Question

A 2 km pipe of 0.2 m diameter connects two reservoirs. The difference between the water levels in the reservoir is 8 m. The Darcy Weisbach friction factor of the pipe is 0.04. Accounting for frictional entry and exit losses. The velocity in the pipe in (m/sec) is

• A. 0.63
• B. 0.35
• C. 2.52
• D. 1.25

Answer 1

The correct option is A 0.63

Frictional loss,

$h_f=\frac{fL{V}^2}{d\times 2g}$

Loss of head at entrance,

$h_L=\frac{0.5V^2}{2g}$

Loss at exit of pipe,

$h_c=\frac{V^2}{2g}$

$\therefore 8=\frac{fL{V}^2}{d\times 2g}+\frac{0.5V^2}{2g}+\frac{V^2}{2g}$

$\Rightarrow 8=\frac{0.04\times 2000\times V^2}{2\times g\times 0.2}+\frac{V^2}{2g}+\frac{0.5V^2}{2g}$

$\Rightarrow 8=20.3873V^2+0.07645V^2$

$\Rightarrow V=0.625m/s$

$\simeq 0.63m/s$