PROPERTIES OF FLUIDS AND THEIR UNITS
2.1 BASIC PROPERTIES OF FLUIDS
PROPERTIES OF FLUIDS AND THEIR UNITS
2.1 BASIC PROPERTIES OF FLUIDS
A fluid is defined as a substance that cannot sustain a shearing stress. A fluid can be liquid or gaseous. The science of fluid power is concerned with the utilization of pressurized liquid or gas to transmit power, but we will be dealing exclusively with hydraulic fluids (i.e., liquids). Many textbooks have units of measurement in the U.S. Customary system based upon the former British (or Imperial) system. The use of the more recently defined S.I. system is becoming more common in U.S. industry and for this reason practicing engineers will have to be familiar with both U.S. basic and S.I.
In many fluid power applications the inch is used as the basic unit of length. Later in this section the use of problems that may occur with the use of mass in the U.S. Customary form of units will be discussed. Knowledge of the individual characteristics of hydraulic fluids is essential and this section deals with their fundamental properties.
Oil density:
This is defined as mass per unit volume. For petroleum based hydraulic fluids the approximate value is ρ = 850 kg/m3. It should be observed that a dynamic analysis that uses lbf/in.2as a pressure unit must be consistent and use mass in lbf· s2/in. Accelerations will be in in./s2. Unfortunately there is no special name for a mass unit in the pound force, inch, second system. A mass unit in the pound force, foot, second system7 systems of units (see Table 2.1).
these units will be demonstrated (see Table 2.2) and some of the special
8 PROPERTIES OF FLUIDS
Figure 2.1
: Definition of absolute viscosity.is the slug where 1 slug = 1 lbf· s2/ft. Some authors use weight per unit volume, then the term Specific Weight should be used.
Specific gravity:
This is the ratio of the mass of a substance divided by the mass of an equal volume of water at some specified temperature, usually 20◦C. The unit is therefore dimensionless and varies between 0.8 for some petroleum based fluids to as high as 1.5 for the chlorinated hydrocarbons.Absolute viscosity:
This is a measure of the resistance to motion offered by a fluid caused by the generation of shear stress over a wetted area (Figure 2.1). The resistance is therefore proportional to the wetted area and to the velocity and inversely proportional to the film thickness.Fv A = µv
` or:
µ = Fv
A(v/`) =τ
˙γ (2.1)
For a piston concentrically located in a circular cylinder with oil in the clearance space, `1, the area A is given by A = πd`2 and the force Fv is given by:
Fv= πd`2µv
`1
(2.2)
Table 2.1
: Conversion between U.S. Customary and SI unitsBasic US Customary Unit S.I. to
to S.I. Basic U.S. Customary
1 in. = 25.40 mm Length 1 m =39.37 in.
1 ft = 0.3048 m 1 m = 3.281 ft
1 lbf= 4.448 N Force 1 N = 0.2248 lbf
1 slug = 14.594 kg Mass 1 kg = 0.0685 slug 1 lbf· s2/in. = 175.128 kg 1 kg = 0.00571 lbf· s2/in.
1 slug/ft3= Density 1 kg/m3=
515.4 kg/m3 1.94E−3 slug/ft3
1 lbf· s2/in4. = 1 kg/m3=
10.69E+6 kg/m3 93.57E−9 lbf· s2/in4. 1 K = 5(◦F − 32)/9 Temperature ◦F = 32 + 1.8(K − 273.2)
◦R = ◦F + 460 K = ◦C + 273.2
1 lbf· s/in.2= 1 reyn Absolute 1 MPa · s = 145 lbf· s/in.2 (= 68.97E+4 Poise) Viscosity (= 10E+7 Poise) 1 psi = 6.985 kPa Pressure 1 MPa = 145.0 lbf/in.2 1 ksi = 6.985 Mpa (or Stress) 1 MN/m2= 145.0 psi 1 lbfft = 1.356 N · m Torque 1 N · m = 0.7376 lbf· ft 1 ft · lbf = 1.356 J Work or 1 J = 0.7376 ft · lbf
1 Btu = 1054 J Energy 1 J = 0.968E−3 Btu
1 hp = 745.7 W Power 1 kW = 1.341 hp
The quantity µ is termed the coefficient of absolute viscosity. Conver-sion between various sets of units can be confusing. Noting that absolute viscosity has the fundamental dimensions F.T/L2, which is equivalent to M/L.T, will allow conversions to be made on a rational basis. Often we measure absolute viscosity in lbf· s/in.2units (called the reyn). Sometimes units using centimeter, gram and second are used (the cgs system), then the unit is called the Poise for viscosity. Thus 1 centipoise = 1 cP = 1.0E−2 Poise = 1 mPa · s = 1.45E−7 reyn.
