Correct Answer - Option 4 : 12.5 m and 0.23 m
Concept:
For a geometrically similar pump, similarity parameters are used to find the unknown quantities by making them equal for both the similar pumps.
The similarity parameters are
Head rise coefficient - \(\frac{{H}}{{{N^2}{D^2}}}\)
Flow coefficient - \(\frac{Q}{{N{D^3}}}\)
Power coefficient - \(\frac{P}{{{N^3}{D^5}}}\)
For two similar pumps, the specific speed will also be the same.
Specific speed - \(\frac{{N\sqrt Q }}{{{H^{\frac{3}{4}}}}}\)
Calculation:
Given N1 = N2 = 1000 rpm, D1 = 0.3 m, H1 = 20 m, Q1 = 20 LPM;
Given the other pump gives half of this discharges rate ⇒ Q2 = 10 LPM;
From the specific speed relation,
\(⇒ \frac{{\sqrt {20} }}{{{{20}^{0.75}}}} = \frac{{\sqrt {10} }}{{H_2^{0.75}}}\)
⇒ H2 = 12.59 m;
From the flow coefficient relation,
\(⇒ \frac {20}{{0.3}^3} = \frac {10}{{D_2}^3}\)
⇒ D2 = 0.238 m;