Question

The velocity v of the flow of blood at a distance "r" from the central axis of an artery of radius "R" is: v = k(R^2^ - r^2^) where k is the constant of proportionality. Find the average rate of flow of blood along a radius of the artery. (use 0 and R as the limits of integration) ...?

Answer 1

As the  The average rate of flow is given by 
(1/(R - 0)) * ∫(r = 0 to R) k(R^2 − r^2) dr 
So what we do is that we proceed like this:
= (k/R) * ∫(r = 0 to R) (R^2 − r^2) dr 
= (k/R) * (R^2 r − r^3/3) {for r = 0 to R} 
= (k/R) * (R^2 * R − R^3/3) - 0 
= (k/R) * (2R^3/3) 
= (2k/3) R^2. 
I hope this can help you for good