Why is a triangular (V-notch) weir preferred over a rectangular notch? In open-channel flow measurement, select the most appropriate reason set explaining why a triangular V-notch is often chosen instead of a rectangular notch, especially for small discharges.

Introduction / Context:
Weirs are standard devices for measuring open-channel discharge. Among common shapes, the triangular (V-notch) weir is widely preferred for laboratory, irrigation, and drainage applications where flows are relatively small and accuracy at low heads is important.

Given Data / Assumptions:

• Sharp-crested notch/weir under free, fully aerated flow.
• Head (h) measured above the notch crest at a standard upstream distance.
• Coefficient of discharge approximately constant over typical operating heads for a V-notch of fixed angle (often 90°).

Concept / Approach:
For a sharp-crested triangular notch, the ideal discharge varies with h^(5/2): Q = (8/15) * C_d * √(2g) * tan(θ/2) * h^(5/2). The stronger head exponent (5/2) compared with the rectangular notch's 3/2 makes the V-notch more sensitive at low heads, improving practical accuracy. Only a single head measurement is needed, and one plate can cover a wide flow range by virtue of the notch geometry.

Step-by-Step Solution:

Verification / Alternative check:
Compare percentage change in Q for a small change in h for V-notch vs rectangular notch; the higher exponent produces larger relative change, hence finer resolution.

Why Other Options Are Wrong:
Each partial statement is true; selecting only one omits other genuine advantages. The comprehensive correct choice is “all the above”.

Common Pitfalls:
Ignoring aeration (submergence reduces accuracy); reading head too close to the nappe; using the rectangular notch for very low flows where measurement resolution suffers.

Final Answer:
all the above