# Moment of the Hydrostatic Force on a body

1. Sep 24, 2012

### squire636

This problem is for a Fluid Dynamics course, but it is mostly math and thus I figured it should be posted here. If it should be moved elsewhere, please let me know and I will do so!

1. The problem statement, all variables and given/known data

We saw in class the hydrostatic force acting on a body at rest in an incompressible fluid. Calculate, using a similar procedure, the moment of the hydrostatic force on the
body.

Here is what we did in class: http://imgur.com/wE3O4

2. Relevant equations

3. The attempt at a solution

Rather than calculating the hydrostatic force, we need to calculate the moment of this force. By definition, we need:

S X x (-pn) dS where X is a position vector, p is the pressure, and n is a normal vector.

Similar to what was done in 6.25 in the image above, I did the following:

= -ρ ∫S (X x n) (g . X) dS

and then tried to apply the divergence theorem

= -ρ ∫v ( x X) ∇(g . X) dV
= -ρgV ∫v ( x X) dV

I know this isn't right, but it's the best I've gotten after about an hour of work. I know that I need to apply the divergence theorem to get from a surface integral to a volume integral, but the cross product is really throwing me off. I'm also pretty sure that I broke some math rules while trying to mimic step 6.25 in the image above. I'm really just grasping at straws here and trying to do something that makes any sort of sense at all.

Any help will be very appreciated, as I've been stuck for a while. Thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution