In Manning's equation Q = (1/n) A R^(2/3) S^(1/2), which parameter is raised to the 2/3 power?

• A. n
• B. A
• C. S
• D. R

Answer: (D)

The term that carries the 2/3 power is the hydraulic radius, R. In Manning's equation Q = (1/n) A R^(2/3) S^(1/2), the exponent 2/3 is attached to R, while the area A is simply multiplied, the slope S is under a square root (exponent 1/2), and the roughness coefficient n appears in the denominator as a simple factor. The hydraulic radius is defined as R = A/P, where P is the wetted perimeter, which links the flow area to the boundary contact with the water. The 2/3 power on R reflects how discharge increases with a larger radius, but with diminishing returns due to the fractional exponent.