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Fluid Mechanics (Shear Stress)

  1. May 28, 2009 #1
    1. Question
    A large plate moves with speed (v.o) over a stationary plate on a layer of oil of thickness (d) and viscosity (u). If the velocity profile is that of a parabola, with the oil at the plates having the same velocity as the plates, what is the shear stress on the moving plate from the oil? If a linear profile is assumed, what is the shear stress on the moving plate? (Answers: u*v.o/(2d) and u*v.o/d)


    2. Relevant equations
    t: shear stress
    t=u*(dv)/(dy)
    v=md^2+c

    3. The attempt at a solution
    So I have the answer, but I cannot figure out the solution. If the velocity changes parabolically, then you have the equation v=md^2+c. dv=2md. So when d=0, v=0 and t=u*(2md-0)/(d-0). This is my solution, but obviously is not correct with the above answers. Any help would be greatly appreciated.
    Thanks
     
  2. jcsd
  3. May 28, 2009 #2

    Hao

    User Avatar

    Parabolically can either mean [tex]v = a y^2 + b[/tex] or [tex]v = a \sqrt{y} + b[/tex], where a and c are constants to be determined. Think carefully about which is the correct profile.

    Furthermore, avoid expressing v immediately as a function where y = d. The velocity profile is [tex]v(y)[/tex]. The velocity at the moving plate is [tex]v(d)[/tex]. You will make mistakes with your derivatives otherwise.
     
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