Problem #$8$

The horizontal $($axial$)$ component of velocity $u$ of steady, viscous, fully$-$developed, incompressible flow

through a circular pipe of radius $R($Figure $8)$ is given by the following relation:

$u(r)=U_{\text{m}\text{a}\text{x}}[1-\frac{r^2}{R^2}]$

Compute the average velocity of flow through the pipe

Please show your work $!$