Question

The absolute percentage error in the computed discharge over a rectangular weir corresponding to an absolute error of 1.5% in the measurement of head over the sill of the weir would be

• A. 1.5
• B. 2.25
• C. 2.5
• D. 3.75

Answer 1

The correct option is B

2.25

For a rectangular weir

$Q=\left(\frac{2}{3}{C}_{d}L\sqrt{2g}\right)H^{3/2}=K{H}^{3/2}$

$dQ=\frac{2}{3}K{H}^{1/2}.dH$

$\Rightarrow \frac{dQ}{Q}=\frac{\frac{3}{2}K{H}^{1/2}}{K{H}^{3/2}}.dH=\frac{3}{2}\frac{dH}{H}$

$\therefore$ For an error of 1.5% in measurement of head, corresponding error in discharge = 1.5 × 1.5 = 2.25%