Discharge over a Cipolletti weir A sharp-crested Cipolletti weir has crest length L = 2.185 m. If the measured head over the crest is H = 1.0 m, estimate the discharge (assume a typical sharp-crest coefficient C_d ≈ 0.62).

Introduction / Context:The Cipolletti (trapezoidal) weir uses 1H:4V side slopes to cancel end-contraction effects so its discharge is approximated by the rectangular suppressed-weir formula using the measured crest length. This problem applies the standard sharp-crested relation with a representative C_d to estimate flow.

Given Data / Assumptions:

• Crest length L = 2.185 m.
• Head over crest H = 1.0 m (measured upstream at standard location).
• Sharp-crested weir; use C_d ≈ 0.62.
• g = 9.81 m/s^2; neglect velocity of approach and submergence.

Concept / Approach:

For a Cipolletti weir, the discharge is approximated by the rectangular suppressed-weir equation: Q = (2/3) * C_d * L * sqrt(2g) * H^(3/2). With H = 1, the power reduces to 1, simplifying evaluation.

Step-by-Step Solution:

Verification / Alternative check:

Reasonable magnitudes: a 2.2 m wide sharp-crest with 1 m head producing roughly 4 m^3/s aligns with standard tables. Minor deviations in C_d (0.60–0.62) change Q by only a few percent.

Why Other Options Are Wrong:

(a–c) Underestimate the computed discharge for H = 1 m. (e) Slight overestimate beyond typical C_d range with H = 1 m and L = 2.185 m.

Common Pitfalls:

Forgetting that Cipolletti geometry eliminates end-contraction correction; using effective length L_e incorrectly; neglecting submergence criteria or velocity-of-approach corrections when they are significant.

Final Answer:

4.0 m^3/s