1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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?

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

    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:

    [tex]
    \frac{\bar u}{\hat u} = \frac{2n^2}{(n+1)(2n+1)}
    [/tex]

    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

    ideasrule

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...