# Total force on surface of a plate?

1. Sep 22, 2014

### eterna

1. The problem statement, all variables and given/known data
http://scienceofdoom.files.wordpress.com/2010/12/convection-basics-1b.png

How do I find the total force on that surface of the plate?

2. Relevant equations

T = μ * u'(y)

where T is the shear stress, μ is a scalar constant - the viscosity and u'(y) is the velocity gradient in the perpendicular direction

Force = T * A

3. The attempt at a solution

Does every point along the plate have a different u(y) distribution so that the shear stress at the surface, μ * u'(y=0) , is different for all of these points?
And so the total force is the sum of μ * u'(y=0) * A for all of those points?

2. Sep 22, 2014

### Staff: Mentor

Yes.

Chet

3. Sep 22, 2014

### eterna

So is the correct integral

from 0 to L(length of the plate) : μ u'(0) width dl ?

And so for the total force( top + bottom of plate), is it just two times that?

4. Sep 22, 2014

### Staff: Mentor

Yes, if the flow is on both sides of the plate.

Chet