In a rectangular open channel with width B and depth y, the hydraulic radius R = A/P. Given A = B y and wetted perimeter P = B + 2 y, what is R?

• A. R = (B y)/(B + 2 y)
• B. R = (B y)/(B + y)
• C. R = (B y)/(2 B + y)
• D. R = (B + 2 y)/ (B y)

Answer: (A)

Hydraulic radius in open-channel flow is found by dividing the cross-sectional area of flow by the wetted perimeter—the portion of the channel boundary actually in contact with water. For a rectangular channel width B and depth y, the flow area is A = B y. The wetted perimeter is the bottom edge plus the two vertical sides, so P = B + 2 y. Put together, the hydraulic radius is R = A / P = (B y) / (B + 2 y).

This aligns with how the radius behaves in limits: if the channel is very wide (B >> y), R ≈ y; if the depth dominates (y >> B), R ≈ B/2. This R is the quantity used in Manning’s equation to relate slope, roughness, and discharge.

The other expressions would imply an incorrect perimeter or invert the ratio, which doesn’t match the actual geometry of a rectangular open channel.