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Hydraulic Fluid - Properties

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/ft3) or (lbf- sec2 / in4)

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 dvx. Shear stress occurs between the fluid layers and is given by

(psi)     (2)

μ is the proportional constant called dynamic viscosity, with units lbf-sec/in2 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

(in2/sec)     (3)

Density – The density, ρ, of a fluid is the mass per unit volume

(lbm/ft3) or (lbf - sec2 / in4)     (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 liquid-air mixtures, an empirical formula for the effective bulk modulus, β’, is

    (8)

where

βisen isentropic bulk modulus of the fluid w/o entrained air

VG0 volume of gas entrained in the liquid at atmospheric pressure

VL0 volume of the liquid at atmospheric pressure

p0 atmospheric pressure

p fluid pressure

k isentropic exponent (normally, k=1.4)

rv 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)

βp 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

do outer pipe diameter

di inner pipe diameter

ν Poisson’s number (0.3 for steel)

S pipe wall thickness


Fluid Properties Example: For a steel pipe with βisen = 200000 psi, 0.5” O.D., S = 0.012”, compute the effects of mechanical compliance on bulk modulus.

μp = 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)

βl bulk modulus of the hydraulic fluid

βMC bulk modulus for mechanical compliance

βg bulk modulus of air

Vg volume of air in the fluid

Vtotal total volume of fluid and air



Note the effective bulk modulus will be less than any of the individual bulk modulus (βl, βMC or Vtβg/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


Mil-Prf-5606


-54 oC

-40 oC

40 oC

100 oC

Viscosity (centistokes)

2500

600

13.2

4.9

Bulk Modulus at 40 oC and 4000 psi: 200,000 psi (minimum)

Specific Gravitity at 60 oF Approx 0.88*

Nominal Density: 50 lbm/ft3

Pour Point: ≤ -60 oC

Flash Point: 82 oC

Coefficient of Thermal Expansion: 8.6E-04 cm3/ (cm3 oC)

* Not specified in MIL-PRF-5606



Mil-Prf-87257


-40 oC

40 oC

100 oC

Viscosity (centistokes)

550 max

6.7 min

2.0 min

Bulk Modulus at 40 oC and 4000 psi: 200,000 psi (minimum)

Specific Gravitity at 60 oF Approx 0.88*

Nominal Density: 49 lbm/ft3

Pour Point: ≤ -60 oC

Flash Point: 160 oC minimum

Coefficient of Thermal Expansion: 8.2E-04 cm3/ (cm3 oC)

* Not specified in MIL-PRF-87257



Mil-Prf-83282


-40 oC

40 oC

105 oC

205 oC

Viscosity (centistokes)

2200

14

3.45

1.0

Bulk Modulus at 60 oC and up to 10000 psi: 200,000 psi (minimum)

Specific Gravitity at 60 oF Approx 0.85*

Nominal Density: 49 lbm/ft3

Pour Point: ≤ -55 oC

Flash Point: 205 oC

Coefficient of Thermal Expansion: 8.2E-04 cm3/ (cm3 oC)



AS1241 Type V (Phosphate Ester)


-54 oC

38 oC

99 oC

Viscosity (centistokes)

2600 (max)

9-12.5

3-4

Bulk Modulus at 40 oC and 4000 psi: 200,000 psi

Density at 25 oC 0.97 – 1.02 g/mL

Nominal Density: 63 lbm/ft3

Pour Point: ≤ -62 oC

Flash Point: 149 oC

Coefficient of Thermal Expansion: 1.0E-03 in3/ (in3 oF)