GATE CE 2024 Set 1 — Question 57
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Water Resources Engineering → Open Channel Flow → Chezy Equation
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Question
A standard round bottom triangular canal section as shown in the figure has a bed slope of 1 in 200. Consider the Chezy's coefficient as 150 m¹/²/s.
The normal depth of flow, y (in meters) for carrying a discharge of 20 m³/s is __________ (rounded off to 2 decimal places).
Correct answer
1.09 to 1.12
Solution
The question provides conflicting information in the figure for the channel section. It specifies the side slope as 1.5H:1V (m=1.5) and also shows a 90° angle at the vertex, which corresponds to a side slope of 1H:1V (m=1). Assuming the side slope value of m=1.5 is correct and the 90° symbol is an error.Given:
Discharge,
Bed slope,
Chezy's coefficient,
Side slope, For a triangular channel, the geometric properties are:
Area of flow,
Wetted perimeter,
Hydraulic radius, Using Chezy's formula for discharge:
Rounding off to 2 decimal places, the normal depth of flow is 1.31 m.
Discharge,
Bed slope,
Chezy's coefficient,
Side slope, For a triangular channel, the geometric properties are:
Area of flow,
Wetted perimeter,
Hydraulic radius, Using Chezy's formula for discharge:
Rounding off to 2 decimal places, the normal depth of flow is 1.31 m.
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