Rectangular Weir – Discharge Formula with End Contractions Given Cd = 0.623, the standard SI form for discharge over a contracted rectangular weir is Q = 1.84 (L − 0.1 n H) H^(3/2), where L is crest length, H is head, and n is the number of end contractions.

Introduction:
The problem checks recognition of the widely used empirical discharge equation for a rectangular weir with end contractions, using a representative coefficient condensed into the constant 1.84 in SI units.

Given Data / Assumptions:

• Rectangular sharp-crested weir with n end contractions.
• Head over crest H measured upstream under standard conditions.
• Composite constant 1.84 corresponds to Cd = 0.623 with g in SI.

Concept / Approach:

From the theoretical broad formula Q = (2/3) * Cd * b * sqrt(2 g) * H^(3/2), with end contractions the effective length is L_e = L − 0.1 n H. Collecting constants in SI yields the practical form Q = 1.84 (L − 0.1 n H) H^(3/2).

Step-by-Step Solution:

Verification / Alternative check:

Dimensional analysis confirms Q in m^3/s when L and H are in meters. Field calibration data support the exponent 3/2 for free overflow under nappe aeration.

Why Other Options Are Wrong:

H^2 and H^3 exponents are not supported by energy integration; H^(5/2) is not the classical sharp-crested relation. Replacing 0.1 n H with n H grossly overcorrects for contractions.

Common Pitfalls:

Measuring H too close to the crest; neglecting aeration or approach velocity corrections; miscounting contractions for sidewall abutments.

Final Answer:

1.84(L - 0.1nH)H3/2