In the horsepower formula provided, what is the purpose of the constant 33,000?

• A. The conversion constant to convert GPM and head to horsepower
• B. The density of water (lb/ft^3)
• C. The acceleration due to gravity
• D. A fudge factor

Answer: (A)

The question is about what the constant 33,000 represents in the horsepower formula. It sets the conversion from a hydraulic power rate expressed in ft-lb per minute to horsepower. One horsepower equals 33,000 ft-lb per minute, so when you multiply flow (GPM) by head (ft) and by the water’s weight per gallon, you get the work done per minute in ft-lb/min; dividing by 33,000 converts that rate into horsepower.

For example, using the common form HP = (GPM × head × SG) / 3960, note that 33,000 divided by 8.34 is about 3,960, which is why that divisor appears. If you plug in water (SG ≈ 1) and relate the constants, you’ll get the same result. So the constant is a unit-conversion factor, not a description of density or gravity or a arbitrary fudge factor.