withstand, and asked to find how many cubic units of fluid the tank can store, at maximum, I'm assuming.

My question is, how do you go about setting up a problem like this in general?

Homework Equations

The Attempt at a Solution

So far I've tried to setup the integral with the force already put in (since its given), but I don't know where to start with how to integrate / solve for volume / find boundaries / etc.

Any help or hints would be appreciated.

 

[lanedance]

start by defining the pressure on a face with depth for a given height h, then intergate over the area of a face to find the force

 

[liberty/death]

By pressure, are you referring to the fluid force? If so, how would you even go about doing that? As the surface of the fluid is not defined.

 

[lanedance]

what do you mean by fluid force? I'm not really familiar with the term..

By pressure I mean force per unit area
$$P = \frac{F}{A}$$

the pressure in a liquid at depth h will be given by:
$$P = \rho g h$$

 

[liberty/death]

Well, this is suppose to be a fluid force problem, though there are many ways to solve it I'm sure. We're suppose to make use of the fluid force equations. Namely:

F=whA and F= the integral of w(strip depth) L(y) dy.

w= weight density of liquid
L(y)=length of strip
A=area

 

[lanedance]

ok yep