Difficulty: Easy
Correct Answer: None of these.
Explanation:
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:
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:
Recognize the V-notch is designed for low discharges: the power of 5/2 on H increases sensitivity.Note that Q can be computed from a single measured head H, given θ and C_d.Understand ventilation: air beneath the nappe maintains atmospheric pressure under the sheet, preventing adherence to the downstream face. Without ventilation, sub-atmospheric pressure can form and alter C_d, causing under-reading.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.
Discussion & Comments