Head–discharge proportionality for notches Choose the correct statement(s) relating discharge Q to head H over a weir/notch under free-flow conditions.

Introduction / Context:
Discharge measurement by notches and weirs is fundamental in hydraulic laboratories and field channels. The head–discharge exponent depends on the crest shape and flow contraction behavior.

Given Data / Assumptions:

• Free, fully aerated overflow without submergence.
• Standard coefficients near calibrated values; end-contraction corrections omitted for proportionality.
• Sharp-crested geometry for the rectangular case; V-notch with fixed angle (e.g., 90°) for the triangular case.

Concept / Approach:

Classical results: rectangular sharp-crested weir Q ∝ H^(3/2); triangular (V-notch) Q ∝ H^(5/2). The larger exponent for the V-notch reflects the narrowing flow area with decreasing head, increasing sensitivity to H.

Step-by-Step Solution:

Verification / Alternative check:

Calibration charts and standard texts confirm these exponents under non-drowned, sharp-crested conditions.

Why Other Options Are Wrong:

Options denying either exponent contradict well-established discharge formulas.

Common Pitfalls:

Using rectangular exponents for V-notches; ignoring submergence or approach velocity corrections when high accuracy is needed.

Final Answer:

Both (a) and (b)