With regard to a hydraulic jump, which of the following is true?

Question

BlackTom AI · Accepted Answer

Question restatement: The prompt asks about hydraulic jumps and which statement among the options is true. The four choices present different claims about downstream depth, flow regime, momentum, and where the jump occurs.

Option 1: The downstream depth depends only on the upstream depth and upstream Froude number.
This is the classic result for a hydraulic jump. The sequent (downstream) depth y2 is determined by the upstream depth y1 and the upstream Froude number Fr1, via the sequent depth relation y2/y1 = (1/2)(-1 + sqrt(1 + 8 Fr1^2)). It shows that y2 is functionally related to y1 and Fr1, and not dependent on downstream conditions except through those upstream parameters. The statement captures the essential dependency and is consistent with hydraulic jump theory.

Option 2: Hydraulic jumps can form in subcritical flow, as long as the depth is less than the normal depth.
This is incorrect. A hydraulic jump typically occurs when inertial forces dominate (Fr1 > 1, i.e., supercritical upstream flow). The jump transitions from supercritical to subcritical, not within subcritical flow under subnormal depth conditions. The condition of “depth less than normal depth” is not the defining criterion for a jump to occur, making this claim false.

Option 3: The momentum of the flow remains the same through the jump, except for losses due to turbulence.
This is false. Across a hydraulic jump, momentum flux is not conserved as a simple constant because the jump involves dissipative processes, pressure distribution changes, and non-negligible energy losses due to turbulence and viscous effects. The statement incorrectly asserts momentum remains essentially constant apart from losses, which mischaracterizes the jump dynamics.

Option 4: Hydraulic jumps tends to form at the point where the depth will jump to the critical depth
This is misleading. While the downstream flow is subcritical (Fr2 < 1) and the jump is associated with a transition from supercritical to subcritical, the position of the jump is not determined by a condition that the depth equals the critical depth. The jump occurs due to energy and momentum considerations during a flow regime change, not because the depth is exactly at the critical depth at the jump location. Therefore this statement is incorrect.

CVEN90051_2025_SM2 Module #1 Practice Quiz

With regard to a hydraulic jump, which of the following is true?

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