Question

A circular pipe of radius R carries a laminar flow of a fluid. The average velocity is indicated as the local velocity at what radial distance, measured from the centre?

• A. 0.50 R
• B. 0.71 R
• C. 0.67 R
• D. 0.29 R

Answer 1

The correct option is B 0.71 R

For laminar flow in a circular pipe, the local velocity may be given as

$u=U_{\text{max}}[1-\frac{r^2}{R^2}]...\left(i\right)$

For laminar flow in a circular pipe, the average velocity may be given as

$V=\frac{U_{\text{max}}}{2}...\left(ii\right)$

Equating (i) and (ii), we get

$\frac{U_{\text{max}}}{2}=U_{\text{max}}[1-\frac{r^2}{R^2}]$

$\Rightarrow \frac{r^2}{R^2}=1-\frac{1}{2}$

$\Rightarrow r^2=0.5R^2$

$\Rightarrow r=0.71R$