Fluids, either liquids or gases, are bodies without shape. Fluids experience great changes in shape under applied forces unless constrained in some manner. The behavior of fluids is characterized by the fluid properties listed below.
Fluid Pressure – Normal tension on the surface element of a fluid
(psi) (1)
Fluid Density – Fluid mass per unit volume. Density is a function of both pressure and temperature.
(lbm/ft^{3}) or (lbf sec^{2} / in^{4})
Viscosity  During the movement of fluid, there is a tangential force that resists movement, called viscosity.
Referring to the above figure, suppose 2 fluid layers are moving at a distance apart of dy, at a relative velocity of dv_{x}. Shear stress occurs between the fluid layers and is given by
(psi) (2)
μ is the proportional constant called dynamic viscosity, with units lb_{f}sec/in^{2} called reyn. μ is also called absolute viscosity or the coefficient of viscosity. μ varies significantly with the type of fluid and fluid temperature. μ also varies with pressure but the effects are smaller.
Kinematic Viscosity  The ratio of coefficient of dynamic viscosity to fluid density is called the coefficient of kinematic viscosity
(in^{2}/sec) (3)
Density – The density, ρ, of a fluid is the mass per unit volume
(lbm/ft^{3}) or (lbf  sec^{2} / in^{4}) (4)
Density is a function of both pressure and temperature
Bulk Modulus  Expanding the above equation for density in a Taylor Series (for 2 variables)
(5)
Mass density increases as pressure increases and decreases as temperature increases as the sign of is positive and the sign of is negative.
Assuming constant temperature so that = 0, then equation (5) becomes
(6)
The quantity
(psi) (7)
is the change in pressure divided by a fractional change in volume at constant temperature. The minus sign indicates a volume decrease with pressure increase. is called the isothermal bulk modulus (or simply bulk modulus) since it was derived assuming constant fluid temperature. The bulk modulus represents fluid compressibility and has a significant effect on the performance of hydraulic systems. Effects of pressure on bulk modulus are large and effects of temperature are usually negligible.
Effective Bulk Modulus  Both entrained air in the fluid or mechanical compliance of tubing/hoses can substantially lower the bulk modulus. Effects of both are additive.
Effects of Entrained Air:
For liquidair mixtures, an empirical formula for the effective bulk modulus, β’, is
(8)
where
β_{isen} isentropic bulk modulus of the fluid w/o entrained air
V_{G0} volume of gas entrained in the liquid at atmospheric pressure
V_{L0} volume of the liquid at atmospheric pressure
p_{0} atmospheric pressure
p fluid pressure
k isentropic exponent (normally, k=1.4)
r_{v} air to liquid volume ratio
Using equation (8), the effects of entrained air are shown in Figure 1 below.
Figure 1 Effects of Entrained Air on Bulk Modulus
Effects of Mechanical Compliance:
For cylindrical pipelines, the effective bulk modulus, β’, can computed using
(9)
β_{p} is the bulk modulus of the pipeline (available in Materials or Engineering Handbooks) and w is given by
for (thick walls) (10)
for (thin walls) (11)
where
d_{o} outer pipe diameter
d_{i} inner pipe diameter
ν Poisson’s number (0.3 for steel)
S pipe wall thickness
Fluid Properties Example: For a steel pipe with β_{isen} = 200000 psi, 0.5” O.D., S = 0.012”, compute the effects of mechanical compliance on bulk modulus.
μ_{p} = ratio of normal stress (on all faces of a cube) to a change in volume
∴ thin walled
Using equation (9)
In this example, the effects of thin walled pipe reduce bulk modulus by 25%.
Combined Effects of Air and Mechanical Compliance:
Effects of entrained air and mechanical compliance combine together like springs in series, i.e.,
(12)
where
β’ effective bulk modulus (psi)
β_{l} bulk modulus of the hydraulic fluid
β_{MC} bulk modulus for mechanical compliance
β_{g} bulk modulus of air
V_{g} volume of air in the fluid
V_{total} total volume of fluid and air
Note the effective bulk modulus will be less than any of the individual bulk modulus (β_{l}, β_{MC} or V_{t}β_{g}/Vg). For air, the bulk modulus is computed using
Basic Effects of Fluid Properties
The effects of temperature and pressure on hydraulic system fluid properties and flow characteristics are listed below.
Density – Effects orifice and valve volume flow rates. As density increases, orifice and valve flow rates will decrease (see orifice flow equations).
Increasing pressure increases density
Increasing temperature decreases density
Kinematic Viscosity – Effects pipe (tube) volumetric flow rate. As viscosity increases, pipe flow rate will decrease (see orifice flow equations). Kinematic viscosity increases with increased pressure and decreasing temperature.
Increasing pressure increases kinematic viscosity
Increasing temperature decreases kinematic viscosity
Bulk Modulus – Effects compressibility of fluid and system response time (see pressure derivative equation). As bulk modulus decreases, the pressure derivative will decrease leading to slower response times. Compressibility will affect the performance of actuators, motors and pumps because the stiffness of the fluid is less as bulk modulus is reduced.
Increasing pressure increases bulk modulus
Increasing temperature decreases bulk modulus
Entrained air and compliance of hoses/tubes/parts decreases bulk modulus
Fluid Properties for Standard Hydraulic Fluids
MilPrf5606

