Hydraulic jump formation criterion: Under what interaction of flow regimes is a hydraulic jump generally produced in an open channel?

Introduction / Context:
A hydraulic jump is a rapid transition from supercritical (shallow, fast) to subcritical (deeper, slower) flow, accompanied by energy dissipation and turbulence. It is essential in spillway stilling basins, chute transitions, and energy dissipation devices.

Given Data / Assumptions:

• Open channel flow; Froude number Fr > 1 indicates supercritical, Fr < 1 indicates subcritical.
• Jump occurs when downstream conditions force a change from supercritical to subcritical.

Concept / Approach:
When a supercritical stream encounters a control that imposes higher depth (e.g., backwater, gate, basin), the flow transitions to subcritical via a jump. The momentum function is conserved across the jump, while there is a loss in specific energy.

Step-by-Step Solution:
Identify upstream regime: supercritical (Fr > 1).Identify downstream regime: subcritical (Fr < 1).Recognize that the jump connects the conjugate depths of these two regimes.Hence select option (c).

Verification / Alternative check:
Hydraulics texts derive the conjugate depth relation using momentum principles, confirming the regime change from Fr > 1 to Fr < 1 through the jump.

Why Other Options Are Wrong:

• (a) Critical-to-supercritical interface is not the canonical jump case.
• (b) Supercritical meeting supercritical does not force the abrupt depth rise.
• (d) Wording implies reverse propagation rather than the local regime change; the key is supercritical-to-subcritical transition.

Common Pitfalls:
Confusing jumps with bores or standing waves; forgetting that energy is not conserved across the jump while momentum (with hydrostatic pressure assumption) is.

Final Answer:
A supercritical (hyper-critical) stream meets a subcritical stream