For discharge Q, the specific speed of a pump is N. For double the discharge with the same head, the specific speed will be

Explanation:

Specific speed: For a centrifugal pump, specific speed is defined as the speed of a geometrically similar pump that would deliver one cubic metre of liquid per second against a head of one metre.

It is given as

\({N_{S}} = \frac{{n\sqrt Q }}{{H^{3/4}}}\)

Where, n = Speed in rpm; Q = Discharge; H = Head

Calculation:

Case 1

\({N_{S1}} =N= \frac{{n\sqrt {Q} }}{{H^{3/4}}}\)

Case 2 

\({N_{S2}} = \frac{{n\sqrt {2\times Q} }}{{H^{3/4}}} = {\sqrt{2}\ N }\)