Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow in open channels
Question Statement:
A trapezoidal channel carries 5 m³·s⁻¹ of water under uniform flow condition. The channel has a bottom width of 2 m, side slope of 2:1 (horizontal : vertical), and a bed slope of 1%. If the Manning roughness coefficient is 0.03, the conveyance of the channel, in m³·s⁻¹, is
Options:
(A) 2
(B) 5
(C) 15
(D) 50
Official Answer Key:
D
Step-by-Step Solution & Explanation
Manning’s equation is: Q = (1/n) A R^(2/3) S^(1/2)
The group (1/n)AR^(2/3) is defined as the conveyance, K, so Manning’s equation becomes:
Q = K √S
Therefore:
K = Q/√S = 5/√0.01 = 5/0.1 = 50 m³·s⁻¹
Note: the bottom width, side slope and Manning’s n are all redundant data here — conveyance follows directly from the definition once Q and S are known. This is a definition-recognition question, not a computation question.
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