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GATE 2016 CE (CE1) – Question 57

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

A 4 m wide rectangular channel, having bed slope of 0.001 carries a discharge of 16 m3/s. Considering Manning's roughness coefficient = 0.012 and g = 10 m/s2, the category of the channel slope is

  1. horizontal
  2. mild
  3. critical
  4. steep

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Show answer and explanation

Correct answer: (B) mild

Explanation

Unit discharge is16/4=4m²/s, so critical depth is(q²/g)^(1/3)=(16/10)^(1/3)=1.1696m. Evaluate Manning discharge at that depth using A=4y, R=A/(4+2y), the given n and slope. It is less than16m³/s, so the required normal depth exceeds critical depth. The bed is therefore **mild, B**.