Error propagation for triangular weirs/notches: For a V-notch (triangular notch), discharge varies with head as Q ∝ H^(5/2). What is the ratio of the percentage error in discharge to the percentage error in measured head over the notch?

Introduction / Context:Flow measurement over notches relies on empirical–theoretical relations between head (H) and discharge (Q). Understanding how measurement errors in H propagate into errors in Q is crucial for instrumentation accuracy and calibration protocols.

Given Data / Assumptions:

• Triangular (V-notch) weir with Q = K H^(5/2), where K includes notch angle and discharge coefficient.
• Small measurement errors relative to the nominal head (linearized error propagation).
• Steady flow; proper approach conditions.

Concept / Approach:

For Q = K H^n, fractional errors relate by dQ/Q = n dH/H. Thus, the percentage error in Q is n times the percentage error in H. For a V-notch, n = 5/2, significantly amplifying head measurement errors.

Step-by-Step Solution:

Verification / Alternative check:

Compare with rectangular notch where Q ∝ H^(3/2): the ratio would be 3/2, confirming the exponent-rule consistency.

Why Other Options Are Wrong:

(a), (b), (c), and (e) correspond to other exponents or are arbitrary; only 5/2 matches the V-notch exponent.

Common Pitfalls:

Using absolute errors instead of fractional; forgetting that the exponent multiplies the fractional error.

Final Answer:

5/2