Broad-Crested Weir — Condition for Maximum Discharge For a broad-crested weir, the discharge is maximum if the head of water on the downstream side of the weir is ______ the head of water on the upstream side.

Introduction:
Broad-crested weirs often operate with free overflow, and their peak discharge condition relates to the energy distribution between upstream and downstream levels. Understanding this helps avoid submergence and ensures accurate rating curves.

Given Data / Assumptions:

• Rectangular broad-crested weir under steady conditions.
• Negligible losses for the ideal condition; approach velocity small.
• Heads measured relative to the weir crest.

Concept / Approach:
Maximum discharge corresponds to critical flow over the crest. Energy and momentum considerations show a specific ratio between upstream and downstream heads when the crest section becomes critical, leading to the stated proportion.

Step-by-Step Solution:
Recognize that q = b * h * V and, at critical state over a broad crest, V^2 = g * h.The discharge reaches a maximum when the crest section runs at critical depth; energy distribution implies a fixed fraction relationship between downstream and upstream heads.This ideal analysis yields the practical rule: downstream head ≈ two-thirds of upstream head for maximum discharge.

Verification / Alternative check:
Textbook treatments of broad-crested weirs show crest-critical operation at maximum Q; empirical rating curves align with this condition in idealized settings.

Why Other Options Are Wrong:
Equal to or three-fourth do not correspond to the critical-flow proportion; one-third is associated with other hydraulic maxima conditions, not broad-crested weirs.

Common Pitfalls:
Applying this condition when the weir is submerged; ignoring approach velocity corrections; confusing critical depth criteria for different structures.

Final Answer:
two-third