If the width of a rectangular channel is twice its depth of flow, then the depth of the flow 'y' varies with discharge 'q' as (consider all parameters constant in Manning's equation)
- Aq0.125
- Bq0.375Correct
- Cq0.475
- Dnone of these
Solution
Concept
Depth–discharge relation
Formula
Q = (1/n) A R2/3 S1/2
Step-by-step solution
1. b = 2y: A = 2y², P = 4y, R = y/2. 2. Q ∝ y² × y2/3 = y8/3. 3. y ∝ Q3/8 = Q0.375.
Explanation
Hydraulic radius also scales with y, so the exponent is 8/3.
Why the other options are wrong
0.125 and 0.475 do not equal 3/8.
Shortcut
y ∝ q3/8.
Common mistake
Forgetting that R changes with y.
Correct answer: B) q^0.375