Question

The discharge in $m^3/s$ for laminar flow through a pipe of diameter 0.04 m having a centre line velocity of 1.5m/s is

• A. $\frac{3\pi }{50}$
• B. $\frac{3\pi }{2500}$
• C. $\frac{3\pi }{5000}$
• D. $\frac{3\pi }{10000}$

Answer 1

The correct option is D $\frac{3\pi }{10000}$

d= 0.04 m
Centre line velocity i.e.,maximum velocity,
$U_{max}=1.5m/s$
also
$U_{max}$ = 2 times average velocity for laminar flow through pipe

$U_{max}=2\overline{u}$

$\therefore 1.5=2\overline{u}$
or
$\overline{u}=\frac{1.5}{2}m/s$

Discharge Q = Cross-sectional area of pipe $\times$ Average velocity

$=\frac{\pi }{4}{d}^2\times \overline{u}=\frac{\pi }{4}\times (0.04{)}^2\times \frac{1.5}{2}$

$=\frac{\pi }{4}\times \frac{4}{100}\times \frac{4}{100}\times \frac{1.5}{2}$

$=\frac{3\pi }{10000}{m}^2/s$