Question

The discharge in m³/s for laminar flow through a pipe of diameter 0.04 m having a centre line velocity of 1.5 m/s.
1. \(\frac{{3\pi}}{{50}}\)
2. \(\frac{{3\pi}}{{2500}}\)
3. \(\frac{{3\pi}}{{5000}}\)
4. \(\frac{{3\pi}}{{10000}}\)

Answer 1

Correct Answer - Option 4 : \(\frac{{3\pi}}{{10000}}\)

Concept:

For laminar flow, Maximum velocity occurs at centre.

∴ Umax = Centre–line velocity 

For laminar flow, \({U_{avg}} = \frac{{{U_{max}}}}{2} \)

Discharge (Q) = Area × Average velocity

Calculation:

Given:

Pipe diameter, d = 0.04 m, Umax = Centre–line velocity = 1.5 m/s

\({U_{avg}} = \frac{{{U_{max}}}}{2} =\frac{{1.5}}{{2}}\Rightarrow 0.75\) m/s

Discharge (Q) = Area × Average velocity = \( \frac{\pi }{4} \times {\left( {0.04} \right)^2} \times 0.75 =\frac{{3\pi}}{{10000}}\)  m³/s.