"Calculate Resultant Force on Vertical Dam Wall

[etothey]

Homework Statement

Pressure_2.jpg: http://www.imageupload.org/thumb/thumb_8609.jpg
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.

Homework Equations

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?

 

[Metaleer]

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.

 

[etothey]

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?

 

[etothey]

anyone?