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GATE 2023 CE (CE2) – Question 43

Hydraulics · Channel hydraulics: specific energy, critical flow, uniform flow, hydraulic jump · 2 marks · Multiple choice

A compound symmetrical open channel section as shown in the figure has a maximum of ______ critical depth(s).

a rectangular main channel of width Bₘ with a raised floodplain of width Bf on each side, main-channel depth yₘ, total depth y, roughness nₘ and nf.
  1. 3
  2. 2
  3. 1
  4. 4

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Correct answer: (A) 3

Explanation

**Specific energy curve.** For a prismatic channel $E=y+\dfrac{Q^2}{2gA^2}$, and a critical depth occurs where $dE/dy=0$, i.e. where $Q^2T/(gA^3)=1$.

In a **compound section** the top width $T$ jumps when the water first spills over the floodplain, so $E(y)$ is not a single smooth curve. As the depth rises through the transition from the main channel to the floodplain, the specific energy can fall, rise and fall again. This gives:

1. one minimum of $E$ in the main channel (below the floodplain level),
2. a local maximum of $E$ near the change in width,
3. a second minimum once the floodplain is wetted.

Each stationary point of $E(y)$ corresponds to a critical depth, so a compound symmetrical section can have **up to three critical depths** (option A).

Official GATE 2023 answer key: https://gate2026.iitg.ac.in/doc/download/Answer_keys2023/CE2_ANS_GATE2023.pdf