A rectangular open-channel section has width B = 5 m and depth y = 1 m. If a step increase of discharge doubles V, how does Froude number change qualitatively?

• A. Fr decreases; flow becomes more subcritical.
• B. Fr remains the same.
• C. Fr doubles; flow becomes more supercritical.
• D. Fr increases slightly but remains subcritical.

Answer: (C)

Froude number in an open-channel flow is the ratio of the flow velocity to the gravity wave speed, Fr = V / sqrt(g y). Here the depth is y = 1 m and the velocity doubles when the discharge step occurs. If the depth doesn’t rise enough to significantly change sqrt(g y), the denominator stays about the same while the numerator doubles, so Fr roughly doubles. A larger Fr means inertia dominates more and the flow is further into the supercritical regime, so the flow becomes more supercritical.