CHAPTER 1
INTRODUCTION
By
Ummikalsom Abidin
C24-316
FKM, UTM
SME 1313 Fluid Mechanics I
Introduction
Fluid Mechanics
Fluid Statics
-
fluid at rest
-
deals with forces
applied by fluids at rest
Buoyant force
applied by fluids on
submerged or
floating bodies
e.g ships,
submarines
Fluid Dynamics
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Hydrostatic forces
on submerged bodies
e.g dam, tanks
storing fluid,
automation actuators
fluid in motion
Hydrodynamics
Gas dynamics
e.g liquid flow in
pipes and open
channel
(hydraulics),
pumps,hydroturbine
s, water cooling
system
e.g gas turbines,
flow of air over a
body
(aerodynamics) –
aircraft, rockets,
automobiles
SME 1313 Fluid Mechanics I
Introduction
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Naturally occuring flows
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Meteorology
Oceanography
Hydrology
SME 1313 Fluid Mechanics I
What is fluid?
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Fluid is a substance that deforms continuously under
the application of a shear (tangential) stress no
matter how small the shear stress may be.
F
F
t0
t1
t2
t2>t1>t0
(a)
(b)
Behavior of (a) solid and (b) fluid, under the action of a constant
shear
SME 1313 Fluid Mechanics I
What is fluid?
„
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Fluids comprise the liquid and gas (or
vapor) phases
Distinction between solid,liquid and gas
Atom Arrangement
Solid
Liquid
Gas
Intermolecular
bonds
Molecules are relatively
fixed position
Strongest
Groups of molecules move
about each other in the
liquid phase
Moderate
Molecules move about at
random in the gas phase
Weakest
SME 1313 Fluid Mechanics I
What is fluid?
Normal to surface
Force acting on area
Fn
dA
Tangent to surface
dA
Ft
Normal stress: σ = Fn/dA
Shear stress: ι = Ft/dA
The normal stress and shear stress at the surface of a fluid element. For fluids at
rest, the shear stress is zero and the pressure is the only normal stress
SME 1313 Fluid Mechanics I
No-slip Condition
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A fluid in direct contact with a solid “sticks” to the surface due
to viscous effects, and there is no slip.
The flow region adjacent to the wall in which the viscous effects
(and thus the velocity gradients) are significant is called
boundary layer.
Uniform approach
Relative velocities of
fluid layers
velocity, V
Zero velocity at
the surface
Plate
A fluid flowing over stationary surface comes to a complete stop
at the surface because of the no-slip condition
SME 1313 Fluid Mechanics I
Classification of Fluid Flows
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Viscous vs. Inviscid Regions of Flow
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Viscous Flow Region – flows in which the frictional effect is
significant
Inviscid Flow Region – viscous forces are negligibly small
compared to inertial or pressure forces
Inviscid flow region
Viscous flow
region
Inviscid flow region
The flow of an originally uniform fluid stream over a flat plate, and the regions of viscous flow (next to the
plate on both sides) and inviscid flow (away from the plate)
SME 1313 Fluid Mechanics I
Classification of Fluid Flows
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Internal vs. External Flow
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Internal flow – flows in which the fluid is completely
bounded by solid surface
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e.g flow in a pipe or duct
Dominated by the influence of viscosity throughout the flow
field
External flow – flows in which the fluid is unbounded over
solid surfaces
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e.g flow over a plate, wire, sphere object
Viscous effects are limited to boundary layers near solid
surfaces and to wake regions downstream of bodies
* Open-channel flow – the flow of liquids in a duct in which the liquid is
partially filled and there is a free surface e.g rivers, irrigation channels
SME 1313 Fluid Mechanics I
Classification of Fluid Flows
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Compressible vs. Incompressible Flow
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Incompressible Flow – density of the fluid remains nearly
constant throughout
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Compressible Flow – density changes of the fluid is
significant
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liquids, gases at low speeds
density changes of gas flows are under 5% or when Ma<0.3
gases at high speeds
density changes of gas flows are above 5% or when Ma>0.3
Mach number,
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(Speed of sound=346 m/s)
Ma = V = Speed of flow
c Speed of sound
Ma=1 (Sonic), Ma<1 (Subsonic), Ma>1(Supersonic), Ma>>1
(Hypersonic)
SME 1313 Fluid Mechanics I
Classification of Fluid Flows
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Laminar vs. Turbulent Flow
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In 1880s, Osborn Reynolds conducted an experiment to see
flow patterns
Tank arranged as above with a pipe taking water from the centre into which dye is injected through a
needle
SME 1313 Fluid Mechanics I
Classification of Fluid Flows
Filament of dye
Laminar (viscous)
Transitional
SME 1313 Fluid Mechanics I
Turbulent
Classification of Fluid Flows
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Reynolds number,
Re =ρud
µ
Laminar flow
Transitional flow
Turbulent flow
Re<2000
2000<Re<4000
Re>4000
SME 1313 Fluid Mechanics I
Classification of Fluid Flows
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Natural (or unforced) vs. Forced Flow
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Forced Flow – fluid is forced to flow over a surface or in a
pipe by external means such as pump or a fan
Natural Flow – any fluid motion is due to natural means such
