# Fluids and pressure

## Homework Statement

A vertical dam wall has a width w. Water is filled to a height H behind the dam. Calculate the resultant force on the dam wall.

P=F/A
P= Pa + p*g*h

## The Attempt at a Solution

Using picture to solve the question
P=F/A
A=H*W
Thus P=Pa g*h*p where p is density and P is pressure.
Thus F=P*A=H*W*(Pa + gHp) where g is gravity.

Is this correct?

Your solution, as I've understood it, would work if the pressure were uniform, that is, constant. However, it changes as you go down, so you would need to perform an integration to determine the net force.

Your solution, as I've understood it, would work if the pressure were uniform, that is, constant. However, it changes as you go down, so you would need to perform an integration to determine the net force.

Aha, I see. This is first fluid question I had involving integration.
Thus, I integrated $$\int$$Po + pgh dh from 0 to H.
Getting P=PaH + pgH^2/2.
Thus
PA = HW(PaH + pgH^2/2).
Better now?

anyone?