FLUID MECHANICS
Lichuanqi
Shandong University
AFD
EFD
CFD
Information and Introduction
Instructor
Li chuanqi
E-mail : lichuanqi@sdu.edu.cn
Tel:
13864163006
Textbook
Fluid Mechanics with Engineering Applications
E.John Finnemore
Joseph B. Franzini
Homework
One
of the best ways to learn something
is through practice and repetition
Therefore, homework assignments are
extremely important in this class!
Homework sets will be carefully designed,
challenging, and comprehensive. If you
study and understand the homework, you
should not have to struggle with the exams
Course Topics
Fluid Properties
Fluid Statics
Pressure at a Point
Force on Surfaces
Concepts of Fluid Flow
Types of Flow
Laminar and Turbulent Flow
Steady Flow and Uniform Flow
Path Lines, Streamlines, and Streak Lines
Course Topics
The fundamental equations of fluid dynamics
Equation of Continuity
Bernoullis Equation
momentum equation
Pipe Flow
Open Channel Flow
My Goals for the next 14 weeks
That each of you develop an intuition for
the fundamental principles of fluid
mechanics
That you leave this course saying,
Fluids makes sense and I can tackle
fluids problems.
That we have an enjoyable 14 weeks
learning together
CH 1
Introduction
Outline
What is Fluid Mechanics?
Why is Fluid Mechanics Important?
Applications of Fluid Mechanics.
Dimension systems and analysis.
1.1 Fluid Mechanics Overview
Fluid Mechanics
Gas
Liquids
Statics
F = 0
i
Air, He, Ar,
N2, etc.
Compressibility Density
Chapter 1: Introduction
F > 0 , Flows
Stability
Pressure Buoyancy
Water, Oils,
Alcohols,
etc.
Viscosity
Dynamics
i
Compressible/
Incompressible
Surface
Laminar/
Tension
Turbulent
Steady/Unsteady
Vapor
Viscous/Inviscid
Pressure
Chapter 2: Fluid Statics
Fluid Dynamics:
Rest of Course
Definition of Fluid Mechanics: Fluid mechanics is the
science of the mechanics of liquids and gases. It involves
many of the same principles of solid Statics and Dynamics,
but fluids is a more complex subject because solids involve
the study of forces on discrete bodies, while in fluids bodies
flow together.
The analysis is based on the fundamental laws of
mechanics, which relate continuity of mass and energy
with force and momentum.
An understanding of the properties and behavior of
fluids at rest and in motion is of great importance in
engineering.
Used in the design of :
Water supply system
-- waste water treatment
Dam spillways
-- valves, flow meters
Shock absorbers, brakes
-- automatic transmissions
ships, submarines
-- breakwaters, marinas
Aircrafts, rockets
-- computer disk drives
Windmills, turbines
-- pumps, HVAC systems
Bearings
-- artificial organs
Sport items: Golf balls
Race cars
Scope of Fluid Mechanics
Science of the mechanics of liquids and gases
z Based on same fundamental principles as solid
Mechanics
z More complicated subject, however, since in fluids
separate elements are more difficult to distinguish
z We'll solve problems of fluids on the surface of
the Earth, within reasonable ranges of pressure and
temperature.
z
Scope of Fluid Mechanics
Branches:
Fluid statics: fluids at rest
Fluid kinematics: velocities and streamlines
Fluid dynamics: velocity & accelerations
forces
Classical hydrodynamics
Mathematical subject
Deals with ideal frictionless fluids
Classical hydraulics:
Experimental science
Deals with real fluids
Scope of Fluid Mechanics
Classical hydrodynamics and hydraulics are now combined into
FLUID MECHANICS
Modern Fluid Mechanics:
Combines mathematical principles with experimental data
Experimental data used to verify or complement theory or
mathematical analysis
Computational Fluid Dynamics (CDF)
Numerical solutions using computers
Methods:
Finite differences * finite elements
Boundary elements * analytic elements
Why is Fluid Mechanics Important?
Knowledge of fluid mechanics in needed
to properly design many engineering
projects, including water pipe systems,
storm water drainage systems, aircraft,
brake systems, heating and air conditioning
systems, golf balls, boats, and cars.
Therefore, most of you will use Fluid
Mechanics in your work.
Historical development (1)
Ancient civilizations: irrigation, ships
Ancient Rome: aqueducts, baths (4th century
B.C.)
