Triangular (V-notch) weir: identify the incorrect statement about its use, accuracy, and ventilation requirements in open-channel flow measurement.

Introduction / Context:
Triangular (V-notch) weirs are widely used in hydraulic laboratories and field gauging to measure small to moderate discharges accurately. Because the discharge varies sensitively with head, V-notches are preferred at low flows where rectangular notches may lose resolution.

Given Data / Assumptions:

• Sharp-crested, well-formed V-notch installed with proper approach conditions.
• Free, ventilated nappe unless otherwise specified.
• Standard head measurement taken vertically above the crest apex at a prescribed distance upstream.

Concept / Approach:

The classical discharge relation for a V-notch is Q = C_d * (8/15) * √(2g) * tan(θ/2) * H^(5/2), where H is the head over the crest. Because Q ∝ H^(5/2), small changes in H produce measurable changes in Q, improving sensitivity at low flows. Only one head reading is needed once the notch angle and coefficient are known.

Step-by-Step Solution:

Verification / Alternative check:

Compare with a rectangular notch (Q ∝ H^(3/2)). For identical measurement resolution in H, the V-notch yields a larger proportional change in Q at small H, confirming its advantage at low flow rates.

Why Other Options Are Wrong:

(a) Correct: V-notches are indeed more accurate at low flows. (b) Correct: only head H is required. (c) Correct: ventilation is necessary to preserve calibration. (e) Incorrect claim; V-notches are specifically recommended for low flows.

Common Pitfalls:

Not ventilating the nappe; measuring H too close to the crest; ignoring approach velocity head corrections for higher velocities.

Final Answer:

None of these.