Using Manning’s equation, which quantity is solved for when discharge Q, roughness n, slope S, and channel shape are known?

Using Manning’s equation, which quantity is solved for when discharge Q, roughness n, slope S, and channel shape are known?

• A. The cross-sectional area
• B. The discharge
• C. The roughness coefficient n
• D. The slope

Answer: (A)

Manning’s equation links discharge to the cross-sectional area A, the hydraulic radius R, the slope S, and the roughness n: Q = (1/n) A R^(2/3) S^(1/2). If Q, n, S, and the channel shape are known, the quantity that must be solved for is A (the cross-sectional area). With a fixed shape, A (and the corresponding depth) uniquely determines R, so you solve for A to match the given discharge under those conditions. The other quantities—Q, n, S, and the channel shape—are given, so they’re not what you solve for.

Manning’s equation links discharge to the cross-sectional area A, the hydraulic radius R, the slope S, and the roughness n: Q = (1/n) A R^(2/3) S^(1/2). If Q, n, S, and the channel shape are known, the quantity that must be solved for is A (the cross-sectional area). With a fixed shape, A (and the corresponding depth) uniquely determines R, so you solve for A to match the given discharge under those conditions. The other quantities—Q, n, S, and the channel shape—are given, so they’re not what you solve for.