that
we have
Due to the effect of the fluid compressibility, the volumetric flow rate at the pump outlet is lower than the volumetric flow rate at the inlet by 0.56%.
Case (b)
In this case, a certain amount of dissolved air is present at the pump inlet, being p1 < pT = pSAT. The amount of air at the inlet port 1 can be evaluated as
where psat = pT, considering the process as isothermal (γ = 1):
Therefore, the density of the fluid at the inlet section is
In the above expression, it is considered that the density of the air at standard conditions is ρg = 1.225 kg/m3.
The density at the pump outlet can be calculated considering that at high pressure (p2 = 100 bar) all the fluid is liquid:
Therefore, from the expression
we have
It is therefore possible to observe how, in this (gaseous) cavitation condition, the reduction in outlet flow is about 4.3%, much more pronounced with respect to the case (a), where there was no cavitation.
A final remark can be made on the evaluation of the equivalent (or effective) bulk modulus. For the typical operating pressure of hydraulic control systems, the elasticity of the material is also not negligible. Consider again the case of Figure 2.12 while also including the elasticity of the walls according to the bulk modulus of the material (similar to the Young modulus definition):
(2.33)
The equivalent bulk modulus for the system becomes
(2.34)
2.8 Contamination in Hydraulic Fluids
A hydraulic oil is subject to various forms of contamination:
Solid contamination. The solid contamination is the most common and intuitive form of contamination; it affects the operation and life of all hydraulic circuits. The solid contamination is due to the presence of undesired solid particles (metallic, plastic, fibers of different types, etc.) within the hydraulic fluid. These particles can accelerate the wear of the hydraulic components or produce the blockage of small flow connections (such as those of small hydraulic orifices). Solid contamination can cause malfunctioning of the hydraulic system and can also lead to the catastrophic failure of some components, like pumps and motors.
Liquid contamination. In general terms, liquid contamination refers to the presence of other liquids in the working fluid that can either be chemically aggressive to the hydraulic components or can deteriorate the properties of the hydraulic fluid. In the majority of the cases, the liquid contaminant is water. For example, water causes rusting in hydraulic components (which can be visible, for example, in the reservoir of the system), reduces the lubrication characteristics of the oil, and can cause unwanted reactions leading to the formation of alcohols, acids, or sludges. In addition, water has a higher vapor pressure values when compared with typical oils. Therefore, the presence of water can lead to instances of vapor cavitation that can cause instabilities and damages of the mechanical parts.
Gas contamination. Gas contamination usually refers the presence of undissolved or entrained air in the hydraulic oil. As mentioned before, this can lead to the premature wear of certain hydraulic components,
