Efficiency formulas for hydraulic systems

The efficiency formula is calculated as the ratio between the energy put into a hydraulic system and the energy obtained from it, i.e., the energy converted into useful work.

In hydraulic systems, efficiency is very high due to the physics involved. Because hydraulics is based on the incompressibility of its medium, it can achieve up to 90% efficiency. Pneumatic systems, which have to accept major compression losses, achieve only low efficiency.

Calculating energy losses in hydraulic systems using the efficiency formula

In theory, pressure in a hydraulic system is transmitted from the source to the consumer without losses. In practice, however, many interfering factors occur that reduce the usable energy in the system:

• Branches, bends and pipe constrictions
• Roughness on the inner wall
• Filters with high resistance
• Expansion
• Leakage

Bends and branches redirect the volumetric flow. In the process, part of the energy is converted into heat. The same happens with roughness on the inner walls of hydraulic lines. The required filters create high resistance to the volumetric flow. Weakened flexible hoses can also contribute to pressure loss. Finally, escaping hydraulic oil inevitably reduces the efficiency of the overall system, potentially to a complete standstill.

All energy losses except leakage are converted into heat. This causes a hydraulic system to heat up quickly. For large systems, appropriate cooling equipment is therefore required. Otherwise, the hydraulic oil would begin to boil and become enriched with compressible gases. This would disrupt the entire operation of the system.

Formulas for hydraulic efficiency

The symbol for efficiency is the Greek letter η (eta). The general formula is E(out) (useful energy) divided by E(in) (input energy).

Alternatively, power P can be used as the basis for calculating efficiency. The resulting value is always between 0 and 1. However, 1 is never reached, as there is no system that can achieve 100% efficiency.

Efficiency formula for the overall system or individual components

The overall efficiency of a pump is the volumetric efficiency multiplied by the hydromechanical efficiency. There are also tables for pumps and motors that can be used as a design basis for efficiency. Typical values are: