# The number of impellers required for a multistage pump to lift 4500 litres/minute against a total head 190 m at speed of 750 rpm with specific speed n

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The number of impellers required for a multistage pump to lift 4500 litres/minute against a total head 190 m at speed of 750 rpm with specific speed not to exceed 700 is
1. 6
2. 8
3. 10
4. 12

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Correct Answer - Option 3 : 10

Concept:

Specific speed is defined as the speed in revolutions per minute at which a geometrically similar impeller would operate if it were of such a size as to deliver one litre per second against one meter of hydraulic head.

Specific speed of pump $= {N_S} = \frac{{N\sqrt Q }}{{{{\left( H \right)}^{3/4}}}}$

Where N = speed in rpm

Q = discharge (in l/s)

Calculation:

N = 750 rpm

Q = 4500 lit/min $= \frac{{4500}}{{60}} = 75\;l/s$

NS = 700

$\Rightarrow 700 = \frac{{750\; \times \;\sqrt {75} }}{{{{\left( H \right)}^{3/4}}}}$

$\Rightarrow {\left( H \right)^{3/4}} = \frac{{750\; \times \;\sqrt {75} }}{{700}} \Rightarrow H = 19\;m$

No. of impellers required $= \frac{{190}}{{19.}} = 9.74 \simeq 10\;Nos.$