Question Bank • QB_SWCE_EXP_081 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Flow in open channels

Question Statement:

A trapezoidal canal has side slope $1.5 : 1$ ($H : V$, so $z = 1.5$) and bottom width $B = 3.0\text{ m}$. If the water depth is $y = 1.0\text{ m}$, calculate the wetted perimeter $P = B + 2 y \sqrt{1 + z^2}$ in $\text{meters}$.

Answer Key:

6.606

Step-by-Step Solution & Explanation

$\sqrt{1 + z^2} = \sqrt{1 + (1.5)^2} = \sqrt{1 + 2.25} = \sqrt{3.25} \approx 1.8028$ $P = 3.0 + 2(1.0)(1.8028) = 3.0 + 3.6056 = 6.6056\text{ m}$
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