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 N_{1} = N_{2} = 1000 rpm, D_{1} = 0.3 m, H_{1} = 20 m, Q_{1} = 20 LPM;

Given the other pump gives half of this discharges rate ⇒ Q_{2} = 10 LPM;

From the specific speed relation,

\(⇒ \frac{{\sqrt {20} }}{{{{20}^{0.75}}}} = \frac{{\sqrt {10} }}{{H_2^{0.75}}}\)

**⇒ H**_{2} = 12.59 m;

From the flow coefficient relation,

\(⇒ \frac {20}{{0.3}^3} = \frac {10}{{D_2}^3}\)

**⇒ D**_{2} = 0.238 m;