GATE 2020 AG – Question 38

Irrigation and Drainage Engineering · Irrigation Water Conveyance and Application Methods · 2 marks · Multiple choice

A channel’s flow passes a 90° triangular weir with head 36 cm, then a 1 m rectangular weir with no intervening loss. Using Francis’ formula, find the rectangular-weir head in cm.

22.1
18.4
15.0
11.8

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Show answer and explanation

Correct answer: (C) 15.0

Explanation

The 90° V-notch discharge is approximately 1.417H^(5/2)=1.417(0.36)^2.5≈0.1102 m³/s. Equate it to the rectangular Francis relation 1.84(L−0.2h)h^(3/2), with L=1 m. Solving gives h≈0.15 m=15.0 cm, C. Both weirs pass the same discharge.

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