A pump that was designed for agricultural irrigation is to be scaled down for use in recirculation...

Question

A pump that was designed for agricultural irrigation is to be scaled down for use in recirculation of water in a small aquarium for pet fish. The irrigation pump supplies 600 gpm at 100 ft of head and is a well-designed pump, with an efficiency of 75% at 1200 rpm. The aquarium pump must deliver 6 gpm at 5 ft of head.   a. Find the proper speed and diameter for the aquarium pump.   b. Estimate the efficiency of the aquarium pump.   c. How do you expect the small pump to deviate from the simple scaling laws?

Dr Shweta · Accepted Answer

Answer
A) Proper speed and diameter of aquarium pump is calculated as below:
1. Speed of the aquarium pump:
n1V1 = n2V2 -----[1]
here, we have
 n1 = 1200 rpm, n2 =? [ rpm = revolutions per minute]
V1 = 600 gpm, V2 = 6gpm [gpm = gallons per minute]
On solving equation 1, we get;
1200 rpm * 600 gpm = n2 * 6 gpm
Or, n2 = 120000 rpm
2. Diameter of aquarium pump is calculated as:
Q2/Q1 = N2/N1 (D2/D1)3    -----[2]
here, we have 
Q1 = 600 gpm
Q2 = 6 gpm
N1 = 1200 rpm
N2 = 120000rpm
D1 = 100 ft
D2 =?
On solving equation 2, we get;

A pump that was designed for agricultural irrigation is to be scaled down for use in recirculation of water in a small aquarium for pet fish. The irrigation pump supplies 600 gpm at 100 ft of head and...

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