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Fluid MechanicsFluid Mechanics
4th SEMESTER
BS Mechanical Engineering(2009-2013)
4th SEMESTER
BS Mechanical Engineering(2009-2013)
Fluid MechanicsFluid Mechanics
It is the study of fluids either in motion or at rest and subsequent effect of fluids on the boundaries.
It is the study of fluids either in motion or at rest and subsequent effect of fluids on the boundaries.
Fluid Mechanics
Fluid StaticsStudy of Mechanics of Fluids at Rest
KinematicsDeals with Velocities and Streamlines
Fluid DynamicsStudy of Fluids in Motion Considering Forces
Dimensions of mechanics are PRIMARY or DERIVED length time mass force temperature
Dimensions of mechanics are PRIMARY or DERIVED length time mass force temperature
aF m aF m
L
T
MMLT-2
Dimensions and UnitsDimensions and Units
Dimension is measure by which a physical variable is expressed qualitativelyUnit is a particular way of attaching a number to dimension.
Dimensions and UnitsDimensions and Units
Quantity SymbolDimensionsVelocity V LT-1
Acceleration a LT-2
Area A L2
Volume L3
Discharge Q L3T-1
Pressure p ML-1T-2
Gravity g LT-2
Temperature T’ Mass concentration C ML-3
Quantity SymbolDimensionsVelocity V LT-1
Acceleration a LT-2
Area A L2
Volume L3
Discharge Q L3T-1
Pressure p ML-1T-2
Gravity g LT-2
Temperature T’ Mass concentration C ML-3
Dimensions and UnitsDimensions and Units
Quantity Symbol DimensionsDensity ML-3
Specific Weight ML-2T-2
Dynamic viscosity ML-1T-1
Kinematic viscosity L2T-1
Surface tension MT-2
Bulk mod of elasticity E ML-1T-2
Quantity Symbol DimensionsDensity ML-3
Specific Weight ML-2T-2
Dynamic viscosity ML-1T-1
Kinematic viscosity L2T-1
Surface tension MT-2
Bulk mod of elasticity E ML-1T-2
These are _______ properties!fluid
HistoryHistoryArchimedes (B.C.) Postulates of buoyancy
Leonardo da Vinci, 1500 Eq. of conservation of mass for incompressible, 1D, viscous flow
Torricelli, 1644 Torricelli’s law
Mariotte, 1686Invented First Wind tunnel to measure drag
Newton, 1687 Newton’s law of viscosity, Calculus
Daniel Bernoulli, 1738
Pressure Gradient is proportional to acceleration for frictionless flow
Leonhard Euler, 1755 Euler Equations, Bernoulli’s Eqd’Alembert, 1752 d’Alembert’s paradox
Navier 1827, Stokes 1845 Navier Stoke Equation
Prandtl, 1904 Boundary Layer Theory
Fluid Mechanics, cont.Fluid Mechanics, cont.
Fluid Mechanics is Based on
Hydrodynamics:o A Mathematical Subjecto Deals with Ideal Fluid o Results are of Limited Value
Hydraulics:o Based on Experimento Gives Empirical Resultso Confined to Water Only
+ Fluid Mechanics
Fluid Mechanics, cont.Fluid Mechanics, cont.
Fluid Mechanics
Theoreticalo Based on Lawso Mostly Applies to
Ideal Situationso Of Little Practical
Value
Experimentalo Supports the
Theoretical Branch
Obstacles1.Geometry2.Viscosity
Concept of FluidConcept of Fluid
Solid Molecules are Closer Hard in Appearance “Requires a Certain
Amount of Stress Before Deformation Occurs”
Solid Molecules are Closer Hard in Appearance “Requires a Certain
Amount of Stress Before Deformation Occurs”
Fluid Molecules are Apart Squashy in
Appearance “Fluid will deform in
Time to the Slightest Stress”
Fluid Molecules are Apart Squashy in
Appearance “Fluid will deform in
Time to the Slightest Stress”
Distinction b/w Gas and LiquidDistinction b/w Gas and Liquid
Liquid Relatively Closely
Packed Strong Cohesion Forces Tends to Retain
Volume Forms a Free Surface
Liquid Relatively Closely
Packed Strong Cohesion Forces Tends to Retain
Volume Forms a Free Surface
Gas Not Closely Packed Week Cohesion
Forces Does not Retain
Volume Volume is Affected
by Pressure
Gas Not Closely Packed Week Cohesion
Forces Does not Retain
Volume Volume is Affected
by Pressure
ContinuumContinuum
All materials, solid or fluid, are composed of molecules discretely spread and in continuous motion.
