M1Q10 PART #2 (METHOD)

Water discharging from a spillway into a rectangular horizontal (wide) channel goes through a hydraulic jump, before returning to a river (see schematic below). PART #2 (method): Which method could be used to determine the height of this step?

Question

M1Q10 PART #2 (METHOD)

Water discharging from a spillway into a rectangular horizontal (wide) channel goes through a hydraulic jump, before returning to a river (see schematic below). PART #2 (method): Which method could be used to determine the height of this step?

BlackTom AI · Accepted Answer

Question restatement: M1Q10 PART #2 (METHOD) involves water discharging from a spillway into a rectangular wide channel, undergoing a hydraulic jump, and returning to a river. The task is to identify a method to determine the height of the step.

Option 1: Use the momentum equation directly between the jump and the river, ignoring energy losses.
- This approach would neglect energy losses that accompany a hydraulic jump and would not accurately relate the post-jump conditions to the downstream river depth. Momentum balance can be informative, but ignoring losses in a jump typically yields incorrect results for step height estimation, since the momentum flux change is influenced by the jump’s dissipative processes and bed geometry. Therefore, this option is flawed for determining step height.

Option 2: Apply the gradually varied flow (step method) from the gate to the river without considering the jump.
- The step method for gradually varied flow is appropriate for transitions along a channel with changing cross-sectional area or slope, but it does not account for the abrupt energy dissipation and depth change caused by a hydraulic jump. If the jump is part of the system, omitting its presence leads to an incomplete and typically erroneous assessment of step height. Hence, this option is not suitable.

Option 3: Assume the step height is equal to the difference between the conjugate depth after the jump and the river depth.
- This option explicitly links the step height to the hydraulic jump’s conjugate depths, recognizing that a hydraulic jump establishes a pair of conjugate depths (sequent depths) across the jump. If the step is designed to accommodate the post-jump water surface elevation relative to downstream river depth, using the difference between the conjugate depth after the jump and the downstream river depth is a practical method grounded in jump hydraulics. This approach directly incorporates the hydraulic jump behavior into the step-height estimation, which is conceptually sound.

Option 4: Apply an energy balance between the post-jump section and the river to estimate the step height.
- An energy balance could be informative for estimating head losses and elevations, but hydraulic jumps involve abrupt, non-conservative losses that complicate a straightforward energy balance. While energy considerations are important, merely applying a simple energy balance between post-jump and river without properly accounting for jump dynamics and conjugate depths may produce inaccuracies in step height estimation. This makes the option less reliable as a sole method in this context.

Summary of reasoning across options:
- Option 1 overlooks energy losses in the jump, misusing momentum balance in a scenario where dissipation matters. 
- Option 2 ignores the jump entirely, thus missing a central feature of the flow that dictates the surface elevation after the jump. 
- Option 3 aligns with hydraulic jump theory by tying the step height to the change in surface elevations across the jump, via the conjugate depth relationship.
- Option 4 attempts an energy-based estimate but must carefully handle non-conservative losses inherent to a jump; without that nuance, it risks inaccuracy.

Overall, option 3 stands out as the method that directly leverages the conjugate-depth concept associated with a hydraulic jump to determine the step height, making it the most appropriate choice among the listed methods.

CVEN90051_2025_SM2 Exam: Civil Hydraulics (CVEN90051_2025_SM2)- Requires Respondus LockDown Browser

M1Q10 PART #2 (METHOD) Water discharging from a spillway into a rectangular horizontal (wide) channel goes through a hydraulic jump, before returning to a river (see schematic below). PART #2 (method): Which method could be used to determine the height of this step?

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