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GATE 2021 ES – Question 59

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

A 900 mm sewer on slope .004 carries .15 m³/s. Manning n=.013. Find actual/full-flow discharge ratio, to two decimals. Use π=3.14.

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Correct answer: .12 to .14

Explanation

For a full circular pipe, A=πD²/4=.63585 m² and R=D/4=.225 m. Full flow is $Q_f=(1/.013)(.63585)(.225)^{2/3}\sqrt{.004}\approx1.1444$ m³/s. Ratio=.15/Qf≈**.13**. Use full hydraulic radius D/4,not the physical radius D/2.

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