The relationship between absolute viscosity and temperature is very non linear. This is shown in Figure 2.2 where the abscissa values are
ab-10 PROPERTIES OF FLUIDS solute temperature values divided by a room temperature of 68◦F (20◦C) also converted to absolute. The ordinate values are the absolute viscos-ity normalized with respect to the absolute viscosviscos-ity at room temperature.
Probably the most important feature of Figure 2.2 is that it shows that fluid power actuators and controls on offroad equipment initially operat-ing at very low temperatures will operate erratically or very slowly until the oil temperature has risen to a higher value. The graph also shows that calculations that assume turbulent flow and viscosity independence are likely to be quite accurate at normal operating temperatures between 68 and 95◦F (20 and 35◦C).
Oil refiners use the term viscosity index to describe the degree of the change in viscosity with temperature. The viscosity index is discussed in more depth in [1].
Kinematic viscosity:
This is the ratio of viscosity to the mass den-sity. Thus:ν = µ
ρ (2.3)
In the cgs system the unit is the Stoke, but the centistoke (1/100 of a Stoke) is a more convenient size. Kinematic viscosity is difficult to measure directly, so an indirect (empirical) measurement is used. The flow of a known quantity of liquid through a given sized orifice under gravity is timed.
0 200 400 600 800 1000 1200 1400 1600
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
NORMALIZED TEMPERATURE
NORMALIZED ABSOLUTE VISCOSITY
Figure 2.2
: Change of absolute viscosity with temperature, 1 is room temperature.Because of the known variation of viscosity with temperature, the apparatus is usually contained in a water bath so this characteristic can be controlled.
The best known unit in the U.S. is the Saybolt second (SSU) and we may write [2]:
ν = 0.216 SSU − 166
SSU centistokes (cS) (2.4) Because density changes much less rapidly with temperature than does absolute viscosity, the relation between kinematic viscosity and temperature The American Society for Testing Materials has determined that certain logarithmic transformations will allow most common hydrocarbon fluids to be displayed as straight lines on specialized kinematic viscosity vs. tem-perature charts over temtem-perature ranges that will be met in practice. Such information is presented in ASTM Standard D341 [3].
2.1.1 Example: Conversion Between Viscosity Units
Consider a petroleum based fluid with a viscosity of 14.3 cS and a density of 0.84 g/cm3 at 38◦C. Determine the absolute viscosity of this oil in inch pound force units. The centistoke is a cgs unit so we can write:
ν = 14.3 cS = 143E−3 cm2 s The kinematic viscosity in inch units is given by:
ν = 143E−3((1/2.54)2in.2/cm2)cm2 s
= 22.17E−3 in.2 s
We now need to find the density in inch units. Start with the standard mass unit the pound mass. This has the conversion between pound mass and the gram of:
1 lbm= 453.59 g so the first step in calculating density is:
ρ = 0.84 ((1/453.59) lbm/g)g ((1/2.54)3in.3/cm3)cm3
= 0.03041 lbm
in.3 closely resembles that shown inFigure 2.2.
12 PROPERTIES OF FLUIDS Next we need to convert from pound mass to the mass unit consistent with a force in lbf and an acceleration of 1 in./s2. This conversion is:
1 lbf· s2
in. = 1 × 32.174 × 12 = 386.09 lbm
Hence density in compatible inch units is:
ρ = 0.03041 lbm
in.3 ×1 lbf· s2/in.
386.088 lbm
= 78.76E−6 lbf· s2 in.4
The absolute viscosity may now be calculated in U.S. Customary inch units:
µ = ρν = 78.76E−6 lbf· s2
in.4 × 2.217E−02in.2 s
= 1.746E−06 lbf· s
in.2 = 1.746 µreyn