A hydraulic jump occurs when a supercritical flow transitions to subcritical flow. If the upstream depth y1 = 0.40 m and downstream depth y2 = 0.90 m in a wide channel, compute r = y2/y1 and Fr1^2 using r, then comment on the flow regime.

• A. r = 2.25; Fr1^2 = 3.656; Fr1 ≈ 1.91 (supercritical upstream; hydraulic jump possible)
• B. r = 1.50; Fr1^2 = 2.25; Fr1 ≈ 1.50 (subcritical upstream; no jump)
• C. r = 2.00; Fr1^2 = 2.00; Fr1 ≈ 1.41 (supercritical upstream; jump unlikely)
• D. r = 2.25; Fr1^2 = 4.00; Fr1 ≈ 2.00 (supercritical upstream; very strong jump)

Answer: (A)

A hydraulic jump is a rapid transition from fast, shallow (supercritical) flow to slower, deeper (subcritical) flow in an open channel, and the relationship between the upstream Froude number and the depth ratio in a wide channel is Fr1^2 = (r^2 + r)/2, where r = y2/y1.

Here y1 = 0.40 m and y2 = 0.90 m, so r = y2/y1 = 0.90/0.40 = 2.25. Plugging into the formula gives Fr1^2 = (2.25^2 + 2.25)/2 = (5.0625 + 2.25)/2 = 3.65625, so Fr1 ≈ 1.91.

Since Fr1 > 1, the upstream flow is supercritical. The downstream depth is larger than the upstream depth (r > 1), which is consistent with a hydraulic jump where the flow transitions to subcritical. This set of values matches a strong jump scenario, with a supercritical upstream condition and the possibility of a jump to subcritical flow downstream.