Weir hydraulics: The commonly used empirical discharge expression for large sharp-crested rectangular weirs is attributed to which formula?

Introduction / Context:

Measuring open-channel flow often relies on sharp-crested rectangular weirs. Empirical coefficients account for approach velocity and contraction. Recognizing the standard formula attribution helps in selecting appropriate coefficients and reference charts.

Given Data / Assumptions:

• Sharp-crested rectangular weir under free overflow conditions.
• Head over the crest within the empirical calibration range.

Concept / Approach:

The widely used discharge relation is often written as Q = C_f * b * H^(3/2), where C_f consolidates 2/3 * C_d * sqrt(2g) and empirical corrections. This expression is historically associated with Francis, whose work calibrated sharp-crested weir coefficients.

Step-by-Step Solution:

Verification / Alternative check:

Bazin and Kutter are associated with channel resistance (Manning/roughness refinements), not weir discharge; Rehbock contributed notch coefficients but Francis is the canonical rectangular weir reference.

Why Other Options Are Wrong:

• Bazin and Kutter relate to open-channel resistance, not sharp-crested weir discharge.
• Rehbock provided corrections but the classic attribution for large rectangular weirs remains Francis.

Common Pitfalls:

• Mixing resistance formulae (Kutter/Bazin) with structure-measurement formulae (weirs).

Final Answer:

Francis formula