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)

H = head (in m)

**Calculation:**

N = 750 rpm

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

N_{S} = 700

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

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

Total Head = 190 m

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