54 ^{o}C 
40 ^{o}C 
40 ^{o}C 
100 ^{o}C 
Viscosity (centistokes) 
2500 
600 
13.2 
4.9 
Bulk Modulus at 40 ^{o}C and 4000 psi: 200,000 psi (minimum)
Specific Gravitity at 60 ^{o}F Approx 0.88*
Nominal Density: 50 lb_{m}/ft^{3}
Pour Point: ≤ 60 ^{o}C
Flash Point: 82 ^{o}C
Coefficient of Thermal Expansion: 8.6E04 cm^{3}/ (cm^{3} ^{o}C)
* Not specified in MILPRF5606
MilPrf87257

40 ^{o}C 
40 ^{o}C 
100 ^{o}C 
Viscosity (centistokes) 
550 max 
6.7 min 
2.0 min 
Bulk Modulus at 40 ^{o}C and 4000 psi: 200,000 psi (minimum)
Specific Gravitity at 60 ^{o}F Approx 0.88*
Nominal Density: 49 lb_{m}/ft^{3}
Flash Point: 160 ^{o}C minimum
Coefficient of Thermal Expansion: 8.2E04 cm^{3}/ (cm^{3} ^{o}C)
* Not specified in MILPRF87257
MilPrf83282

40 ^{o}C 
40 ^{o}C 
105 ^{o}C 
205 ^{o}C 
Viscosity (centistokes) 
2200 
14 
3.45 
1.0 
Bulk Modulus at 60 ^{o}C and up to 10000 psi: 200,000 psi (minimum)
Specific Gravitity at 60 ^{o}F Approx 0.85*
Nominal Density: 49 lb_{m}/ft^{3}
Pour Point: ≤ 55 ^{o}C
Flash Point: 205 ^{o}C
Coefficient of Thermal Expansion: 8.2E04 cm^{3}/ (cm^{3} ^{o}C)
AS1241 Type V (Phosphate Ester)

54 ^{o}C 
38 ^{o}C 
99 ^{o}C 
Viscosity (centistokes) 
2600 (max) 
912.5 
34 
Bulk Modulus at 40 ^{o}C and 4000 psi: 200,000 psi
Density at 25 ^{o}C 0.97 – 1.02 g/mL
Nominal Density: 63 lb_{m}/ft^{3}
Pour Point: ≤ 62 ^{o}C
Flash Point: 149 ^{o}C
Coefficient of Thermal Expansion: 1.0E03 in^{3}/ (in^{3} ^{o}F)