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How to Calculate Pump Horsepower

While pumps are highly variable in their complexity, their basic function and effectiveness is measured in terms of power. Technical […]

While pumps are highly variable in their complexity, their basic function and effectiveness is measured in terms of power. Technical applications use watts or kilowatts as their unit of measure, but popular culture dictates that mechanical output also be calculated in terms of horsepower.

What follows is a basic breakdown of that horsepower calculation for centrifugal pumps, as well as an interactive tool that allows you to see the interplay between different variables and horsepower.

Pump Horsepower Calculator










Horsepower: {{calculation.findHorsePower | number : 1}} HP


$$ HP = { Head^{ft} * Capacity^{GPM} * Specific Gravity  \over 3960 } $$

{{calculation.findHorsePower | number : 1}} HP = ( {{calculation.head}} ft * {{calculation.capacity}} gpm * {{calculation.specgrav}} ) /3960

Definitions:

First, we must define the different variables that and constants that we’ll use in our calculation.

Head:
The vertical distance traveled by the liquid through the system. For the sake of simple calculations we are discounting friction loss from the pipe.

Capacity:
The rate of flow through the system in gallons per minute

Specific Gravity:
The relative specific gravity of the liquid in the system. Water has a Specific Gravity value of 1.

8.33 Lbs/Gallon:
The constant weight of one gallon of water. Inter-played with a specific gravity value, this constant provides the basis for work accomplished

33,000 lb-ft/minute:
One (1) horsepower is defined as displaying 1 lb a distance of 33,000 ft in one minute.

Calculation:

Once these variables are defined, it’s as simple as applying them to the calculation of power and cancelling out units of measure until we arrive at our desired Horsepower output.

At its most basic, work is a product of force and displacement:

$$ Work = Force * Displacement $$

And Power is a calculation of work over time;

$$ Power = {Work \over Time}  $$ which is the same as $$ Power  = { Force * Displacement \over Time } $$

We can plug our pre-defined variables into this equation with the following substitutes.

Power in horsepower is 33,000 lb-ft/minute

Force is the product of our capacity, constant weight (8.33 lbs / gallon), and specific gravity.

Displacement is simply our head (ft.) distance.

And time is in minutes.

$$ 33,000 ^{lb-ft. \over min.} = { Head * Capacity * 8.333 * Specific Gravity  \over minutes } $$

Once these variables are in place, we can divide both sides by the constant 33,000 lb-ft/minute and further simplify the constants on the right-hand side. $$ {8.3333 \over 33,000} = { 1 \over 3960} $$

This gives us our final horsepower equation of:

$$ HP = { Head * Capacity * Specific Gravity  \over 3960 } $$

Use the tool to see how changes to these variables effect the overall horsepower output.

Look for future blogs, where we’ll take this calculation a step further and see how we can calculate the efficiency of a pump based on the relationship between input and output horsepower.

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