2081 Chaitra · 1+2 marks

Discharge and head loss in horizontal pipe

Short answer

Discharge Q = A·V = 0.0353 m³/s. Head loss from Darcy–Weisbach: h_f = f (L/D)(V²/2g) = 0.02×(1000/0.15)×(2²/19.62) = 27.18 m.

Water flows through a 1 km long horizontal pipe of 150 mm diameter with a velocity of 2 m/s. Calculate the discharge and head loss in the pipe if the friction factor is 0.02.

Given: $L = 1000$ m, $D = 0.15$ m, $V = 2$ m/s, $f = 0.02$ (Darcy).

Discharge

\begin{aligned} Q &= \frac{\pi}{4}D^2 V = \frac{\pi}{4}(0.15)^2 \times 2 \\ &= 0.01767 \times 2 = 0.03534\ \text{m}^3/\text{s} \end{aligned}

Head loss (Darcy–Weisbach)

\begin{aligned} h_f &= f\frac{L}{D}\frac{V^2}{2g} = 0.02 \times \frac{1000}{0.15} \times \frac{2^2}{2 \times 9.81} \\ &= 133.33 \times 0.2039 = 27.18\ \text{m} \end{aligned}

Answer: $Q = 0.0353$ m³/s (35.3 L/s); head loss $h_f = 27.18$ m of water.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Discharge and head loss in horizontal pipe

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