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Total force on surface of a plate?

  1. Sep 22, 2014 #1
    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. jcsd
  3. Sep 22, 2014 #2
    Yes.

    Chet
     
  4. Sep 22, 2014 #3
    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?
     
  5. Sep 22, 2014 #4
    Yes, if the flow is on both sides of the plate.

    Chet
     
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