Weirs – behavior of nappe at the ends of a rectangular crest As water flows over a rectangular weir (crest/sill), what happens to the jet stream along the ends of the sill due to side-edge effects?
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Aexpands
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Bdoes not change
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Ccontracts
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Doscillates periodically with no mean change
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Ethickens only at the center
Answer
Correct Answer: contracts
Explanation
Introduction:Side contractions are a hallmark of sharp-crested rectangular weirs that do not span the entire channel width. The nappe narrows near the side edges, reducing the effective width and requiring a correction when computing discharge. This question asks for the qualitative change at the ends of the sill.
Given Data / Assumptions:
- Free (not submerged) rectangular weir with end contractions present.
- Side walls are away from the nappe edges so lateral contraction can occur.
- Sharp crest; typical heads where standard formulas apply.
Concept / Approach:
Because flow lines near the side edges bend around the corners, the jet contracts laterally at each end, forming a reduced effective width. Empirical weir equations incorporate this via an “end contraction” correction, often expressed as L_e = L − k * n * H, where n is the number of contracting ends (usually 2) and k is an empirical factor of order unity.
Step-by-Step Solution:
Recognize geometry: finite crest length with free side edges.Identify effect: streamlines converge near edges causing a narrower nappe.Implication: use effective length L_e smaller than physical length L.Verification / Alternative check:
Laboratory observations show visible narrowing and a drop in discharge relative to a suppressed weir (no side contraction), verifying the contraction phenomenon.
Why Other Options Are Wrong:
Expands/does not change: Opposite of observed end-contraction effect.Oscillation/thickening at center: Not the primary behavior explained by edge contraction.
Common Pitfalls:
Confusing end contraction with velocity-of-approach correction; they are separate effects.
Final Answer:
contracts