Question

For a fully developed laminar flow of water (dynamic viscosity 0.001 Pa-s) through a pipe radius 5 cm, the axial pressure gradient is -10 Pa/m. The magnitude of axial velocity (in m/s) at a radial location of 0.2 cm is___________

• A. 6.24

Answer 1

The correct option is A 6.24
$\mu =0.001Pa-s$

R=5 cm =0.05 m

$\frac{\partial P}{\partial x}=-10Pa/m$

r=0.2 cm=0.002 m


For incompressible laminar flow through pipe,
Local velocity,

$U=-\frac{1}{4\mu }\frac{\partial P}{\partial x}[R^2-r^2]$

$=-\frac{1}{4\times 0.001}\times (-10)\left[\right(0.05{)}^2-\left(0.002{)}^2\right]$

=6.24 m/s