- +25%
- -18.25%
- -10.5%
- +10.5%

Option 3 : -10.5%

Free

CT 1: Ratio and Proportion

2672

10 Questions
16 Marks
30 Mins

As per Darcy-weisbach equation

\({h_f} = \frac{{4fL{V^2}}}{{2gd}} = \frac{{4fL}}{{2gd}}{V^2} = \frac{{4fL}}{{2gd}}{\left( {\frac{{4Q}}{{\pi {d^2}}}\;} \right)^2} = \frac{{32f{Q^2}}}{{{\pi ^2}g}}\left( {\frac{L}{{{d^5}}}} \right) \Rightarrow Q \propto \frac{1}{\sqrt{f}}\)

If f is misjudged by +25%, now Q will be proportional to \(\sqrt {\frac{1}{{1.25}}}\) i.e. 89.44%

i.e. it is reduced about 10.56%
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