by John Willis
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Most conversions from gallons per minute (GPM) to revolutions per minute (RPM) are pump related. For example, if you are designing a pump to recirculate a spa, you need to know the speed at which the pump should run, given the size of the pump cylinder. There are formulas to guide you through these conversions. The formulas use fixed and variable values; the values of the variables are usually estimates. The only way to fully adjust the estimates is to run a real-world test to correct for the variables.
If you think of a cylinder-driven pump, such as a car engine, you might think of the pump’s output as displacement times revolutions. In other words, if you have a pump with a 1-gallon cylinder, it should pump a gallon for every revolution, and you can extrapolate from there, it doesn’t. Hydrodynamics is not that efficient. Each revolution of the pump pumps a factor less than the total volume of the cylinder.
Conversion with an output test
In real-world applications, the output depends on the design of the cylinder, piston, inlet and outlet ports, what is 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. Run the pump at 1000 RPM, for example. Once 1000 RPM is reached, direct the fluid being pumped into a measuring container for one minute. This will give you the exact GPM measurement of your pump at 1,000 RPM. With this measurement, you can estimate the RPM of the pump if you know the amount of water being pumped every minute, although it is an estimate. Just because the pump moves “X” amount of water at 1000 RPM does not mean it will move “X” 10 times at 10,000 RPM.
Output variation with speed
If your pump moves 10 gallons per minute at 1,000 RPM, you can estimate that it will move 20 gallons at 2,000 RPM. Hydrodynamics conspires against the perfect scale of revolutions to volume or ratio of volume to revolutions. Here is an example. Imagine that you are pumping something very viscous, like oil. At low speeds, the effects of oil viscosity can have a negligible effect on your pumping efficiency, for example 500 RPM. At 5,000 RPM, viscosity can play a bigger role in pump efficiency. At a few higher RPMs, the viscosity can lock the liquid like sand – even though it is liquid, it becomes as dense as it can be, creating a limit on how fast the pump can pump it. These efficiency curves also apply to factors other than viscosity.
Understanding the limitations of conversion, you start with a set ration and scale your conversion up or down. Let’s say you measured your pump and you know that 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 output of the pump and find that it has pumped 2.3 gallons in one minute, you can estimate that its RPM is 2,300.