If error in the measurement of head in a V-notch is 1%, then the error in the measurement of discharge will be
- A1%
- B1.5%
- C2%
- D2.5%Correct
Solution
Concept
Sensitivity of V-notch discharge to head error
Formula
Q ∝ H5/2, dQ/Q = (5/2) · dH/H
Step-by-step solution
1. For a V-notch Q = (8/15) Cd √(2g) tan(θ/2) H5/2. 2. dQ/Q = 2.5 × dH/H = 2.5 × 1% = 2.5%.
Explanation
The discharge of a triangular notch varies as H2.5, so the percentage error in discharge is 2.5 times the percentage error in head. A rectangular notch has H1.5, giving 1.5 times the error.
Shortcut
V-notch → 2.5 × error in head. Rectangular → 1.5 × error in head.
Common mistake
Using the rectangular notch exponent 1.5.
Correct answer: D) 2.5%