Problem 4.9.2

A pump can provide 45 feet head to water flowing at 345 cubic feet per second when operating at 225 rpm. Pump has a discharge diameter of 72 inches. It is desired to provide 60 feet head to water flow rate of 200 cubic feet per second when operating at similar efficiency. What impeller size and speed should be used?

Develop the characteristic curves based on the new impeller size and impeller speed if data points (Q,H) for prototype are (200,60), (345,45), and (459, 25).

Solution:

Pump similitude relationships are: (1) H over N² over D² and (2) Q over N over D³. Plugging in the values of H (45), and Q (345), N²D² is 3.4992 time 10⁸ and ND³ is 4.865 time 10⁷. N can be found to be 366.7 rpm. Nearest synchronous speed is given by 3600 over N_p= 360 rpm. Impeller outlet diameter, D₂, is N₁ over N₂ sqrt of H₂ over H₁ time D₁ or 51.96 inches or 52 inches. Q2 can be calculated to be N₂ over N₁ D₂³ over D₁³ time Q₁ or 208 cubic feet per second.

Equations for transforming a point on the characteristic curve of a prototype pump to the new pump are:

H_B = N₂²D₂² over N₁²D₁² H_A or 1.335 H_A.

Q_B=N₂D₂³ over N₁D₁³ Q_A or 0.603 Q_A.

Point 1: (200, 60) is transformed to (121, 80),

Point 2: (345, 45) is transformed to (208, 60)

And Point 3: (459, 25) is transformed to (277, 33).