Weirs/notches – error propagation for a triangular (V) notch If the measured head over a triangular notch crest (H) has a +1% error, the resulting percentage error in computed discharge is approximately:

Introduction:
Discharge over notches and weirs is a power function of head. Understanding error propagation helps prioritize measurement accuracy for key variables.

Given Data / Assumptions:

• Triangular (V) notch with standard calibration.
• Empirical relation: Q ∝ H^(5/2) (ignoring minor corrections).
• Small error approximation for differential changes.

Concept / Approach:
For Q ∝ H^n, the relative error relation is dQ/Q = n * dH/H for small perturbations. For a V-notch, n = 5/2 = 2.5, which amplifies head measurement errors by a factor of 2.5.

Step-by-Step Solution:
1) Write Q = K * H^(5/2).2) Take logarithms and differentiate: dQ/Q = (5/2) * dH/H.3) With dH/H = 0.01, compute dQ/Q = 2.5 * 0.01 = 0.025 = 2.5%.4) Hence, a 1% head error gives about 2.5% discharge error.

Verification / Alternative check:
A rectangular notch has Q ∝ H^(3/2), so a 1% head error would yield ~1.5% Q error—smaller than the triangular notch case, consistent with the higher exponent for V-notches.

Why Other Options Are Wrong:

• 1%, 1.5%, 2%: underestimate the amplification factor n = 2.5.
• 5%: doubles the correct amplification; not supported by Q–H relation.

Common Pitfalls:
Applying rectangular-notch exponents to V-notches; ignoring that error propagation assumes small percentage errors.

Final Answer:
2.5%