In this article we'll dive into hydraulic motor calculations and the important topic of efficiency. Many hydraulic calculators ignore efficiency altogether and merely calculate theoretical values with 100% efficiency. Manufacturers typically don't get too deep into efficiency either.

First we'll present the equations for various parameters of a hydraulic motor in both SI and US units.

## Motor Equations - SI

## Motor Equations - US

## Hydraulic Motor Efficiencies

There are three types of efficiency associated with a hydraulic motor.

- Volumetric efficiency.
- Mechanical/hydraulic efficiency.
- Total efficiency.

Volumetric efficiency accounts for the leakage of fluid through the motor that doesn't do any work. Mechanical/hydraulic efficiency accounts for friction losses. Total efficiency is volumetric efficiency X mechanical/hydraulic efficiency.

Depending on what you're calculating, one of these efficiencies will be important. For flow rate and speed, volumetric efficiency is important. For displacement, pressure drop, and torque, mechanical efficiency is important. Finally, for output power, total efficiency is important.

A hydraulic motor has two input variables: pressure and flow. We'll look at the cases of constant pressure drop and constant flow rate to illustrate the efficiencies.

### Constant Pressure Drop

Consider the motor data below for a constant pressure drop. The theoretical values for pressure drop, speed and torque where calculated using the hydraulic motor equations using 100% efficiencies.

If we plot the flow rate vs. speed for the actual and theoretical data, there is an offset. In other words, for a given flow rate, the actual speed is less than the theoretical speed. This difference is due to volumetric efficiency.

## Constant Flow Rate

Data for the case of constant flow rate is shown below. Again, the theoretical values are calculated assuming 100% efficiencies.

If we plot the pressure drop vs. output torque for the actual and theoretical data, there is an offset. In other words, for a given pressure drop, the actual torque is less than the theoretical torque. This difference is due to mechanical/hydraulic efficiency.

## Finding Efficiency In Between Data Points

Often manufacturer's performance data is in tabular form for specific flow rates and pressure drops. If the operating point is somewhere in between the data points, interpolation is necessary to determine efficiencies.

As an example, let's say a motor has a pressure drop of 1750 psi and a flow rate of 17.5 GPM. The motor performance data only covers pressure drops of 1500 and 2000 psi, and flow rates of 15 and 20 GPM. We've already calculated efficiencies for the 2000 psi pressure drop above. If we calculate for 1500 psi drop, we can plot efficiencies together and interpolate.

To keep it simple, we'll only look at mechanical/hydraulic efficiency, but the others are similar.

If we enter the chart at 17.5 GPM on the x-axis and go to the midpoint between the curves, we can get mechanical/hydraulic efficiency on the y-axis. In this case, efficiency is 87%.

If we have a constant flow rate condition, we can follow a similar procedure except we would plot Δ pressure vs. mechanical/hydraulic efficiency.