How to Solve Hydrostatics Problems with Curved Surfaces?

[Fionn00]

Hi I am really stuck on this problem and would greatly appreciate some help.

Homework Statement

Homework Equations

The Attempt at a Solution

I would be able to solve this if the dam wasn't curved. I would just use integration to find the magnitude of the force f = pghA. I would express a in h and integrate from 0 to 3. and then the direction would be at right angles to the wall but this is curved so I don't know how to find the force or how to express the area in h.

Thanks for help.
I know hot to calculate the moments and get the solution once I have the magnitude and position of the force.

 

[tiny-tim]

Hi Fionn00!

The force at each point of the dam is normal to the surface, and the force per area is pressure (which of course is the same in every direction at any particular point).

 

[pongo38]

Can I postulate that the overturning moment about A is independent of the shape of the dam cross-section? In other words use pressure distribution as if the dam was vertical and use the projected (vertical) area.

 

[tiny-tim]

but the pressure is always perpendicular to the dam, so surely the angle does matter?

 

[nvn]

Isn't the angle on strut BC missing?

Fionn00: Because you know how to do an integration, try drawing a free-body diagram (FBD), and set up an integral that is applicable to the situation at hand.

 

[pongo38]

Sorry for post #3. I stand corrected.