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Fluid Mechanic Integration

  1. Jul 19, 2010 #1
    1. The problem statement, all variables and given/known data
    For turbulent flow in a smooth, circular tube with a radius R, the velocity profile varies according to the following expression at a Reynolds number of about 10^5.

    Vx= Vxmax * [(R-r)/R)]^(1/7)

    where r is the radial distance from the center and Vmax the maximum velocity at the center. Derive equation relating the average velocity ( bulk velocity ) Vav to Vmax for an incompressible fluid.
    ( Hint: The integration can be simplified by substitution z for R-r )

    2. Relevant equations

    3. The attempt at a solution
    i don't know which equation i should integrate and how?
  2. jcsd
  3. Jul 19, 2010 #2
    I guess the average speed is defined as [tex]<v>=\frac{Q}{A}[/tex] where Q is the volume of fluid passing through the cross section of area A in 1 second. How do you find Q? :wink:
  4. Jul 19, 2010 #3
    i think working with volume rate is useless
  5. Jul 19, 2010 #4
    Okay, why and what do you think of the solution?
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