Ancient Greece: Archimedes buoyancy (3rd
century B.C.)
Leonardo (1452-1519): experiments, research
on waves, jets, eddies, streamlining, flying
Historical development (2)
Newton (1642-1727): laws of motion, law of
viscosity, calculus
18th century mathematicians: solutions to
frictionless fluid flows (hydrodynamics)
17th & 18th century engineers: empirical
equations (hydraulics)
Late 19th century: dimensionless numbers,
turbulence
Historical development (3)
Prandtl (1904): proposes idea of the boundary layer
Flow fields of low-viscosity fluids divided into two zones:
A thin, viscosity-dominated layer near solid surfaces
An effectively inviscid outer zone away from boundaries
Explains paradoxes
Allow analysis of more complex flows
20th century: hydraulic systems, oil explorations,
structures, irrigation, computer applications
Historical development (4)
Beginning of 21st century:
No complete theory for the nature of turbulence
Still a combination of theory and experimental data
History
Faces of Fluid Mechanics
Archimedes
(C. 287-212 BC)
Navier
(1785-1836)
Newton
(1642-1727)
Stokes
(1819-1903)
Leibniz
(1646-1716)
Reynolds
(1842-1912)
Bernoulli
Euler
(1667-1748)
(1707-1783)
Prandtl
Taylor
(1875-1953)
(1886-1975)
Significance
Fluid Mechanics is omnipresent
Weather & climate
Aerodynamics
Combustion
Energy generation
Geology
Hydraulics and Hydrology
Hydrodynamics
Ocean and Coastal Engineering
Water Resources
Sports & recreation
numerous other examples
Weather & Climate
Tornadoes
Thunderstorm
Global Climate
Hurricanes
Aerodynamics
Energy generation
Geology
River Hydraulics
Hydraulic Structures
Hydrodynamics
Water Resources
Environmental
London Sewer
Environmental
Stream Habitat
Transportation
Culverts
Geotechnical
Groundwater and Seepage
Structural
Snow Load
Structural
Wind Load
Analytical Fluid Dynamics
The theory of mathematical physics problem
formulation
Control volume & differential analysis
Exact solutions only exist for simple geometry and
conditions
Approximate solutions for practical applications
Linear
Empirical relations using EFD data
Analytical Fluid Dynamics
Lecture Part of Fluid Class
Definition and fluids properties
Fluid statics
Fluids in motion
Continuity, momentum, and energy principles
Surface resistance
Flow in conduits
Analytical Fluid Dynamics
Example: laminar pipe flow
UD
< 2000
Assumptions: Fully developed, Low Re =
Approach: Simplify momentum equation,
Schematic
integrate, apply boundary conditions to
determine integration constants and use
energy equation to calculate head loss
0
2
0
0
u 2u
p
Du
=
+ 2 + 2 + gx
y
x
Dt
x
Exact solution :
u(r) = 1 ( p )(R2 r 2)
4 x
8 du
8 w = dy w = 64
f
=
Friction factor:
V 2 V 2 Re
p1
p2
L V 2 32 LV
+ z1 =
+ z2 + h f
=
hf = f
Head loss:
D 2g
D2
Experimental Fluid Dynamics (EFD)
Definition:
Use of experimental methodology and procedures for solving 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.
Integration of UA into all test phases should be a key part of entire
experimental program
test design
determination of error sources
estimation of uncertainty
documentation of the results
Applications of EFD
Application in research & development
Example of industrial application
NASA's cryogenic wind tunnel simulates flight
conditions for scale models--a critical tool in
designing airplanes.
Tropic Wind Tunnel has the ability to create
temperatures ranging from 0 to 165 degrees
Fahrenheit and simulate rain
Full and model scale
Scales: model, and full-scale
Selection of the model scale: governed by dimensional analysis and similarity
Computational Fluid Dynamics
CFD is use of computational methods for solving fluid
engineering systems, including modeling (mathematical &
Physics) and numerical methods (solvers, finite differences,
and grid generations, etc.).
Rapid growth in CFD technology since advent of computer
ENIAC 1, 1946
IBM WorkStation
Modeling (example)
Free surface animation for ship in regular waves
Dimensions and Units (1)
z
Units needed to properly express a physical quantity
z Systems to be used:
S.I. (Systeme Internationale d'Unites)
Adopted in 1960
Used by nearly every major country, except the U.S.
