Difficulty: Medium
Correct Answer: Cd x L x 2g [(H + ha)3/2 - ha3/2]
Explanation:
Introduction / Context:
For rectangular weirs, the classical discharge relation assumes negligible approach velocity. When approach velocity is significant, the upstream total head includes both the static head over the crest and the velocity head, requiring a correction to avoid overestimation of discharge.
Given Data / Assumptions:
Concept / Approach:
The effective head driving flow is not just H but (H + h_a). However, the measured head gauge usually reads H referenced to a stilling point. The established correction subtracts the portion that would be counted if the approach section were also treated as a weir section (h_a term), leading to the standard form with a negative h_a^{3/2} correction.
Step-by-Step Solution:
Verification / Alternative check:
When v_a → 0, h_a → 0 and the expression reduces to the classical rectangular weir formula proportional to H^{3/2}, as expected.
Why Other Options Are Wrong:
(a) adds h_a^{3/2} instead of subtracting; (c) and (d) incorrectly replace H with H − h_a, which is not the effective upstream total head.
Common Pitfalls:
Using gauge readings too close to the crest (velocity effects not dissipated); neglecting the velocity of approach for high specific discharges.
Final Answer:
Cd x L x 2g [(H + ha)3/2 - ha3/2]
Discussion & Comments