- #1

mathfied

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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.