Question

In a laminar flow through a circular pipe of diameter 200 mm, the maximum velocity is found to be 1 m/s. The velocity at a radial distance of 50 mm from the axis of the pipe will be

• A. 0.5 m/s
• B. 0.25 m/s
• C. 0.75 m/s
• D. 1.25 m/s

Answer 1

The correct option is C 0.75 m/s

In laminar flow, velocity

$u=-\frac{1}{4\mu }\left(\frac{\partial P}{\partial x}\right)(R^2-r^2)$

$\text{Maximum velocity will be at}r=0$

$\Rightarrow -\frac{1}{4\mu }\left(\frac{\partial P}{\partial x}\right)=\frac{1}{(100{)}^2}$

$\therefore \text{Velocity at}r=50\text{mm}$

$u=-\frac{1}{4\mu }\frac{\partial P}{\partial x}({100}^2-{50}^2)$

$=\frac{1}{(100{)}^2}\left[\right(100{)}^2-\left(50{)}^2\right]$

$=0.75\text{m/sec.}$