# How many impellers are required for a multi-stage pump to lift 4000 lpm against a total head of 80 m at a speed of 750 rpm; given that Ns for each imp

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How many impellers are required for a multi-stage pump to lift 4000 lpm against a total head of 80 m at a speed of 750 rpm; given that Ns for each impeller should be between 720 to 780 units?
1. 6
2. 5
3. 4
4. 3

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Correct Answer - Option 2 : 5

The specific speed of a pump, Ns is given by

${N_s} = \;\frac{{N\sqrt Q }}{{{H^{3/4}}}}$

N is in rpm and Q is in lps and H is in m.

Or

$H = {\left( {\frac{{N\sqrt Q }}{{{N_s}}}} \right)^{\frac{4}{3}}}$

Now,

Putting N = 750 rpm, Q = 4000 lpm and Ns = 720 in above equation, we get H = 17.36 m

Putting N = 750 rpm, Q = 4000 lpm and Ns = 780 in above equation, we get H = 15.6 m

Average head for one impeller, Ha = (17.36 + 15.6) /2 = 16.48 m

No of impellers required will be = Total head/head per impeller = 80/16.48 = 4.85 i.e. 5 nos. of impeller required.