# Pressure on the Bottom of a tank

## Homework Statement

A lobster tank in a restaurant is 8 ft long by 7 ft wide by 2 ft deep. Find the water force on the bottom and on each of the four sides. The density of water is 62.4 lb/ft3.

## Homework Equations

Pressure = density * gravity * height
Force = Pressure * Area

## The Attempt at a Solution

Force on the bottom = density * gravity * height * area
= 62.4g(2)(56)

It is asking for the Force in Lb
In my book we used integrals for this type of problem but I don't see the point..

I'm trying to put the answer in webassign.

For the sides would it be the same equation without gravity, as gravity is only in play in the up and down directions?

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Office_Shredder
Staff Emeritus
Gold Member
First, you should review the difference between mass and weight to understand why you do not need to multiply by g if your units are in pounds.

For the sides you are going to need to do calculus (not terribly hard calculus, but calculus nonetheless). The water pressure pushes equally in ALL directions, including out to the sides. So there is force from the water on the sides of the lobster tank, and the amount of force in any small area of the tank is going to depend on the water pressure at the depth of that area

First, you should review the difference between mass and weight to understand why you do not need to multiply by g if your units are in pounds.

Ahh, yes. The notes I wrote down were throwing me off, they weren't in lbs like i was assuming.

HallsofIvy
Homework Helper

## Homework Statement

A lobster tank in a restaurant is 8 ft long by 7 ft wide by 2 ft deep. Find the water force on the bottom and on each of the four sides. The density of water is 62.4 lb/ft3.

## Homework Equations

Pressure = density * gravity * height
Force = Pressure * Area

## The Attempt at a Solution

Force on the bottom = density * gravity * height * area
= 62.4g(2)(56)

It is asking for the Force in Lb
In my book we used integrals for this type of problem but I don't see the point..
There is no point if you are finding the total force on the bottom because the pressure at each point is the same. But if you want to find the total force on the sides, the pressure varies with depth. Imagine a thin strip across a side at a specific height, z, and thickness dz. The pressure is given by the height of water above that height. Since the 2 feet deep, the height of water above z is 2- z. The weight of water pressing down is 64.2(2- z)(dz). That's the force on that strip. To find the total force on the side, integrate that for z going from 0 to 2.

I'm trying to put the answer in webassign.

For the sides would it be the same equation without gravity, as gravity is only in play in the up and down directions?
"Without gravity" there would be no force! A fluid, such as a liquid or a gas, presses in all directions, not just up or down. The sideways force due to water at every point is exactly the same as the downward force, the density times the volume of water above that point.