Download Introduction to Fluid Mechanics

AKM 205
AKIŞKANLAR MEKANİĞİ
“TEMEL KAVRAMLAR
&
TANIMLAR”
Yrd.Doç.Dr. Onur Tunçer
İstanbul Teknik Üniversitesi
Introduction to Fluid Mechanics
• Fluid Mechanics is concerned with the behavior of fluids at rest and in
motion
• Distinction between solids and fluids:
– According to our experience: A solid is “hard” and not easily
deformed. A fluid is “soft” and deforms easily.
– Fluid is a substance that alters its shape in response to any force
however small, that tends to flow or to conform to the outline of its
container, and that includes gases and liquids and mixtures of solids
and liquids capable of flow.
– A fluid is defined as a substance that deforms continuously when
acted on by a shearing stress of any magnitude.
Flow
• Continuous deformation
• Change of velocity of particles with respect to location
• If all particles move with the same velocity, there is no flow
(example: translation or rotation)
Movement but not flow!
Movement but not flow!
water
From our point of view these are related to fluid statics!
Some applications of fluid mechanics
1. Hydraulics: the flow of water in rivers, pipes, canals, pumps, turbines.
2. Aerodynamics: the flow of air around airplanes, rockets, projectiles.
3. Meteorology: the flow of the atmosphere.
4. Particle dynamics: the flow of fluids around particles, the interaction of
particles and fluids (i.e., dust settling, slurries, pneumatic transport,
fluidized beds, air pollutant particles, corpuscles in our blood).
5. Hydrology: the flow of water and water-borne pollutants in the ground.
6. Reservoir engineering: the flow of oil, gas, and water in petroleum
reservoirs.
7. Multiphase flow: coffee percolators, oil wells, carburators, fuel
injectors, combustion chambers, sprays.
8. Combinations of fluid flow: with chemical reactions in combustion,
with electromagnetic phenomena in magnetohydrodynamics, with
mass transport in distillation or drying.
9. Viscosity-dominated flows: lubrication, injection molding, wire coating,
lava, and continental drift.
BASIC IDEAS IN FLUID MECHANICS
1. The principle of the conservation of mass.
2. The first law of thermodynamics (the principle of the
conservation of energy).
3. The second law of thermodynamics.
4. Newton’s second law of motion, which may be
summarized in the form F = ma.
Each of these four ideas is a generalization of experimental data. None of them can
be deduced from the others or from any other prior principle. Rather, they stand on
their ability to predict correctly the results of any experiment ever run to test them.
Methods of Analysis
• System
(or “Closed System”)
 Control Volume
(or “Open System”)
Dimensions and Units
In fluid mechanics we must describe various fluid characteristics in
terms of certain basic quantities such as length, time and mass
• A dimension is the measure by which a physical variable is expressed
qualitatively, i.e. length is a dimension associated with distance, width,
height, displacement.

Basic dimensions:
Length, L
(or primary quantities)
Time, T
Mass, M
Temperature, Q
 We can derive any secondary quantity from the primary quantities
i.e. Force = (mass) x (acceleration) : F = M L T-2
• A unit is a particular way of attaching a number to the qualitative
dimension: Systems of units can vary from country to country, but
dimensions do not
Dimensions and Units
Primary
Dimension
SI Unit
British
Gravitational
(BG) Unit
English
Engineering
(EE) Unit
Mass [M]
Kilogram (kg)
Slug
Pound-mass
(lbm)
Length [L]
Meter (m)
Foot (ft)
Foot (ft)
Time [T]
Second (s)
Second (s)
Second (s)
Temperature [Q]
Kelvin (K)
Rankine (°R)
Rankine (°R)
Force [F]
Newton
(1N=1 kg.m/s2)
Pound (lb)
Pound-force (lbf)
 Conversion factors are available in the textbook inside of front cover.
Units of Force: Newton’s Law F=m.g
• SI system: Base dimensions are Length, Time, Mass, Temperature
 A Newton is the force which when applied to a mass of 1 kg
produces an acceleration of 1 m/s2.
 Newton is a derived unit: 1N = (1Kg).(1m/s2)
• BG system: Base dimensions are Length, Force, Time, Temperature
 A slug is the mass which produces an acceleration of 1 ft/s2 when
a force of 1lb is applied on it:
 Slug is a derived unit: 1slug=(1lb) (s2)/(ft)
• EE system: Base dimensions are Length, Time, Mass, Force and
Temperature
 The pound-force (lbf) is defined as the force which accelerates
1pound-mass (lbm), 32.174 ft/s2.
Units of Force – EE system
To make Newton’s law dimensionally consistent we must include a
dimensional proportionality constant:
g
F  m
gc
where
gc  32.1740
(lb m )( ft )
(lb f )(s)2
Example: Newton’s Law
• An astronaut weighs 730N in Houston, TX, where the local
acceleration of gravity is g=9.792 m/s2. What is the mass of the
astronaut? What is his weight on the moon, where g=1.67 m/s2?
• Redo the same problem in EE units. In EE units the astronaut weighs
164.1lbf, gHouston=32.13 ft/s2 and gmoon=5.48 ft/s2.
Dimensional Homogeneity
• All theoretically derived equations are dimensionally homogeneous:
dimensions of the left side of the equation must be the same as those
on the right side.
