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GATE 2021 CE (CE1) – Question 19

Hydraulics · Channel hydraulics: specific energy, critical flow, uniform flow, hydraulic jump · 1 mark · Multiple choice

Water flows at equal depth in the most hydraulically efficient triangular and rectangular channels. The ratio of the triangular hydraulic radius to the rectangular hydraulic radius is

  1. $1/\sqrt2$
  2. $\sqrt2$
  3. 1
  4. 2

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Show answer and explanation

Correct answer: (A) $1/\sqrt2$

Explanation

The best triangular channel has side slope 1:1, giving $A=y^2$, $P=2\sqrt2y$ and $R=y/(2\sqrt2)$. The best rectangle has width 2y and $R=y/2$. Their ratio is therefore **1/√2 (A)**.