Weir Discharge Formula — Ogee vs Sharp-Crested Rectangular Is the discharge formula for a sharp-crested weir and an ogee (ogee-crest) weir effectively the same as that of a rectangular sharp-crested weir, subject to appropriate coefficients?

Introduction:
Weir equations relate discharge to head over the crest. Ogee weirs are shaped to follow the lower nappe of a sharp-crested weir, allowing high accuracy at design heads.

Given Data / Assumptions:

• Free, fully aerated nappe conditions.
• Steady approach flow with appropriate approach velocity correction.
• Empirical coefficient of discharge C_d applied.

Concept / Approach:
For sharp-crested rectangular and ogee weirs, Q ≈ C_d * (2/3) * b * sqrt(2*g) * H^(3/2), with b as crest width and H as head above crest. Ogee weirs use similar head-discharge relation but with coefficients tuned to crest shape and approach conditions.

Step-by-Step Solution:
Start from the theoretical rectangular sharp-crest formula.Apply discharge coefficient C_d to account for contraction and viscosity.For an ogee crest, the same head exponent (3/2) applies; the profile mainly affects C_d and sensitivity to submergence.

Verification / Alternative check:
Standards (e.g., IS/USBPR/USACE) tabulate C_d for ogee and sharp crests; both retain Q proportional to H^(3/2) under free overflow, confirming functional sameness with adjusted coefficients.

Why Other Options Are Wrong:
Disagree: ignores the common formulation with different coefficients.
Depends on notch angle only: angle pertains to V-notch (triangular) weirs, not rectangular/ogee.
Only valid for triangular weirs: incorrect; the rectangular/ogee relation is independent of V-notch theory.

Common Pitfalls:
Using rectangular formula without velocity of approach correction; ignoring submergence; misapplying coefficients outside design head range.

Final Answer:
Agree