When water flows over a rectangular suppressed weir, a nappe forms and air may be entrained beneath it. Considering the pressure beneath the freely ventilated nappe, how does any negative (sub-atmospheric) pressure under the nappe influence the measured discharge for a given head over the crest?

Introduction / Context:
Free overfall from a sharp-crested, rectangular suppressed weir produces a nappe with atmospheric or sub-atmospheric conditions beneath it depending on aeration. The pressure regime under the nappe impacts the effective head and therefore the discharge for a given upstream head measurement point.

Given Data / Assumptions:

• Sharp-crested, rectangular suppressed weir.
• Head measured at a standard upstream location where velocity of approach is either negligible or corrected.
• Nappe ventilation may be present or partially restricted, leading to negative pressure beneath nappe.

Concept / Approach:
Bernoulli’s principle with the appropriate discharge coefficient shows that reduced pressure under the nappe increases the pressure differential across the crest. This raises the effective head driving flow, hence the actual discharge rises for the same measured upstream head.

Step-by-Step Reasoning:
Weir formula: Q = C_d * b * (2g)^(1/2) * H^(3/2), where H is the head over crest.If sub-atmospheric pressure develops under the nappe, the pressure at the crest control section is reduced below atmospheric.Effective head becomes H_eff > H_measured, because downstream/under-nappe pressure is lower.Therefore Q_actual = C_d′ * b * (2g)^(1/2) * H_eff^(3/2) increases compared with the fully ventilated case.

Verification / Alternative Check:
Field practice recommends ventilating the nappe to maintain near-atmospheric pressure beneath it; otherwise discharge coefficients must be adjusted upward to account for increased flow at the same indicated head.

Why Other Options Are Wrong:
Decreases discharge: opposite of the pressure-head effect.No appreciable effect: contradicted by experiments; effect can be significant.Flow reversal: physically unrealistic for ordinary heads.Only C_v changes: net impact is increased Q unless compensated in coefficients; statement is incomplete.

Common Pitfalls:

• Ignoring ventilation; unventilated nappes can produce measurement errors.
• Applying standard coefficients without checking nappe aeration.
• Neglecting approach velocity correction, compounding error.

Final Answer:
It increases the discharge for the same measured head