In Manning's equation, what does R stand for?

• A. Hydraulic radius, defined as A divided by wetted perimeter.
• B. Flow velocity.
• C. Slope of the channel.
• D. Discharge.

Answer: (A)

In Manning's equation, R stands for the hydraulic radius, a geometric measure of the cross-section of flow. It is defined as the cross-sectional area of the flow A divided by the wetted perimeter P: R = A / P. This quantity captures how the shape of the channel and the length of the contact between water and the channel affect flow resistance, feeding into the velocity relation V = (1/n) R^(2/3) S^(1/2).

For example, in a wide, shallow rectangular channel with width b and depth y, A = by and P ≈ b + 2y, so R = (by) / (b + 2y). As the channel geometry changes, R changes, altering velocity for the same roughness and slope.

Flow velocity, slope, and discharge are different quantities: velocity is V, slope is S, and discharge is Q = A*V.