It requires 151 HP to operate a centrifugal pump having a 14.75 inch impeller at 1800 RPM, at a capacity of 2250 GPM with a 218 foot head. If during an overhaul of the pump, the impeller diameter is reduced to 14 inches, the horsepower requirement to operate the pump at the same RPM would be __________.
ā¢ Pump affinity laws for changes in impeller diameter at constant RPM ā¢ How horsepower relates to changes in impeller diameter when speed is unchanged ā¢ The ratio of new diameter to old diameter and how exponents affect power
ā¢ First, write the ratio of new impeller diameter to old impeller diameter, then think about how that ratio affects power according to the pump laws. ā¢ Ask yourself: at the same RPM, which variables change with the first power, which with the square, and which with the cube of the diameter? ā¢ Once you apply the correct exponent to the diameter ratio, multiply this factor by the original 151 HP to estimate the new required horsepower and compare that to the answer choices.
ā¢ Be sure you are using the pump law that relates power (HP) to impeller diameter, not the ones for flow or head. ā¢ Double-check your diameter ratio: use 14 / 14.75, and carry enough decimal places before applying the exponent. ā¢ After calculating, confirm that the new horsepower is less than 151 HP, since the impeller is smaller, and see which option is closest to your computed value.
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