The GATE Grind

GATE 2025 ES – Question 56

Water Resources and Environmental Hydraulics · Environmental Hydraulics · 2 marks · Numerical answer

A circular sewer with Manning n=.01 and slope1:100 flows80% full at 2 m³/s. Find diameter in metres, to three decimals.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 0.825 to 0.875

Explanation

Let wetted central angle $\theta=2\cos^{-1}(1-2y/D)=2\cos^{-1}(-.6)=4.428595$ rad. Then $A=D^2(\theta-\sin\theta)/8$ and $R_h=D(\theta-\sin\theta)/(4\theta)$. Substitute into Manning $Q=A R_h^{2/3}S^{1/2}/n$ with $Q=2,S=.01,n=.01$. Solving gives $D=.8539929$ m, rounded **0.854 m**. The hydraulic radius is A divided by wetted perimeter, not D/4 for this partial-depth flow.

More Environmental Hydraulics questions

All Environmental Hydraulics questions →