Composite notches – discharge over a trapezoidal notch The discharge over a trapezoidal (Cipolletti-type) notch can be expressed as the discharge over an equivalent rectangular notch __________ the discharge over a triangular (V) notch:

Introduction:
A trapezoidal notch combines a rectangular section and sloping sides that behave like a triangular notch. Conceptually, its flow is the superposition of the two components.

Given Data / Assumptions:

• Standard notch coefficients apply, with the trapezoid composed of a central rectangle and two equal triangles.
• Head H is measured above the crest.
• Coefficient variations with H are modest over the calibrated range.

Concept / Approach:
For small viscosity and surface-tension effects, discharges add linearly: Q_total = Q_rectangular + Q_triangular. The rectangular part scales roughly with H^(3/2), while the triangular side portions scale with H^(5/2).

Step-by-Step Solution:
1) Split area into a rectangle (width b) and two triangles (side slope m:1).2) Use standard formulae: Q_rect proportional to b * H^(3/2); Q_tri proportional to m * H^(5/2).3) Superpose to get Q_trap = Q_rect + Q_tri.

Verification / Alternative check:
Cipolletti notch (with specific side slope) is designed so that the triangular side discharge compensates for end contractions of the rectangular portion, reinforcing the additive concept.

Why Other Options Are Wrong:

• Minus, multiply, divide, or exponentiate: physically incorrect for independent parallel flow paths combining at the nappe.

Common Pitfalls:
Forgetting coefficient-of-discharge corrections; while the conceptual addition holds, coefficients must be applied appropriately in calculations.

Final Answer:
plus