INTRODUCTION AND FLUID PROPERTIES - Ioan NISTOR
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INTRODUCTION TO FLUID MECHANICS – CVG 2116
INTRODUCTION AND
FLUID PROPERTIES
Ioan NISTOR
inistor@uottawa.ca
Things to remember…
• Attend the tutorial!!!
• Attend the lectures!!
• REVISE CVG 2149 (Civil Eng. Mechanics) and
MAT1322 (Calculus) You will BADLY need it throughout
the course!
Vi t l Campus
•Virtual C (Blackboard
(Bl kb d Learning
L i System)
S t ) is
i
operational!
1
WHY do we study Fluid Mechanics?...
Dams and Reservoirs
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3
Water Distribution and Treatment
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4
River and Coastal Works
http://www.nab.usace.army.mil/pbriefs/lhfloodpro.html CVG 2116
Environment
Air pollution River hydraulics
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5
Vehicles
Aircraft Surface ships
High-speed rail Submarines
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Weather & Climate
Tornadoes Thunderstorm
Global Climate Hurricanes
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6
Physiology and Medicine
Blood pump Ventricular assist device
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Sports & Recreation
Water sports Cycling Offshore racing
Auto racing Surfing
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7
Fluid Mechanics
• Fluids essential to life
– Human body 95% water
– Earth’s surface is 2/3 water
– Atmosphere extends 17km above the Earth’s surface
• History shaped by fluid mechanics
– Geomorphology
– Human migration and civilization
– Modern scientific and mathematical theories and methods
– Warfare
• Affects every part of our lives
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History and personalities of Fluid
Mechanics
Archimedes Newton Leibniz Bernoulli Euler
(C. 287-212 BC) (1642-1727) (1646-1716) (1667-1748) (1707-1783)
Navier Stokes Reynolds Prandtl Taylor
(1785-1836) (1819-1903) (1842-1912) (1875-1953) (1886-1975)
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8
History of Fluid Mechanics – several cornerstones
• Well drilling by the Chinese engineers around 2000 B.C.
• Irrigation works by Egyptians around 500 B.C.
• Stream
St flow
fl started
t t d to
t be
b measured
d in
i Rome
R iin 97 A
A.D.
D
• Leonardo da Vinci developed correct relations for flow as it relates to
velocity and area ; Q = VA
• Perrault made RF/Runoff measurements in Seine River – 1694
• Pitot tube & Venturi meter for measuring velocity - 1700s
• Chézy formula developed for a canal in Paris (1768)
• Rhine River monitored at Basel in 1867
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Fluids Engineering
Reality
Fluids Engineering System Components Idealized
Experimental Mathematical Physics Problem Formulation
Fluid Mechanics
Analytic fluid Computational
Mechanics fluid mechanics
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Analytical Fluid Dynamics
• Example: laminar pipe flow
ρUD
Assumptions: Fully developed, Low Re = < 2000
Approach: Simplify momentum equation, μ
integrate, apply boundary conditions to S h
Schematic
ti
determine integration constants and use
energy equation to calculate head loss
0
Du 0 ∂ p ⎡ ∂ 2u ∂ 2u ⎤ 0
=− + μ ⎢ 2 + 2 ⎥ + gx
Dt ∂x ⎣ ∂x ∂y ⎦
Exact solution :
u(r) = 1 (− ∂p )(R2 − r 2)
4μ ∂x
8μ du
= 8τ w = dy w = 64
Friction factor: f
ρV 2 ρV 2 Re
p1 p L V 2 32μ LV
Head loss: + z1 = 2 + z2 + h f hf = f =
γ γ D 2g γ D2
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Experimental Fluid Dynamics (EFD)
Definition:
Use ofo experimental
e pe e ta methodology
et odo ogy a
and
dpprocedures
ocedu es for
o so
solvingg
fluids engineering systems, including full and model scales, large
and table top facilities, measurement systems (instrumentation,
data acquisition and data reduction), uncertainty analysis, and
dimensional analysis and similarity.
EFD philosophy:
• Decisions on conducting experiments are governed by the ability
of the expected test outcome, to achieve the test objectives within
allowable uncertainties.