However, in dealing with fluid-flow relations on a mathematical basis, it is necessary to replace the actual molecular structure by a hypothetical continuous medium, called the continuum.
All materials, solid or fluid, are composed of molecules discretely spread and in continuous motion.
However, in dealing with fluid-flow relations on a mathematical basis, it is necessary to replace the actual molecular structure by a hypothetical continuous medium, called the continuum.
Continuum, contd.Continuum, contd.
Density = Mass / Unit Volume Molecules are Always in Motion so What is
the Meaning of Density of a Fluid????
Density = Mass / Unit Volume Molecules are Always in Motion so What is
the Meaning of Density of a Fluid????
For Air,10-9 mm3 has 3*107
molecules
Continuum, contd.Continuum, contd.
Fluid in Which Properties Vary Continually and Smoothly
Differential Calculus can be Employed to Analyze the Problems
Fluid in Which Properties Vary Continually and Smoothly
Differential Calculus can be Employed to Analyze the Problems
Flow VelocityFlow Velocity
“Distance Travelled by an Object per Unit Time in a Particular Direction”
It is a Vector Quantity For a Fluid, Velocity is a Point Property It Has Three Components u, v, w V(x, y, z, t) = iu(x, y, z, t ) + jv(x, y, z, t ) +
kw(x, y, z, t )
“Distance Travelled by an Object per Unit Time in a Particular Direction”
It is a Vector Quantity For a Fluid, Velocity is a Point Property It Has Three Components u, v, w V(x, y, z, t) = iu(x, y, z, t ) + jv(x, y, z, t ) +
kw(x, y, z, t )
Viscosity _______ Density _______ Specific weight _______ Relationships between Pressure and volume
Ideal Gas Law __________ Bulk Modulus of Elasticity _______
Vapor Pressure _______ Surface Tension _______
Viscosity _______ Density _______ Specific weight _______ Relationships between Pressure and volume
Ideal Gas Law __________ Bulk Modulus of Elasticity _______
Vapor Pressure _______ Surface Tension _______
PV=nRTPV=nRTKK
PvPv
Fluid PropertiesFluid Properties
Fluid Properties, Contd.Fluid Properties, Contd.
DENSITY:- (Specific Mass) “It is the Mass of a
Substance Per Unit Volume” Density is a Point Property
Specific Weight (weight per unit volume) __________________
DENSITY:- (Specific Mass) “It is the Mass of a
Substance Per Unit Volume” Density is a Point Property
Specific Weight (weight per unit volume) __________________
950960970980990
1000
0 50 100Temperature (C)
Den
sity
(kg
/m3 )
= g = 9806 N/m3
R is the universal gas constant T is in Kelvin P is in N/m2
R is the universal gas constant T is in Kelvin P is in N/m2
Perfect Gas LawPerfect Gas Law
PV nRTN m
8314Kgmol K
R
Use absolute pressure for P and absolute temperature for T
gasP R T2
2
m287
s Kgas p v airgas
RR c c R
M
Fluid Deformation between Parallel Plates
Fluid Deformation between Parallel Plates
Side viewSide view
Force F causes the top plate to have velocity U.Force F causes the top plate to have velocity U.What other parameters control how much force is What other parameters control how much force is required to get a desired velocity?required to get a desired velocity?
Distance between plates (b)Distance between plates (b)
Area of plates (A)Area of plates (A)
F
b
U
Viscosity!Viscosity!
Shear StressShear Stress
M
L T
M
L T
change in velocity with respect to distancechange in velocity with respect to distance
AFAF
2m
N
2m
N
dydu dydu
b
AUF
b
AUF Fb
AU
Fb
AU
2
N s kg
m m×sor
2
N s kg
m m×sor
dimension of
Tangential force per unit area
rate of shear
U
b
U
b
b
Ub
U
s
1
s
1
Rate of angular deformation
units of
dimension of units of2
M
L T
2
M
L T
dimension of units of1
T
1
T
Fluid classification by response to shear stress
Fluid classification by response to shear stress
Newtonian Ideal Fluid Ideal plastic
Newtonian Ideal Fluid Ideal plastic
Shear stress Shear stress
Rat
e of
def
orm
atio
nR
ate
of d
efor
mat
ion
dydu
dydu dydu
Ideal FluidNewtonian
Ideal plastic
1
molasses, tar, 20w-50 oil
Examples of highly viscous fluids ______________________
Fundamental mechanisms Gases - transfer of molecular momentum
Viscosity __________ as temperature increases. Viscosity __________ as pressure increases.
