Solve Mass Flow Rate Problem: U(max) at R=0.16 m

[ACE_99]

Homework Statement

At a point upstream the measured mass flow rate is 10 kg/s, downstream of this location the velocity profile is measured and obeys the relationship u(r) = U(max)(1-(r/R)^(1/5)) where R is 0.16 m. Find U(max). The diagram provided with the question is provided below.

Homework Equations

mass flow rate (dm/dt) = $$\rho$$VA

The Attempt at a Solution

I'm really not sure were to start with this problem any help would be greatly appreciated.

http://i429.photobucket.com/albums/qq12/ACE_99_photo/Untitled.jpg"

 

[siddharth]

Consider a circular strip around the central axis of radius r and width dr. What's the volume of the fluid flowing through this strip per unit time? Multiply this by the density, and you get the mass flow rate through that strip.

Now, if you integrate this over r, you'll get the total mass flow rate which is 10 kg/s, and from this you'll be able to find U(max)