Fluids: Introduction
Fluids: Introduction
1. Stress vs. Strain (Shear and Normal)
2. No-slip condition
2. Differences between Solids and Fluids (reaction to shear)
3. Types of Flow
• Laminar vs. Turbulent
• Steady vs. Unsteady
• Internal vs. External
• Compressible vs. Incompressible
• Viscous vs. Inviscid
Shear stress = force acting tangent to the surface divided
by the area over it acts.
Shear strain = ratio (dimensionless)of the
displacement (angular displacement) to the transverse
dimension.
Shear stress is proportional to shear strain when the
forces is small enough, that Hooke’s law is obeyed.
layer
boundary
When a constant shear force is applied, a solid eventually stops deforming at some fixed strain angle.
When a constant shear force is applied, a solid eventually stops deforming at some fixed strain angle,
whereas a fluid never stops deforming and approaches a constant rate of strain.
The highly ordered fluid motion characterized by smooth layers of fluid is called
laminar.
separation point
on
a
The highly disordered fluid motion that typically occurs at high velocities and is characterized by
velocity fluctuations is called turbulent.
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Steady implies no change of properties, velocity, temperature, etc., at a point with time.
The term uniform implies no change with location over a specified region.
Conditions do not change with position in the stream or with time.
Conditions change from point to point in the stream but do not change with time.
At a given instant in time the conditions at every point are the same, but will change with time.
Every condition of the flow may change from point to point and with time at every point.
The volume of every portion of fluid remains unchanged over the course of its motion when the flow is
approximated as incompressible.
A pressure of 210 atm, for example, causes the density of liquid water at 1 atm to change by just 1 percent. Hence,
liquids are generally approximated as incompressible.
The fluid flow is an internal flow when it is completely bounded by
solid surfaces.
The fluid flow is an external flow when it is completely unbounded by
solid surfaces.
boundary layer
Flows in which the frictional effects are significant are called viscous flows.
There are regions (typically regions not close to solid surfaces) where viscous forces are negligibly small
compared to inertial or pressure forces. Such flow is called inviscid flow.
A fluid is defined as a sub- stance that deforms continuously when acted on by a shearing stress of any
magnitude. It includes the phases liquids, and gases.
Solid (shear stress is applied) Fluid (shear stress is applied)
Measures of Fluid Mass and Weight
A. Density (!)
B. Specific weight (#)
C. Specific gravity (SG)
D.Absolute Viscosity ($)
E. Dynamic Viscosity (%)
F. Surface Tension (&)
The density of a fluid, designated by the Greek symbol (rho), is defined as its mass per unit volume
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Question: Which is denser: 1 kg gold or a ring of gold?
Question: Which is denser: 1 kg gold or a ring of gold?
ANSWER: The same since density is an intensive physical property.
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Density and variation in pressure and temperature (Liquids)
The value of density can vary widely between different fluids, but for liquids, variations in pressure and
temperature generally have only a small effect on the value of !.
The specific weight of a fluid, designated by the Greek symbol " (gamma).
It is defined as its weight per unit volume.
Recall
p My
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v
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! = #$
The specific gravity of a fluid, designated as SG, is defined as the ratio of the density of the fluid to the density of water
at some specified temperature. Usually the specified temperature is taken as 4 °C (39.2 °F).
1
Relative density
"!"# = 700 − 950 )*/,$
fluid
#$ =
! Kmt
!!"# &' 4 ℃
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When SG > 1, ____________________________________________________________.
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When SG < 1 ____________________________________________________________.
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Derivation of the equation of viscosity and its physical implication on fluid flow
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Pay
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to
T Fluids which obey this
Mdf
are Newtonian fluids
fluid's viscosity
Example 1 Weight
8 0
A 40-lb, 0.8-ft-diameter, 1-ft-tall cylindrical tank slides slowly down a ramp with a constant speed of 0.1 ft/s as shown in
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the figure. The uniform-thickness oil layer on the ramp has a viscosity of 0.2 -. !. Determine the angle, /, of the ramp.
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W 40lb Ver
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Example 2 Ir Mangy
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A Newtonian Fluid having a specific gravity of 0.92 and a kinematic viscosity of 4 " 10!" %/' flows past a fixed surface.
Due to no slip condition, the velocity at the fixed surface is zero, and the velocity profile near the surface is shown in the
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figure. Determine the magnitude and direction of the shearing stress developed on the plate. Express your answer in terms
of (, *+, -, ./0ℎ ( *+, - expressed in units of meters per second and meters, respectively.