Likely to be adopted by the U.S. in the near future
B.G. (British Gravitational system)
Used in the technical literature for years
Preferred system in the U.S.
Dimensions and units (2)
Basic dimensions used in fluid mechanics:
Length (L)
Mass (M)
Time (T)
Temperature ()
Dimensions of acceleration: [a] = LT-2
Newton's 2nd law: F = [m][a] = MLT-2
Only 3 of the four basic units can be assigned
arbitrarily, the fourth becoming a derived unit
Derived quantities (1)
Basic dimensions: mass (M), length (L), time (T)
Velocity = Length / Time
Acceleration = Velocity / Time = Length / Time2
Discharge = Volume / Time
Force = Mass Acceleration
Pressure = Force / Area (also Stress)
Work = Force Length (also Energy, Torque)
Power = Work / Time = Force Velocity
Angular Velocity = Angle / Time
Angular Acceleration = Angular Velocity / Time
Example
Newtons second law
F = ma = MLT-2
In this case, acceleration is a derived unit,
because it is derived from combining basic
units.
CH 2 Properties of Fluids
Section Goals
1. What is the differences between solids, liquids and gases?
2. Learn definitions that specify basic fluid properties (density,
specific weight, specific volume, and specific gravity) and
how to use these definitions for solving problems.
3. Understand the concept of compressibility and how it applies
to fluid mechanics.
4. Understand the concept of Newtonian fluids and viscosity
and how to solve for forces in a Newtonian fluid.
5. Understand the concept of surface tension and vapor pressure
and how to find the capillary rise of a fluid.
2.1 What is a fluid?
A fluid is a substance in the gaseous or liquid form
Distinction between solid and fluid?
Solid: can resist an applied shear by deforming. Stress is
proportional to strain
Fluid: deforms continuously under applied shear. Stress is
proportional to strain rate
Solid
F
=
A
Fluid
F
V
A
h
What is a fluid?
Stress is defined as the force per
unit area.
Normal component: normal
stress
In a fluid at rest, the normal
stress is called pressure
Tangential component: shear
stress
What is a fluid?
A liquid takes the shape of the
container it is in and forms a free
surface in the presence of
gravity
A gas expands until it
encounters the walls of the
container and fills the entire
available space. Gases cannot
form a free surface
Gas and vapor are often used as
synonymous words
What is a fluid?
solid
liquid
gas
Fluids can be ...
liquids,
or gases!
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
In a continuum, the physical variable at a point in space
is the averaged value of the variable in a small sphere.
How good is the assumption?
3x1010 molecules of air
10-3cm
2.2 Distinction between a solid and a fluid (1)
Molecules of solid closer together than those of fluid
Solid: intermolecular forces larger than in fluid
Elastic solid
deforms under load
recovers original state when unloaded
Plastic solid:
deforms under sufficient load
continues deforming as long as load is applied
does not return to original state
Distinction between a solid and a fluid (2)
Intermolecular forces in fluid not large enough to hold
elements together
Fluid flows under slightest stress and continues flowing
as long as stress is present
Distinction between a gas and a liquid (1)
Fluids: gases or liquids
GAS:
Molecules farther apart
Very compressible
Tends to expand indefinitely
LIQUID:
Relatively incompressible
If external pressure removed, does not expand
May have a free surface (subject to its own vapor
pressure)
2.3 Density, Specific Weight, Specific
Volume, and Specific Gravity
Density
Density of a fluid, ,
Definition: mass per unit volume,
slightly affected by changes in temperature and pressure.
= mass/volume
Units: kg/m3
Typical values:
Water = 1000 kg/m3;
Air = 1.23 kg/m3
2.3.1 Density
The density of a fluid is defined as mass per unit volume.
m
=
v
m = mass, and v = volume.
Different fluids can vary greatly in density
Liquids densities do not vary much with pressure and temperature
Gas densities can vary quite a bit with pressure and temperature
Density of water at 4 C : 1000 kg/m3
Density of Air at 4 C : 1.20 kg/m3
Alternatively, Specific Volume:
Specific weight
Specific weight of a fluid, [gamma]
Definition: weight of the fluid per unit volume
Arising from the existence of a gravitational force
The relationship and g can be found using the following:
Since
therefore
= m/V
= g
Units: N/m3
Typical values:
Specific weight of water at 4 C : 9.80 kN/m3
Specific weight of air at 4 C : 11.9 N/m3
Specific gravity
The specific gravity (or relative density) can be defined in two ways:
Definition 1: A ratio of the density of a substance to the density
of water at standard temperature (4C) and
atmospheric pressure, or
Definition 2: A ratio of the specific weight of a substance to the
specific weight of water at standard temperature
(4C) and atmospheric pressure.
