Page 28 - Fluid mechanics, heat transfer, and mass transfer

NEWTONIAN AND NON-NEWTONIAN FLUIDS 5

. What is kinematic viscosity? Give its units. & An ideal gas obeys the equation
& Kinematic viscosity, n, is the ratio of viscosity to
2 PV ¼ nRT: ð1:4Þ
density, m/r. SI units of kinematic viscosity are m /s.
2
The cgs unit is Stoke, which is 1 cm /s. & For a nonideal gas,
& Kinematic viscosity is a measure of how resistive the
PV ¼ ZnRT or Z ¼ PV=nRT: ð1:5Þ
flow of a fluid is under the influence of gravity.
& Kinematic viscometers usually use the force of grav- & For example, a gas for which Z ¼ 0.90 will occupy
ity to cause the flow through a calibrated orifice, only 90% of the volume occupied by an ideal gas at
while timing the flow. the same temperature and pressure.
. How does viscosity (m) of a gas changewith temperature & The values of Z range from about 0.2 to a little over
and pressure? 1.0 for pressures and temperatures of up to 10 times
the critical values.
& Viscosity of gases increases as temperature increases
and is approximately proportional to the square root & Z is a complex function of reduced temperature (T r ),
of temperature. This is due to the increase in the reduced pressure (P r ), critical compressibility factor
frequency of intermolecular collisions at higher tem- (Z c ), acentric factor (v), or other parameters.
peratures. Since most of the time the molecules in a
gas are flying freely through the void, anything that 1.3 NEWTONIAN AND NON-NEWTONIAN FLUIDS
increases the number of times one molecule is in
contact with another will decrease the ability of the . What is rheology?
molecules as a whole to engage in the coordinated & Rheology is defined as the study of the change in
movement. The more these molecules collide with form and the flow of matter, embracing elasticity,
one another, the more disorganized their motion viscosity, and plasticity.
becomes. . What are the differences between Newtonian and non-
. What is SAE classification? Newtonian fluids?
& Society of Automotive Engineers (SAE) has devel- & Newtonian Fluids: In these fluids, viscosity is con-
oped a numbering system based on viscosities for stant regardless of the shear forces applied to the
application to lubricants. The SAE numbering layers of fluid. At constant temperature, the viscosity
scheme describes the behavior of motor oils under is constant with changes in shear rate or agitation.
low- and high-temperature conditions—conditions & These are unaffected by magnitude and kind of fluid
that correspond to starting and operating tempera- motion.
tures. The first number, which is always followed by & Examples of Newtonian fluids include water, milk,
the letter W, describes the low-temperature behavior
alcohol, aqueous solutions, hydrocarbons, and so on.
of the oil at start-up while the second number de-
& Fluids for which a plot of shear stress versus shear
scribes the high-temperature behavior of the oil after
rate at a given temperature is a straight line with a
the engine has been running for some time. Lower
constant slope, independent of the shear rate, are
SAE numbers describe oils that are meant to be used
called Newtonian fluids. This slope is called absolute
at lower temperatures. Oils with low SAE numbers
viscosity of the fluid, represented by the equation
are generally less viscous than oils with high SAE
m ¼ t/g, as given earlier.
numbers, which tend to be thicker.
Absolute viscosity is sometimes called shear viscos-
& SAE 0W, 5W, 10W, 15W, 20W, and 25W are grades
ity. When written as t ¼ m du/dy, the equation
of motor lubricating oils for low-temperature appli-
represents Newton’s law and the fluids that follow
cations. SAE numbers 20, 30, 40, 50, and 60 are
Newton’s law are Newtonian fluids.
indicative of high-temperature applications.
& All fluids for which viscosity varies with shear rate
& For example, 10W-40 oil would have a viscosity not
are called non-Newtonian fluids. For such fluids,
more than 7000 mPa s in a cold engine crankcase
viscosity, defined as the ratio of shear stress to shear

even if its temperature should drop to 25 Cona
rate, is called apparent viscosity to emphasize the
cold winter night and aviscosity not less than 2.9 mPa
distinction from Newtonian behavior. For such fluids,
s in the high-pressure parts of an engine very near the
apparent viscosity is given by
point of overheating (150 C).

t ¼ hg; ð1:6Þ
. Define compressibility factor and state its significance.
& Compressibility factor quantifies the departure from where t is the shear stress, h is the apparent viscosity,
ideal conditions for a gas. and g is the shear rate.