In a wide rectangular channel, compute critical depth y_c for Q = 3 m^3/s, width B = 4 m, g = 9.81 using y_c = [Q^2/(g B^2)]^(1/3).

• A. 0.250 m
• B. 0.500 m
• C. 0.386 m
• D. 0.310 m

Answer: (C)

Critical depth is the depth where the flow is exactly at the transition between subcritical and supercritical, meaning the Froude number equals 1. For a wide rectangular channel, the flow velocity is V = Q/(B y), and the condition Fr = V/√(g y) = 1 becomes Q/(B y) = √(g y). Squaring and rearranging leads to y^3 = Q^2/(g B^2), so y_c = [Q^2/(g B^2)]^(1/3).

Plugging in Q = 3 m^3/s, B = 4 m, g = 9.81 m/s^2 gives Q^2 = 9, g B^2 = 9.81×16 = 156.96, yielding Q^2/(g B^2) ≈ 0.0573. The cube root of 0.0573 is about 0.386 m. Therefore, the critical depth is approximately 0.386 m.