Liquids - cohesion and momentum transfer Viscosity decreases as temperature increases. Relatively independent of pressure (incompressible)
Examples of highly viscous fluids ______________________
Fundamental mechanisms Gases - transfer of molecular momentum
Viscosity __________ as temperature increases. Viscosity __________ as pressure increases.
Liquids - cohesion and momentum transfer Viscosity decreases as temperature increases. Relatively independent of pressure (incompressible)
Fluid ViscosityFluid Viscosity
increases
_______
increases
______________
Example: Measure the viscosity of water
Example: Measure the viscosity of water
The inner cylinder is 10 cm in diameter and rotates at 10 rpm. The fluid layer is 2 mm thick and 10 cm high. The power required to turn the inner cylinder is 50x10-6 watts. What is the dynamic viscosity of the fluid?
The inner cylinder is 10 cm in diameter and rotates at 10 rpm. The fluid layer is 2 mm thick and 10 cm high. The power required to turn the inner cylinder is 50x10-6 watts. What is the dynamic viscosity of the fluid?
Outer Outer cylindercylinder
Thin layer of waterThin layer of water
Inner Inner cylindercylinder
Solution SchemeSolution Scheme
Restate the goal Identify the given parameters and represent the
parameters using symbols Outline your solution including the equations
describing the physical constraints and any simplifying assumptions
Solve for the unknown symbolically Substitute numerical values with units and do the
arithmetic Check your units! Check the reasonableness of your answer
Restate the goal Identify the given parameters and represent the
parameters using symbols Outline your solution including the equations
describing the physical constraints and any simplifying assumptions
Solve for the unknown symbolically Substitute numerical values with units and do the
arithmetic Check your units! Check the reasonableness of your answer
Viscosity Measurement: SolutionViscosity Measurement: Solution
hr
Pt322
hr
Pt322
23-32
6-
s/mN 1.16x10m) (0.1m) (0.05(1.047/s)2
m) (0.002 W)10(50
x 23-32
6-
s/mN 1.16x10m) (0.1m) (0.05(1.047/s)2
m) (0.002 W)10(50
x
tAU
F t
AUF U U A A
thr
F22
thr
F22
P P
thr
P322
thr
P322
r 2rh
Fr
Outer Outer cylindercylinder
Thin layer of waterThin layer of water
Inner Inner cylindercylinder
r = 5 cmt = 2 mmh = 10 cmP = 50 x 10-6 W10 rpm
Role of ViscosityRole of Viscosity
Statics Fluids at rest have no relative motion between
layers of fluid and thus du/dy = 0 Therefore the shear stress is _____ and is
independent of the fluid viscosity Flows
Fluid viscosity is very important when the fluid is moving
Statics Fluids at rest have no relative motion between
layers of fluid and thus du/dy = 0 Therefore the shear stress is _____ and is
independent of the fluid viscosity Flows
Fluid viscosity is very important when the fluid is moving
zerozero
Dynamic and Kinematic Viscosity
Dynamic and Kinematic Viscosity
Kinematic viscosity (__) is a fluid property obtained by dividing the dynamic viscosity (__) by the fluid density
Kinematic viscosity (__) is a fluid property obtained by dividing the dynamic viscosity (__) by the fluid density
3mkg
smkg
3mkg
smkg
[m2/s]
2m
sN
2m
sN
2s
mkgN
2s
mkgN
Bulk Modulus of ElasticityBulk Modulus of Elasticity
Relates the change in volume to a change in pressure changes in density at
high pressure pressure waves
_________ ______ __________
Relates the change in volume to a change in pressure changes in density at
high pressure pressure waves
_________ ______ __________
soundsoundwater hammerwater hammer
/v
dpE
d
2.00
2.05
2.10
2.15
2.20
2.25
2.30
2.35
0 20 40 60 80 100
Temperature (C)
Bul
k M
odul
us o
f el
asti
city
(G
Pa)
Water
vE
a
vEa speed of soundspeed of sound
/v
dpE
dV V
Vapor PressureVapor Pressure
0
1000
2000
3000
4000
5000
6000
7000
8000
0 10 20 30 40
Temperature (C)
Vap
or p
ress
ure
(Pa)
liquid
What is vapor pressure of water at 100°C?101 kPa
Connection with phenomenon called cavitation!
CavitationCavitation
Cavitation DamageCavitation Damage
Video clip of cavitation processVideo clip of cavitation process
Surface TensionSurface Tension
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