Triangular (V) notch discharge–head relationship Identify how discharge varies with head H for a sharp-crested triangular notch.

Introduction:Flow measurement over notches and weirs relies on empirical–theoretical relations between discharge Q and head H. For triangular (V) notches, the exponent of H is a key discriminant. This question checks whether you know that Q varies with H to the power 5/2.

Given Data / Assumptions:

• Sharp-crested, well-ventilated triangular notch.
• Free, fully contracted flow without submergence.
• Coefficient of discharge treated as approximately constant over small H ranges.

Concept / Approach:Elementary derivation integrates elemental discharge strips across the varying width b(y) of the notch opening with local velocity proportional to sqrt(2gH_local). For a V-notch of angle theta, width b ∝ y, and integration yields Q = C_d * (8/15) * tan(theta/2) * sqrt(2g) * H^(5/2). Hence, the dependence is Q ∝ H^(5/2).

Step-by-Step Solution:

Verification / Alternative check:Standard hydraulics texts list Q = K * H^(5/2) for V-notches, distinguishing them from rectangular weirs where Q ∝ H^(3/2).

Why Other Options Are Wrong:

• H^(3/2) (direct or inverse): characteristic of rectangular weirs, not V-notches.
• Inverse proportionalities: unphysical for increasing head producing more flow.
• Independent of H: contradicts basic weir theory.

Common Pitfalls:Mixing up the H exponents between rectangular and triangular notches or forgetting the role of notch angle in the proportionality constant, not in the exponent.

Final Answer:directly proportional to H5/2