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Homework Help: Flow Velocity

  1. Dec 5, 2009 #1
    Hi Guys.
    I have an absurd problem and no idea to solve it. Please could you help me?

    \frac{u}{\hat u} = \left [ \frac{y}{R} \right ]^{1/n} = \left [1- \frac{r}{R} \right ]^{1/n}

    Suppose the turbulent flow velocity distribution in a pipe of Radius R can be described by the equation above (Power Law relation).

    y= distance from wall
    r= radial distance from the axis
    [tex] \hat u [/tex] = velocity on the axis

    If [tex] \bar u [/tex] is the space mean average velocity in the pipe, show that:

    \frac{\bar u}{\hat u} = \frac{2n^2}{(n+1)(2n+1)}

    Any solutions please? I know I haven't posted my solutions but that's simply because I have no idea on this question.
  2. jcsd
  3. Dec 5, 2009 #2


    User Avatar
    Homework Helper

    Typically, "average velocity" is defined so that average velocity * area = volume flow, because that's the most useful definition of the "average". So the first step is to find the volume flow across this pipe, using integration.
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