In a control meter (flow-measuring section), a hydraulic jump will form upstream (above the control) under which initial depth condition?

Introduction / Context:
Hydraulic jumps occur when rapidly varied flow transitions from supercritical to subcritical conditions, dissipating energy. In control meters or flumes, the location of any jump (upstream vs. downstream) depends on approach depth relative to the critical depth at the control.

Given Data / Assumptions:

• Prismatic approach channel.
• Control section imposes critical depth at or near the throat.
• Steady flow with negligible lateral inflow.

Concept / Approach:
Supercritical flow has depth less than critical; subcritical flow has greater depth. A control (e.g., sharp-crested weir, flume throat) tends to fix depth near critical. If the approach (original) depth is less than critical (supercritical), the control can cause backwater and a hydraulic jump to form upstream (above the control) as the flow must adjust to, or be influenced by, the control condition. Conversely, if approach depth is much greater than critical (subcritical), the supercritical condition typically occurs downstream of the control and the jump forms downstream in the recovery reach.

Step-by-Step Solution:

Verification / Alternative check:
Flow profiles near flumes and weirs in open-channel texts show upstream jumps when approach flow is already supercritical and must transition before the control section.

Why Other Options Are Wrong:

• More than critical: Subcritical approach usually places the jump downstream after the control-induced supercritical zone.
• Equal to critical: Marginal case; jump formation location is not necessarily upstream.
• None: A correct upstream condition exists.

Common Pitfalls:

• Confusing the terms 'above' (upstream) and 'below' (downstream) of control.
• Ignoring tailwater constraints that can shift jump position.

Final Answer:
Original flow depth is less than the critical depth