Fluid Mechanics: Worked Out Problem, Check Work?

[verd]

Hi,

I have two problems that I'm having difficulty with, and I don't think that my answers are correct.


Problem:
A swimming pool measures 5.0m long x 4.0m wide x 3.0m deep. Compute the force exerted by the water against a) the bottom; b) either end. (Hint: Calculate the force on a thin, horizontal strip at a depth h, and integrate this over the end of the pool.) Do not include the force due to air pressure.

This what I did:
(I worked out the side of the pool, not the bottom yet)
http://www.synthdriven.com/images/deletable/14_help03.jpg


The second problem is just a more difficult version of the first. ...And I know I got it wrong:
A dam has the shape of a rectangular solid. The side facing the lake has area A and height H. The surface of the freshwater lake behind the dam is at the top of the dam. a) Show that the net horizontal force exerted by the water on the dam equals 1/2(rho)gHA, that is, the average gauge pressure across the face of the dam times the area. b) Show that the torque exerted by the water about an axis along the bottom of the dam is (rho)gH^2A/6. c) How do the force and torque depend on the size of the lake?

What I got:
http://www.synthdriven.com/images/deletable/14_help04.jpg

Could someone tell me where I went wrong? What are the mistakes I've made?


Thanks,
HM

 

[andrevdh]

One problem is that the $P_o$ term is for the air pressure on top of the water, which should not be included in the calculation. Also the pressure increases in the water with an increase in depth, working with height is rather confusing - what does it mean anyway - when the height is zero the pressure is zero? I might be wrong, but your formula $P=P_o-\rho g h$ is for the air pressure above the surface?