Question

When flow velocity in a pipe is increased by 10%, the loss of head due to friction increases by
1. 21%
2. 25%
3. 5%
4. 11%

Answer 1

Correct Answer - Option 1 : 21%

Concept:

Head loss due to friction in a pipe:

\({h_f} = \frac{{f'L{V^2}}}{{2gd}}\)

h_f = head loss due to friction, f’ = friction factor, L = length of the pipe, V = average velocity of the fluid in the pipe, g = acceleration due to gravity, d = diameter of the pipe.

Hence keeping all other parameters to be same, h_f ∝ V²

Calculations: 

Given:

Final velocity (V₂) = 1.10 × Initial velocity (V₁)

\(\frac{V_2}{V_1}=1.1\)

∵ h_f ∝ V²

∴ \(\frac{h_{f2}}{h_{f1}}=\left(\frac{V_2}{V_1}\right)^2\)

\(\frac{h_{f2}}{h_{f1}}=(1.1)^2\)

\(\frac{h_{f2}}{h_{f1}}=1.21\)

Final head loss (h_f2) = 1.21 × Initial head loss (h_f1)

Hence head loss will increase by 21 %.