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Two geometrically similar pumps are running at 1000 rpm speed (both). If one pump has impeller diameter of 0.3m and discharges 20 LPM against 20 m head, and the other pump gives half of this discharges rate; calculate head and diameter of second pump
1. 12.5 m and 0.12 m 
2. 10.5 m and 0.12 m
3. 10.5 m and 0.23 m 
4. 12.5 m and 0.23 m

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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;

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