• Key parts of an experimental program:
• test design
• determination of error sources
• estimation of uncertainties
• documentation of the results
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10Applications of EFD (cont.)
Example of industrial application
NASA's cryogenic wind tunnel simulates flight
conditions for scale models--a critical tool in
designing airplanes.
Application in teaching
Fluid dynamics laboratory
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Full and model scale
• Scales: model, and full-scale
• Selection of the model scale: governed by dimensional analysis and similarity
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11Computational Fluid Dynamics
• CFD is use of computational methods for solving fluid
engineering systems, including modeling
(mathematical & physics) and numerical methods
(
(solvers, f
finite differences,
ff and grid generations, etc.).
)
• Rapid growth in CFD technology since the advent of
computers
ENIAC 1, 1946 IBM WorkStation
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Modeling (examples)
Developing flame surface (Bell et al., 2001)
Free surface animation for ship in
regular waves
Evolution of a 2D mixing layer laden with particles of Stokes
Number 0.3 with respect to the vortex time scale (C.Narayanan)
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12SI System of Units
Six primary units and a number of secondary units, derived from the primary ones
PRIMARY UNITS
Quantity SI Unit Dimension
length meter, m L
mass kilogram, kg M
time second, s T
temperature Kelvin, K Θ
current ampere A
ampere, I
luminosity candela Cd
First four are most important in fluid mechanics!!!
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There are many derived (secondary) units all obtained from combination of
the above primary units. Those most used are shown in the table below:
Quantity SI Unit Dimension
SECONDARY UNITS
velocity m/s ms-1 LT-1
acceleration m/s2 ms-2 LT-2
TIP: write down the units of
N
force
kg m/s2
kg ms-2 M LT-2 any equation you are using.
If at the end the units do not
Joule J
match you know you have
energy (or work) N m, kg m2s-2 ML2T-2
kg m2/s2 made a mistake. For
example if you have at the
Watt W
Nms-1 end of a calculation,
power N m/s ML2T-3
kg m2s-3
kg m2/s3
30 kg/m s = 30 m !!!!
Pascal P,
Nm-2
pressure ( or stress) N/m2, ML-1T-2
kg/m/s2
kg m-1s-2 you have certainly made a
mistake - checking the units
d it
density k / 3
kg/m k
kg m-3 ML-3
can often help find the
specific weight
N/m3
kg m-2s-2 ML-2T-2 mistake.
kg/m2/s2
a ratio 1
relative density
no units no dimension
N s/m2 N sm-2
viscosity M L-1T-1
kg/m s kg m-1s-1
N/m Nm-1
surface tension MT-2 CVG 2116
kg /s2 kg s-2
13OTHER SYSTEMS OF UNITS – “TRADITIONAL” UNITS
Referred in many countries as the “English” or “Imperial” system:
Quantity SI Unit Conversion to SI
length foot, ft 0.3048 m
mass slug slug
slug, 14 59 kg
14.59
pound mass,
mass 0.453 kg
lbm
pound force,
weight
lbf
time second, s
power horsepower 746 W
temperature Celsius, K K = 273+OC
Properties related to the total mass of the system: extensive properties (use
upper letters) – mass M, weight W = M x g, etc.
Properties independent of the amount of fluid: intensive properties (use
lowercase letters) – pressure p, mass density ρ, etc.
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2.3 PROPERTIES INVOLVING MASS
MASS DENSITY
DEFINITION: Mass Density, ρ (pronounced “rho”) , is defined as the mass of
substance per unit volume.
Units: Kilograms per cubic meter, Kg/m3 (or Kgm-3 )
Dimensions: ML-3
Typical values: Water = 1000 Kg/m3 (62.4 lbm/ft3), Mercury = 13546 Kg/m3,
Air = 1.23Kg/m3, Paraffin Oil = 800 Kg/m3
(all of them, at pressure =1.013x105 N/m2 and Temperature = 288.15 K (4 oC)
DENSITY VARIATION Two different situations:
AIR: highly compressible, large density variation (examples?)
WATER: low compressibility (why??)
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142.3 PROPERTIES INVOLVING MASS (cont.)
