Question
Download Solution PDFThe head over a rectangular sharp crested notch at the end of a channel is 0.75 m. If an error of 1.5 mm is possible in the measurement of the head, then the percentage error in computing the discharge will be:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Discharge through rectangular notch
\(Q = \frac{2}{3}{c_d}.b\sqrt {2g} {\left( H \right)^{3/2}}\)
Where,
H = Height of water above will of notch
b = width of the notch
Cd = coefficient of discharge
\(\therefore dQ = \frac{2}{3}{C_d}b\sqrt {2g} \times \frac{3}{2}{\left( H \right)^{1/2}}dH\)
\(dQ = \left( {\frac{2}{3}{C_d}b\sqrt {2g} \times {H^{\frac{1}{2}}} \times H} \right) \times \frac{3}{2}\frac{{dH}}{H}\)
\(dQ = Q \times \frac{3}{2}\frac{{dH}}{H}\)
\(\frac{{dQ}}{Q} = \frac{3}{2}\frac{{dH}}{H}\)
Calculation:
\(\frac{{dQ}}{Q} = \frac{3}{2}\times\frac{{1.5}}{750} \times 100= 0.3\)%
Last updated on May 28, 2025
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