SSC JE Civil Engineering 30-Oct-2020 Shift 1 Paper

Question : 135 of 200

Marks: +1, -0

The 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:

Validate

Solution:

Concept:
Discharge through rectangular notch

{\Q}={2}/{3} {\c}_{{\d}}.{\b} √{{2 {\g}}}({\H})^{3 / 2}

Where,
H = Height of water above will of notch
b = width of the notch

\C_\d

= coefficient of discharge

∴ {\dQ}={2}/{3} {\C}_{{\d}} {\b} √{{2 \g}}× {3}/{2}({\H})^{1 / 2} {\dH}

{\dQ}=({2}{3} {\C}_{{\d}} {\b} √{{2 \g}} × {\H}^{{1}\/{2}}× {\H}) × {3}/{2} {{\dH}}/{{\H}}

{\dQ}={\Q} × {3}/{2} {{\dH}}/{{\H}}

{{\dQ}}/{{\Q}}={3}/{2} {{\dH}}/{{\H}}

Calculation:

{{\dQ}}/{{\Q}}={3}{2} ×{1.5}/{750}=0.3 \%

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