Hydraulic pumps are the heart of a hydraulic system. In this article we'll present the equations for hydraulic pump calculations and explore efficiencies.

We'll start with the equations in SI and US units.

## Pump Equations - SI

## Pump Equations - US

## Hydraulic Pump Efficiencies

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

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

Volumetric efficiency accounts for the leakage of fluid in the pump 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 rise, and torque, mechanical efficiency is important. Finally, for input power, total efficiency is important.

We'll look at the cases of constant pressure rise and constant speed to illustrate the efficiencies.

### Constant Pressure Rise

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

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

## Constant Speed

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

If we plot the pressure rise vs. input torque for the actual and theoretical data, there is an offset. In other words, for a given pressure rise, the actual torque is greater 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 or chart form for a discrete number of operating conditions. If the operating point is somewhere in between the data points, interpolation is necessary to determine efficiencies.

As an example, let's say a pump is operated at 2000 RPM and has a pressure rise of 125 bar. The pump performance data only covers pressure rise of 100 and 150 bar. We've already calculated efficiencies for the 100 bar pressure rise above. If we calculate for 150 bar rise, we can plot efficiencies together and interpolate.

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

If we enter the chart at 2000 RPM on the x-axis and go to the midpoint between the curves, we can get the total efficiency on the y-axis. In this case, efficiency is 87.4%.

If we have a constant pressure rise condition, we can follow a similar procedure except we would plot Δ pressure vs. total efficiency.