How Does Bulk Velocity Relate to Maximum Velocity in Turbulent Tube Flow?

[chronicals]

Homework Statement

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 )

Homework Equations

The Attempt at a Solution

i don't know which equation i should integrate and how?

 

[hikaru1221]

I guess the average speed is defined as <v>=\frac{Q}{A} where Q is the volume of fluid passing through the cross section of area A in 1 second. How do you find Q?

 

[chronicals]

I guess the average speed is defined as <v>=\frac{Q}{A} where Q is the volume of fluid passing through the cross section of area A in 1 second. How do you find Q?

i think working with volume rate is useless

 

[hikaru1221]

Okay, why and what do you think of the solution?