Calculating Horsepower for Water Pump

What is the horsepower of a pump that moves 520 lbs of water against a discharge head of 500 feet?

Final answer:

The horsepower required for a pump can be calculated using the joint variation formula, considering the weight of water and the discharge head length. The constant of variation is found from the information given for an 8.8 HP pump. Using that constant, the horsepower for a new scenario can be determined.

Explanation:

The horsepower of a water pump is said to vary jointly with the weight of the water moved and the length of the discharge head. This relationship is represented by the formula HP = k × w × d, where HP is the horsepower, w is the weight of the water, d is the discharge head, and k is the constant of variation.

From the given information, an 8.8 horsepower pump moves 441 lbs of water against a discharge head of 400 feet. We can calculate the constant k using this information:

k = HP / (w × d) = 8.8 / (441 × 400)

To find the horsepower of a pump that moves 520 lbs of water against a discharge head of 500 feet, use the formula with the previously calculated k:

HP = k × 520 × 500

Simply plug in the value of k, and calculate the horsepower required for the new conditions.