GATE AG 2022 • Q38 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Fluid Mechanics

Subtopic: Flow in open channels

Question Statement:

The flow rate per unit width of a wide rectangular clean-earth channel is 20 m³ s⁻¹ m⁻¹. The calculated critical flow depth in meter will be __________. [round off to two decimal places] (Take g = 9.81 m s⁻²)

Official Answer Key:

3.42 to 3.46

Step-by-Step Solution & Explanation

• For a wide rectangular channel, critical depth yc = (q²/g)^(1/3) • yc = (20²/9.81)^(1/3) = (40.775)^(1/3) = 3.44 m Computed value: 3.44 m (within official range 3.42–3.46)

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