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In Manning's equation, how does discharge change when the roughness coefficient n increases while A, R, and S stay constant?
Correct Answer:
It decreases because Q is inversely proportional to n
Explanation:
The key idea is how discharge responds to channel roughness in Manning’s equation when cross-sectional area, hydraulic radius, and slope are fixed. Manning’s equation shows Q = (1/n) A R^{2/3} S^{1/2}. If A, R, and S are constant, Q changes directly with 1/n, so increasing the roughness coefficient n reduces Q in proportion to 1/n. Physically, a rougher channel slows the flow due to greater friction, lowering discharge even though the channel’s size and grade don’t change. That’s why discharge decreases as n increases, matching the statement that Q is inversely proportional to n.

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