A centrifugal pump discharges 300 gpm against a head of 55 ft when the speed is 1500 rpm. The diameter of the impeller is 15.5 in. and the brake horsepower is 6.0. (a) Determine the efficiency of the pump. (b) What should be the speed of a geometrically similar pump of 15 in. diameter running at a capacity of 400 gpm?

Answer: Question 1: Efficiency is 0.6944

Question 2: speed of similar pump is 2067rpm

Explanation:

Question 1:

Flow rate of pump 1 (Q1) = 300gpm

Flow rate of pump 2 (Q2) = 400gpm

Head of pump (H) = 55ft

Speed of pump1 (v1) = 1500rpm

Speed of pump2 (v2) = ?

Diameter of impeller in pump 1 = 15.5in = 0.3937m

Diameter of impeller in pump 2 = 15in = 0.381

B. H. P = 6.0

Assuming cold water, S. G = 1.0

eff = (H x Q x S. G) / 3960 x B. H. P

= (55x 300x 1) / 3960x 6

= 0.6944

Question 2:

Q = A x V. (1)

A1 x v1 = A2 x V2. (2)

Since A1 = A2 = A (since they are geometrically similar

A = Q1/V1 = Q2/V2. (3)

V1 (m/s) = r x 2π x N (rpm) / 60

= (0.3937x 2 x π x 1500) / 2x 60

= 30.925m/s

Using equation (3)

V2 = (400 x 30.925) / 300

= 41.2335m/s

To rpm:

N (rpm) = (60 x V (m/s)) / 2 x π x r

= (60 x 41.2335) / 2 * π * 0.1905

= 2067rpm.