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Absolute viscosity/dynamic viscosity
Kinematic Viscosity
viscosity
absolute
dynamic
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The intensity of the molecular attraction per unit length along any line in
the surface is called the surface tension.
maximize volume
to I I minimized SA
What dictates how the fluid will behave on these cases at the boundary layer?
adhesion cohesion
adhesion cohesion adhesion cohesion
adhesion
cohesion 10te Etienne
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Capillary Action
Capillary action can be defined as the ascension of liquids through slim tube, cylinder or permeable substance
due to adhesive and cohesive forces interacting between the liquid and the surface.
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Capillary Action
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Example 2 Eg OH
Surface tension forces can be strong enough to allow a double-edge steel razor blade to “float” on water, but a single-edge
blade will sink. Assume that the surface tension forces act at an angle 2 relative to the water surface as shown in the figure.
0.00064kg
(a) The mass of the double-edge blade is 0.64 " 10!# kg, and the total length of its sides is 206 mm. Determine the value of
2 required to maintain equilibrium between the blade weight and the resultant surface tension force.
(b) The mass of the single-edge blade is 2.61 " 10!# kg, and the total length of its sides is 154 mm. Explain why this blade
sinks. Support your answer with the necessary calculations.
0.00261 kg M 0.6415kg
millimeter
Fx 1 206 10m
Fy F Ey
y 1103 m
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Recall
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My
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def
Bulk Modulus (!! ) ng
The behavior of a particular fluid on how easily its volume (and also density) can change when there is a change in pressure.
Evi
Ev t
if dp Pdp
apip I
Ipa
Bulk Modulus (!! )
The behavior of a particular fluid on how easily its volume (and also density) can change when there is a change in pressure.
When gases are compressed (or expanded), the relationship between pressure and density depends on the nature of the process.
A. Isothermal
Compression or expansion takes place under constant temperature conditions
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When gases are compressed (or expanded), the relationship between pressure and density depends on the nature of the process.
B. Isentropic U QtW
Compression or expansion is frictionless and no heat is exchanged with the surrounding. t
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Pti at constant p
saithheat
pie
p constant p It specific heat at constant V
R Cp Cr
Sample Problem: absolute pressure I gage pressure gauge
Oxygen at 30 degrees C and 300 kPa absolute pressure expands isothermally to an absolute pressure of 140
kPa. Determine the final density of the gas.
1 P
Given Ti 300C
I
constant
300C
Tf
II
300 103Pa
Pi 300kPa
Pf 140KPA 140 XPPa
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Pf
g pp
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D Pf
dimly laxity
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m3
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sound WAVE
Minion In TRANSVERSE WAVE
direction
G'TUDINAL
MECHANICAL WAVE
motion
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requires medium
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WAVE
pf
Another important consequence of the compressibility of fluids is that disturbances
introduced at some point in the fluid propagate at a finite velocity.
Lyde
The velocity at which these small disturbances propagate is called the acoustic velocity or the speed of sound, c.
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Eve
g
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df ftp.p
solid Liquid Gass PC E
I
fastest slowest
The velocity at which these small disturbances propagate is called the acoustic velocity or the speed of sound, c.
For gases undergoing isentropic process (no heat is exchanged and friction is negligible ):
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1
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p My
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The velocity at which these small disturbances propagate is called the acoustic velocity or the speed of sound, c.
For gases undergoing isentropic process (no heat is exchanged, and friction is negligible ):
The velocity at which these small disturbances propagate is called the acoustic velocity or the speed of sound, c.
What is Mach Number?
It is the ratio of the velocity of a fluid to the velocity of sound in that fluid.
What is Mach Number?
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Constant
v 344 mls
Problem:
An important dimensionless parameter concerned with very high speed flow is the Mach number, defined as V/c, where V is the
speed of the object, such as an airplane or projectile, and c is the speed of sound in the fluid surrounding the object. For a
projectile traveling at 800 mph through air at 50 F and standard atmospheric pressure, what is the value of the Mach number?
Vo 800mph Vsound C I ptfkRT standard atmosphericpressure ta
Ti
p
50 F
1 Atm
Mach No
usound fania 00 5,15017 32
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If the lid on a completely liquid-filled, closed container is raised
(without letting any air in), a pressure will develop in the space as a
result of the vapor that is formed by the escaping molecules.
When an equilibrium condition is reached so that the number of
molecules leaving the surface is equal to the number entering, the
vapor is said to be saturated and the pressure the vapor exerts on the
liquid surface is termed the vapor pressure, py.