SPECIFIC WEIGHT
Specific weight, γ (“gamma”), is defined as the weight of a fluid per unit volume.
γ = ρg
Where: g – gravitational acceleration = 9.81 m/s2
Units: Newtons per cubic meter, N/m3 (or Nm-3 )
Dimensions: ML-2T-2
T i l values:
Typical l
Water = 9.79 KN/m3, Mercury = 132.9 KN/m3, Air = 11.8 N/m3, Paraffin Oil = 7.85 KN/m3
(at pressure =1.013x105 N/m2 and Temperature = 288.15 K (4 oC)
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2.3 PROPERTIES INVOLVING MASS (cont.)
SPECIFIC GRAVITY
S- Ratio of the specific weight of a fluid to the specific weight of water
γ fluid ρ fluid
S= =
γ water ρ water
Units: non-dimensional
Typical values:
γ hg 133 kN m3
S Hg = = = 13.6
γ H O 9.81 kN m3
2
(at temperature = 20 oC)
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152.3 PROPERTIES INVOLVING MASS (cont.)
IDEAL GAS LAW
The fundamental equation of state for an ideal gas relates pressure, specific
volume and temperature for a pure substance:
R – universal gas constant (same for all gases)
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162.4 PROPERTIES INVOLVING THE FLOW OF HEAT
- Capacity to store thermal energy,
energy or the amount of thermal energy that must
be transferred to a unit of mass to raise its temperature by one degree K
cP − pressure is held constant during the change of state
cv − volume is held constant during the change of state
-The energy a substance possess as a result of molecular energy.
- A function of temperature and pressure
Depend only on the
temperature alone for an
ideal gas CVG 2116
2.5 VISCOSITY
Difference between steel and a viscous fluid:
STEEL: shear stress is proportional to the shear strain. The proportionality
factor is called elastic modulus (E).
VISCOUS FLUID: shear stress is p proportional
p to the time rate of strain. The
proportionality factor is called dynamic (absolute) viscosity (μ).
dV
τ =μ
dy
Where:
τ - shear
h stress
t (" tau"
t ")
μ - the dynamic viscosity (" miu" )
dV dy - the rate of strain
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τ N m2
Units: μ= = = N × s / m 2 = poise
dV dy (m s ) m
1 poise = 1dyne − s / cm 2 = 0.1N ⋅ s / m 2
In the English (traditional) system units : lbf × s / ft 2
Typical values:
Water dynamic viscosity = 1 centipoises (10-2 poise) = 10-3 Ns/m2
(at temperature T = 20 oC)
More often, in fluid mechanics, the kinematic viscosity,
y ν ((niu),
) is being
g used
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EXAMPLE:
The density of an oil is 850 kg/m3. Find its relative density (specific gravity) and
the kinematic viscosity if the dynamic viscosity is 5 x 10-3 kg/ms.
ρoil = 850 kg/m3 ρ water = 1000 kg/m3
Soil = 850 / 1000 = 0.85 (relative density)
Dynamic viscosity = μ = 5X10-3 kg/ms
Kinematic viscosity = ν = μ / ρ
μ 5 ×10 −3
ν= = = 5.9 ×10 −6 m 2 s −1
ρ 850
The dynamic viscosity of a fluid varies with the temperature!!
μ = Ceb T
Where: μ - the dynamic viscosity (" miu" )
C , b - empirical constants (see fig. A2 and A3 in the Appendix of the book)
T - temperature
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19NEWTONIAN vs. NON-NEWTONIAN FLUIDS
Fluids for which the shear stress is proportional with the rate of strain are called
Newtonian fluids as opposed to non-Newtonian fluids.
Our course
focus!!!!
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2.6 ELASTICITY
Bulk modulus of elasticity
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2.7 SURFACE TENSION
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EXAMPLE:
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222.8 VAPOR PRESSURE
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Summary
• SI system of units
• Properties involving mass: mass density, weight,
specific gravity
gravity, ideal gas law
law.
• Properties involving the flow of heat: specific heat,
specific internal energy, specific enthalpy.
• Viscosity: dynamic and kinematic
• Elasticity
• Surface tension
• Vapor pressure
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