Question

Two pipelines of equal length with diameters of 15 cm and 10 cm are in parallel & connected to two reservoirs. The difference in water levels in the reservoirs is 3m. If the friction is assumed to be equal, the ratio of the discharges due to the larger diameter pipe to that of the smaller diameter pipe is
1. 3.375
2. 2.756
3. 2.256
4. 3.285

Answer 1

Correct Answer - Option 2 : 2.756

\({h_f} = \frac{{fL{V^2}}}{{d \times 2g}}\)

So, \(V\alpha \surd d\)

Now, \(\frac{{{Q_1}}}{{{Q_2}}} = \frac{{{A_1}{V_1}}}{{{A_2}{V_2}}} = {\left( {\frac{{{d_1}}}{{{d_2}}}} \right)^{\frac{5}{2}}}\)

\(\Rightarrow \frac{{{Q_1}}}{{{Q_2}}} = {\left( {\frac{{15}}{{10}}} \right)^{\frac{5}{2}}} = 2.756\)