What is the efficiency of a pump system that pumps 100 gallons per minute of water at a pressure of 100 feet of water column using a 7.5-horsepower motor?

This question is woefully deficient of information needed to calculate pump efficiency. Nonetheless, we can examine different approaches to reaching a solution.

A quick way to estimate pumping efficiency is to confirm the pump is operating on its pump curve, read the efficiency of the pump at this operating condition from the pump curve, and then multiply it by an estimated motor efficiency. Note that the pump curve (if available) reflects a new pump, which may not be an accurate representation of an existing pump that may be worn.

The pump system efficiency is the ratio of the hydraulic energy produced to the electrical energy consumed. The hydraulic energy produced can be calculated as:

100 gpm x 100 feet x 1.00 specific gravity / 3960 = 2.53 horsepower

The electrical energy consumed at this operating condition can be measured with a portable instrument that measures the electrical energy consumed by the motor. The efficiency of the pump system can then be calculated.