# Find the loss of head due to friction in a smooth pipe of rectangular cross section of 1 m × 0.5 m and 10 m long. Velocity of flow is 10 m/s and the f

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Find the loss of head due to friction in a smooth pipe of rectangular cross section of 1 m × 0.5 m and 10 m long. Velocity of flow is 10 m/s and the friction coefficient is 0.01962.
1. 4 m
2. 6 m
3. 8 m
4. 10 m

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Correct Answer - Option 2 : 6 m

Concept:

Head loss due to friction in the pipe is given by the Darcy’s formula

${h_f} = \frac{{4fL{V^2}}}{{2gD}}$

where, f = Darcy’s coefficient, L = length of pipe, V = velocity of liquid flow, D = diameter of pipe

Calculation:

Given:

f = 0.01962, L = 10 m, V = 10 m/s, D = Hydraulic diameter = 4AC/P

$D = \frac{{4 \times 1 \times 0.5}}{{2\left( {1 + 0.5} \right)}} = 0.66\;m$

${h_f} = \frac{{4 \times 0.01962 \times 10 \times {{10}^2}}}{{2 \times 9.81 \times 0.66}} = 6.06\;m$