Page 27 - Fluid mechanics, heat transfer, and mass transfer

FLUID MECHANICS BASICS
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tension acting across an interface between a liquid & It is used in characterizing densities of petroleum oils
and a gas, or between two immiscible liquids. and other liquids.
& Mach number, M ¼ V/c ¼ fluid velocity/sonic veloc- & It provides a stretched scale for expressing densities
ity. Mach number is commonly used both with and is useful in easily distinguishing different oils.
objects traveling at high speed in a fluid and with & Sp. gr. in the above equation corresponds to 15.6 C

high-speed fluid flows inside channels such as noz- (60 F), referenced to that of water at the same

zles, diffusers, or wind tunnels. temperature.
The speed represented by Mach 1 is not a constant. . What is viscosity? What are its units?
For example, it depends on temperature and atmo-
& Viscosity is the measure of the internal friction of a
spheric composition. In the stratosphere, it remains
fluid. This friction becomes apparent when a layer of
constant irrespective of altitude even though the air
fluid is made to move in relation to another layer. The
pressure varies with altitude.
greater the friction, the greater the amount of force
Since the speed of sound increases as the temper-
required to cause this movement, which is called
ature increases, the actual speed of an object traveling
shear. Shearing occurs whenever the fluid is phys-
at Mach 1 will depend on the fluid temperature
ically moved or distributed, as in pouring, spreading,
around it. Mach number is useful because the fluid
spraying, mixing, and so on. Highly viscous fluids,
behaves in a similar way at the same Mach number.
p 2 therefore, require more force to move than less
& Knudsen number, Kn ¼ l/L ¼ k B T/ (2ps PL) ¼
viscous materials.
molecular mean free path length/representative phys-
& Consider two parallel planes of fluid of equal area,
ical length scale. Example of length scale could be the
separated by unit distance and moving in the same
radius of a body in a fluid. L is the representative
direction at different velocities. The force required to
physicallengthscale(m),k B istheBoltzmannconstant maintain this difference in velocity is proportional to
(1.38 10 23 J/K), T is the temperature (K), s is the
the difference in velocity through the liquid, called
particle diameter (m), and P is the total pressure (Pa).
2 velocity gradient.
& Fanning friction factor, f ¼ DDP/2rV L ! 2t w /
& Velocity gradient is a measure of the change in
2
rV ¼ wall shear stress/velocity head.
velocity at which the intermediate layers move with
2
& Drag coefficient, C D ¼ F D /(ArV /2) ¼ drag force/
respect to each other. It describes the shearing the
(projected area velocity head).
liquid experiences and is thus called shear rate. Its
3
& Flow number, N Q ¼ Q /(ND ), represents actual flow 1
0
unit of measure is called the reciprocal second (s ).
during mixing in a vessel. Q is the flow rate/pumping The force per unit area required to produce the
0
capacity, N is the speed of rotation of the impeller shearing action is called shear stress.
(rev/s), and D is the impeller diameter. & The defining equation for viscosity is called
3
5
& Power number, P o ¼ P/N D r ¼ ratio of energy
Newton’s equation, which is
causing local turbulence to that providing bulk flow.
t ¼ mðdu=dyÞ; ð1:2Þ
& Deborah number, D e ¼ t c /t p ¼ ratio of the relaxation
time,characterizingtheintrinsicfluidityofamaterial, where t is the shear stress, m is the viscosity, and
andthecharacteristictimescale ofanexperiment(ora du/dy is the shear rate, g.
computer simulation) probing the response of the & The equation for viscosity becomes
material. t c refers to the relaxation timescale and t p
m ¼ t=g; ð1:3Þ
refers to the timescale of observation. The smaller the
Deborah number, the more fluid the material appears.
which is the ratio of shear stress to shear rate. m is the
2
3
& Archimedes number, A r ¼ gL r L (r r L )/m , is used
absolute viscosity that is sometimes called shear
to determine the motion of fluids due to density viscosity, t is the shear stress, and g is the shear rate.
differences. It is useful in applications involving & Absolute (dynamic) viscosity is a measure of how
resistive the flow of a fluid is between two layers of
gravitational settling of particles in a fluid. r r L
is the density difference between the body and the
fluid in motion.
fluid and m is the viscosity of the fluid.
& Viscosity affects the magnitude of energy loss in a
flowing fluid.
& High-viscosity fluids require greater shearing forces
1.2 FLUID PROPERTIES
than low-viscosity fluids at a given shear rate.
. Define API gravity? Where is it used? What is its use?
Units of Viscosity: 1 poise is equal to 100 centipoise
& Degree API ¼ð141:5=sp:gr:Þ 131:5: ð1:1Þ (cP). SI units of viscosity are kg/(m s) or Pa s.