Pressure, force, and Area: Calculating the net Force Applied on A dam by Water

[Beginner@Phys]

Homework Statement

Water stands at depth d behind a dam of width w . Find an expression for the net force of the water on the dam. Express your answer in terms of the variables w,d,p (density), and appropriate constants.

Homework Equations

P=F/A or pressure=Force/Area
Hydrostatic pressure: p=p_0+pgd

The Attempt at a Solution

Fnet=P*A=(pgd)*A =pgd*w*d

I guess that p_0 cancels out, because atmospheric pressure is felt both by the dam and the water. Does this make sense?

 

[Doc Al]

The Attempt at a Solution

Fnet=P*A=(pgd)*A =pgd*w*d

Careful. Is the pressure the same at every depth?

I guess that p_0 cancels out, because atmospheric pressure is felt both by the dam and the water. Does this make sense?

That part makes sense.

 

[thomate1]

Yes, your solution is correct. The hydrostatic pressure equation, p=p_0+pgd, takes into account the atmospheric pressure (p_0) and the pressure due to the weight of the water (pgd). Since both the dam and the water are exposed to the same atmospheric pressure, it cancels out in the net force calculation. Therefore, the net force on the dam is simply given by pgd*w*d, where p is the density of water, g is the acceleration due to gravity, d is the depth of the water, and w is the width of the dam.