Total force on surface of a plate?

[eterna]

Homework Statement

http://scienceofdoom.files.wordpress.com/2010/12/convection-basics-1b.png

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

Homework 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

The Attempt at a Solution

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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?

 

[Chestermiller]

Yes.

Chet

 

[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?

 

[Chestermiller]

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

Chet