Application of notches in open-channel measurements: A notch is used to measure which quantity of liquids?

Introduction / Context:
Notches (small weirs) are openings in the side of a tank or channel used to measure flow rate by relating head over the crest to discharge through empirical/analytical formulas. They are widely used in laboratories and small channels for convenient discharge measurement.

Given Data / Assumptions:

• Free-flow (non-submerged) condition across the notch.
• Calibration constants for the specific notch geometry available (e.g., C_d).
• Steady approach conditions with sufficient head over crest.

Concept / Approach:
For a rectangular, triangular (V-notch), or trapezoidal (Cipolletti) notch, discharge Q is a function of head H over the crest: Q = C * H^n, where n depends on notch geometry (e.g., n ≈ 3/2 for rectangular). Thus, notches measure flow rate (discharge), not static pressure, instantaneous point velocity, or stored volume.

Step-by-Step Solution:

Verification / Alternative check:
Comparing volumetric tank-rise method with the notch-based Q over time validates the discharge measurement within experimental uncertainty, confirming that notches quantify flow rate.

Why Other Options Are Wrong:

• Pressure: Measured with manometers/transducers.
• Velocity: Measured with Pitot tubes, ADV, or current meters.
• Volume: A cumulative integral of discharge over time, not a direct notch measurement.

Common Pitfalls:
Reading head too close to the nappe; neglecting approach velocity corrections; using submerged formulas when downstream level drowns the nappe; poor crest sharpness causing calibration error.

Final Answer:
discharge