– Some empirical formulas used in engineering practice are not
dimensionally homogeneous
• All equations must use consistent units: each term must have the
same units. Answers will be incorrect if the units in the equation are
not consistent. Always chose the system of units prior to solving the
problem
Properties of Fluids
 Fundamental approach: Study the behavior of individual molecules
when trying to describe the behavior of fluids
 Engineering approach: Characterization of the behavior by considering
the average, or macroscopic, value of the quantity of interest, where the
average is evaluated over a small volume containing a large number of
molecules
Treat the fluid as a CONTINUUM:
Assume that all the fluid
characteristics vary continuously throughout the fluid
Measures of Fluid Mass and Weight
• Density of a fluid, r (rho), is the amount of mass per unit volume of a
substance:
r=m/V
r  r ( P, T )
– For liquids, weak function of temperature and pressure
– For gases: strong function of T and P
from ideal gas law: r = P M/R T
where R = universal gas constant, M=mol. weight
R= 8.314 J/(g-mole K)=0.08314 (liter bar)/(g-mole K)=
0.08206 (liter atm)/(g-mole K)=1.987 (cal)/(g-mole K)=
10.73 (psia ft3)/(lb-mole °R)=0.7302 (atm ft3)/(lb-mole °R)
(1.1)
Fluid as a Continuum
Fluid as a Continuum
Velocity Field
Velocity Field
Consider also
• Steady and Unsteady Flows
• 1D, 2D, and 3D Flows
• Timelines, Pathlines, and Streaklines
Stress Field
Density
m
r
V
Measures of Fluid Mass and Weight
• Specific volume:
u=1/r
• Specific weight is the amount of weight per unit volume of a substance:
g=w/V=rg
• Specific Gravity (independent of system of units)
SG 
r
r H 2 O @ 4 C
Description & Classification of Fluid Motions
•
•
•
•
Viscous and Inviscid Flows
Laminar and Turbulent Flows
Compressible and Incompressible Flows
Internal and External Flows
Internal Flows
– Flows completely bounded by solid surfaces.
Examples: Flow in ducts and vessels; flow in pumps, fans, and compressors.
– Open-channel flow
The internal flow of liquids in which the ducts does not flow full.
Examples: Flow in rivers, irrigation ditches, and aqueducts.
External Flows
– Flow over bodies immersed in an unbounded fluid.
Examples: Flow over a submerged submarine, flow over an airplane, and
flow over a gulf ball, etc.
Fluid types: Gas vs Liquid
If the fluid is a gas: it will expand readily, filling
all the space vacated by the piston; gases
can expand without limit to occupy space
made available to them.
If the fluid is a liquid: as the piston is raised, the
liquid can expand only a small amount, and
then it can expand no more. What fills the
space between the piston and the liquid? Part
of the liquid must turn into a gas by boiling,
and this gas expands to fill the vacant space.
(When the molecules separate more than this
distance, they cease behaving as a liquid and
behave as a gas)
Because of their closer molecular spacing,
liquids normally have higher densities,
viscosities, refractive indices, etc., than
gases. This frequently leads to quite different
behaviors of liquids and gases.
Specific gravity
Viscosity (resistance to flow)
Shear
stress
g 
Newtonian vs non-Newtonian rheology
  f ( )
Units of viscosity
• The viscosity is the slope of the line of shear stress versus shear rate
so its SI unit is 1 Pa / (1/s) = 1 Pa · s
• The customary unit of viscosity is the poise , however it is too large a
unit for most common fluids.
• By sheer coincidence the viscosity of pure water at about is 0.01
poise; for that reason the common unit of viscosity in the US is the
centipoise.
g
1 cP  0.01
cm  s
1 cP  0.001 Pa  s
1 cP  6.72  10
-4
kg
1 Pa  s  1
ms
lbm
ft  s
 1000 cP 
Kinematic viscosity
Exercise: What is the kinematic viscosity of air in
strict SI ?
Surface tension
Surface Tension
Surface Tension
Units
1 N/m = 1 kg / s2
(lbf/in)
dyne/cm
1 dyne/cm = 0.001 N/m
Pressure: compressive force divided by area
Ordinary fluids cannot permanently
resist shear forces, so the water
begins to flow and finally flows
away.
If we really wanted to squeeze the
water, we would put it in some
container that would prevent its
flowing out to the side.
The pressure at a point in a fluid at
rest is the same in all directions.
The usual definition of pressure in a
solid is as follows: Pressure at a
point is the average of the
compressive stresses measured
in three perpendicular directions.
m
kg  2
N
kg
1 Pa  1 2  1 2 s  1
m
m
m  s2
lbf
lbf
1 psi  1 2  144 2
in
ft
Absolute and gauge pressure
-7.25 psig
Summary
1. Fluid mechanics is the study of forces and motions in fluids.
2. Fluids are substances that move continually when subjected to a shear force as long as
the force is applied. Solids are substances that deform slightly when subjected to a shear
force and then stop moving and permanently resist the force. (There are, however,
intermediate types of substances.)
3. Fluid mechanics is based on the principle of the conservation of matter, the first two laws
of thermodynamics, Newton’s laws of motion, and careful experiments.
4. Gases have weak intermolecular attractions and expand without limit. Liquids have much
stronger intermolecular attractions and can expand very little. With increasing
temperature and pressure, the differences between liquids and gases gradually
disappear.
5. Density is mass per unit volume. Specific gravity of liquids is density / (density of water at
). Specific gravity of gases is density / (density of air at the same T and P).
6. Viscosity is a measure of a fluid’s resistance to flow. Most simple fluids are represented
well by Newton’s law of viscosity. The exceptions (non-Newtonian fluids) are generally
complex mixtures, some of which are of great practical significance. Kinematic viscosity
is viscosity divided by density.
7. Surface tension is a measure of a liquid’s tendency to take a spherical shape, caused by
the mutual attraction of the liquid’s molecules.
8. Pressure is compressive force divided by area. It is the same in all directions for a fluid at
rest and practically the same in all directions for most moving fluids.
9. Much of fluid mechanics can be based either on force and momentum, or on energy. We
base most of fluid mechanics on energy.