# Fluid Mechanic Integration

## 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 )

## The Attempt at a Solution

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

## Answers and Replies

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 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

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