Question Bank • QB_SWCE_FM_005 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Laminar and turbulent flow in pipes, Darcy–Weisbach and Hazen–Williams equations

Question Statement:

Water flows through a straight commercial pipe of diameter $0.15\text{ m}$ and length $300\text{ m}$ at a mean velocity of $2.0\text{ m/s}$. The Darcy friction factor is $f = 0.024$. Taking $g = 9.81\text{ m/s}^2$, the head loss due to friction in metres is ________ (round off to 2 decimal places).

Answer Key:

9.79

Step-by-Step Solution & Explanation

Using the Darcy-Weisbach formula: $h_f = \frac{f \cdot L \cdot v^2}{2 \cdot g \cdot D}$ Given: • $f = 0.024$ • $L = 300\text{ m}$ • $v = 2.0\text{ m/s} \implies v^2 = 4.0\text{ m}^2\text{/s}^2$ • $D = 0.15\text{ m}$ • $g = 9.81\text{ m/s}^2$ $h_f = \frac{0.024 \times 300 \times 4.0}{2 \times 9.81 \times 0.15} = \frac{28.8}{2.943} \approx 9.786\text{ m} \approx 9.79\text{ m}$
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