SG =
s
w @ 4C
Unit: dimensionless.
s
w @ 4C
2.3.2 Viscosity
Viscosity is a measure of a
fluid's resistance to flow..
The force a flowing fluid
exerts on a body in the
flow direction is called the
drag force, and the
magnitude of this force
depends, in part, on
viscosity.
Viscosity is a fluids resistance to flow.
Fluid motion can cause shearing stresses
(a) Deformation of material placed between two parallel plates.
(b) Forces acting on upper plate.
Behavior of a fluid placed between two parallel plates
The shearing stress is increased by P, the rate of shearing strain is increased
in direct proportion,
Viscosity
Problem
Three black marbles are dropped at the
same time into three different fluids - oil,
water, and glycerol. Will they all fall at
the same rate of speed?
The marble will drop the fastest in the water
and slowest in the glycerol.
The reason is due to the different viscosities
of the fluids.
Viscosity: Kinematic Viscosity
Definition: Ratio of absolute viscosity to the density;
= /
Appears in many problems in fluids.
Called kinematic viscosity because it involves no force
(dynamic) dimensions
Units: m2/s
Typical values:
Water = 1.14x10-6 m2/s;
Air = 1.46x10-5 m2/s;
In general,
viscosity of liquids with temperature, whereas
viscosity of gases with
in temperature.
Viscosity: Newtonian vs. Non-Newtonian
Toothpaste
Latex
Paint
Corn
Starch
Newtonian Fluids are Linear Relationships between stress and
strain: Most common fluids are Newtonian.
Non-Newtonian Fluids are Non-Linear between stress and strain
Newtonian and Non-Newtonian Fluid
Fluid
obey
Newtons law
of viscosity
refer
Newtons law of viscosity is given by;
du
=
dy
(1.1)
= shear stress
= viscosity of fluid
du/dy = shear rate, rate of strain or velocity gradient
Newtonian fluids
Example:
Air
Water
Oil
Gasoline
Alcohol
Kerosene
Benzene
Glycerine
The viscosity is a function only of the condition of the fluid, particularly its
temperature.
The magnitude of the velocity gradient (du/dy) has no effect on the magnitude of .
Newtonian and Non-Newtonian Fluid
Do not obey
Fluid
Newtons law
of viscosity
Non- Newtonian
fluids
The viscosity of the non-Newtonian fluid is dependent on the
velocity gradient as well as the condition of the fluid.
Newtonian Fluids
a linear relationship between shear stress and the velocity gradient (rate
of shear),
the slope is constant
the viscosity is constant
non-Newtonian fluids
slope of the curves for non-Newtonian fluids varies
2.3.3 Compressibility of Fluids:
Bulk Modulus(
2.3.4 Vapor Pressure
Vapor Pressure
liquid
Vapor pressure (Pa)
8000
7000
6000
water
5000
4000
3000
2000
1000
0
0
10
20
30
Temperature (C)
What is vapor pressure of water at 100C? 101 kPa
40
2.3.5 Surface Tension
Two non-mixing fluids (e.g., a
liquid and a gas) will form an
interface. The molecules below
the interface act on each other
with forces equal in all
directions, whereas the
molecules near the surface act
on each other with increased
forces due to the absence of
neighbors. That is, the
interface acts like a stretched
membrane
Surface Tension: Capillary Action
Capillary action in small tubes which involve a liquid-gas-solid interface is
caused by surface tension. The fluid is either drawn up the tube or pushed down.
Wetted
Non-Wetted
Adhesion
Cohesion
Adhesion
Cohesion
Adhesion > Cohesion
Cohesion > Adhesion
h is the height, R is the radius of the tube, is the angle of contact.
The weight of the fluid is balanced with the vertical force caused by surface
tension.
Review: Fluid Properties
Viscosity
Density and Specific Weight
Elasticity
Vapor Pressure
Surface Tension
du
=
dy
See you next time.
