Problem 4.9.3

It is required to supply water to a location that is 350 feet high through a pipe having a length of 9400 feet at a flow rate of 5835 gallons per minute. Pipe is 2.5 feet in diameter. Fanning friction factor is 0.0055. The pump impeller is rotating at 1700 rpm. What is the specific speed of the pump or pumps for the following cases: (1) Single pump, (2) Two pumps in series, and (3) Two pumps in parallel ?

Solution:

Skin friction losses are found to be 9 foot pound-force per pound-mass. Head that needs to be provided is delta Z plus h_f or 359 foot pound-force per pound-mass. Specific speed is given by N times Q^0.5 over H^0.75.

For single pump, N_s is found as 1700 times 5835^0.5 over 359^0.75 or 1575 rpm.

For pumps in series, Q is 5835 gpm, but H is reduced to one half or 179.5, thus specific speed is 2648 rpm.

For pumps in parallel, Q is reduced to one half or 2918 gpm, but H remains the same as 359, thus specific speed is 1113 rpm.