If the roughness coefficient n increases, what happens to discharge Q for a fixed cross-sectional area and slope?

If the roughness coefficient n increases, what happens to discharge Q for a fixed cross-sectional area and slope?

• A. Decrease
• B. Increase
• C. Remain the same
• D. Depends on other factors

Answer: (A)

Roughness n represents friction along the wetted surface, and in Manning’s equation for uniform flow the discharge is Q = (1/n) A R^(2/3) S^(1/2). With the cross-sectional area and slope fixed, A, R, and S stay constant, so Q is inversely proportional to n. As n increases, the friction losses grow, the flow slows, and discharge decreases. So the discharge decreases when n increases.

Roughness n represents friction along the wetted surface, and in Manning’s equation for uniform flow the discharge is Q = (1/n) A R^(2/3) S^(1/2). With the cross-sectional area and slope fixed, A, R, and S stay constant, so Q is inversely proportional to n. As n increases, the friction losses grow, the flow slows, and discharge decreases. So the discharge decreases when n increases.