# GPM to RPM Conversion

by John Willis
Zedcor Wholly Owned/PhotoObjects.net/Getty Images

Most gallon per minute (GPM) to revolutions per minute (RPM) conversions relate to pumps. For example, if you're designing a pump to recirculate a spa, you need to know the speed at which the pump must run, given the size of the pump's cylinder. There are formulas to guide you in these conversions. The formulas use fixed and variable values; the variable values are usually estimates. The only way to completely adjust for the estimates is to conduct a real-world test to fix the variables.

## Pump Displacement

If you think of a cylinder-driven pump -- just like a car engine -- you may think the output of the pump is the displacement times the revolutions. In other words, if you have a pump with a 1-gallon cylinder, it should pump one gallon for every revolution, and you can extrapolate from there -- not so. The hydrodynamics are not nearly so efficient. Each revolution of the pump pumps some factor less than the full volume of the cylinder.

## Conversion With an Output Test

In real-world applications, the output depends on the design of of the cylinder, piston, intake and outlet ports, what's being pumped, how hot or cold it is and other factors. The most accurate way to convert GPM to RPM is to do a test. Run the pump at 1,000 RPM, for example. Once 1,000 RPM is reached, direct the fluid being pumped into a measuring container for one minute. This will give you the accurate GPM measure of your pump at 1,000 RPM. With this measure, you can estimate the RPM of the pump if you know the amount of water being pumped every minute, thought it is an estimate. Just because the pump moves "X" amount of water at 1,000 RPM doesn't mean it will move 10 times "X" at 10,000 RPM.

## Output Variance With Speed

If your pump moves 10 gallons a minute at 1,000 RPM, you can estimate it will move 20 gallons at 2,000 RPM. Hydrodynamics conspires against the perfect scaling of revolutions to volume or volume to revolutions ratio. Here's one example. Imagine you're pumping something very viscous, such as oil. At low speeds, the effects of the oil's viscosity may have a negligible effect on its pumping efficiency -- 500 RPM, for example. At 5,000 RPM, the viscosity may play a bigger role in the pump efficiency. At some higher RPM, the viscosity may lock the liquid together like sand: Though it's liquid, it becomes as dense as it can be, effectively creating a limit to how fast the pump can pump it. Such efficiency curves apply to factors other than viscosity, too.

## Output Calculation

Understanding the limitations of the conversion, you start with one fixed ration and scale your conversion up or down. Let's say you measured your pump and know it pumps 100 gallons per minute at 1,000 RPM. The ratio is 1 gallon for every 10 RPM, or 1:10. Now if you measure the pump's output and find it has pumped 2.3 gallons in one minute, you can estimate its RPM is 2,300.