as buoyancy effect, where warmer (and thus lighter) fluid
rises and cooler (and thus denser) fluid falls
Schlieren image of a hot water (left) and ice water (right)
in a glass
SME 1313 Fluid Mechanics I
Classification of Fluid Flows
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Steady vs. Unsteady Flow
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Steady Flow – no change of fluid properties (velocity,
pressure) at a point with time
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„
Devices that are intended for continuous operation e.g
turbines, pumps, boilers, condensers
t1=5 s
t2=10 s
V1=10 m/s
V2=10 m/s
Unsteady Flow – fluid properties change at a point with time
„
Transient – used for developing flows
t1=5 s
V1=10 m/s
SME 1313 Fluid Mechanics I
t2=10 s
V2=11 m/s
Classification of Fluid Flows
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Uniform vs. Non-uniform Flow
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Uniform Flow – no change of fluid properties with location
over a specified region
1
2
V1=10 m/s
„
V2=10 m/s
or
V=10 m/s
Non-uniform Flow – if at a given instant, fluid properties
change with location over a specified region
V2=10 m/s
1
2
V1=10 m/s
V2=11 m/s
or
SME 1313 Fluid Mechanics I
V1=10 m/s
Classification of Fluid Flows
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Steady uniform flow
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Steady non-uniform flow
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Conditions change from point to point in the stream but do not
change with time e.g flow in tapering pipe with constant velocity at
inlet, but velocity change along the length of the pipe toward the
exit
Unsteady uniform flow
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Conditions do not change with position and with time e.g flow of
water in a pipe of constant diameter at constant velocity
At a given instant of time, the conditions at every point are the
same, but will change with time e.g pipe of constant diameter
connected to a pump pumping at a constant rate which is then
switched off
Unsteady non-uniform flow
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Every condition of the flow may change from point to point and
with time at every point e.g waves in channel
SME 1313 Fluid Mechanics I
Classification of Fluid Flows
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One-, Two-, and Three-Dimensional Flows
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1-D Flow – flow parameters (such as velocity, pressure, depth)
vary in one primary dimensions
2-D Flow - flow parameters vary in two primary dimensions
3-D Flow - flow parameters vary in three primary dimensions
Developing velocity profile,
V(r,z)
Fully developed velocity
profile, V(r)
r
z
The development of the velocity profile in a circular pipe, V=V(r,z) and thus the
flow is 2-D in the entrance region, and becomes 1-D downstream when the velocity
profile fully develops and
remain
in theI flow direction, V=V(r)
SME
1313 unchanged
Fluid Mechanics
Classification of Fluid Flows
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The dimensionality of the flow also depends on the choice of
coordinate system and its orientation
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Rectangular coordinates, V(x,y,z)
Cylindrical coordinates, V(r,θ,z)
Higher dimensionality should be considered if only very high
accuracy is required
SME 1313 Fluid Mechanics I
Application Areas of Fluid Mechanics
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Human body (Bio-fluid Mechanics)
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Cardiovascular system
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Pulmonary system
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Artificial heart
Breathing machine
Building
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Water supply system
Sewerage system
Heating and air-conditioning
Aerodynamics forces and flow fields around
structure
SME 1313 Fluid Mechanics I
Application Areas of Fluid Mechanics
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Automobiles
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Hydraulic brakes, power steering, automatic
transmission
Fuels line, fuel pump, fuel injectors
Lubrication systems
Cooling systems
Air-conditioning
Aerodynamics design
Aircraft
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Aerofoil design
Gas turbine
SME 1313 Fluid Mechanics I
Application Areas of Fluid Mechanics
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Ship, submarines, hovercraft
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Industry
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Cooling of electronics
Automation system
Recreational
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Hydrodynamics design
Buoyancy and stability
Badminton shuttle and golf ball aerodynamics
Geophysical fluid dynamics
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Meteorology
Oceanography SME 1313 Fluid Mechanics I
System and Control Volumes
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System – quantity of matter or a region in space chosen for
study
Surroundings – mass or region outside the system
Boundary – Real or imaginary surface that separates the system
from its surroundings (fixed or movable)
SURROUNDINGS
SYSTEM
BOUNDARY
SME 1313 Fluid Mechanics I
System and Control Volumes
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Closed System (Control Mass)
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Consists of a fixed amount of mass, and no work, can cross the
boundary
Energy in the form of heat and work can cross the boundary
E.g piston-clinder device
Open System (Control Volume)
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Both mass and energy can cross the boundary
E.g compressor, turbine, nozzle, car radiator
Imaginary
boundary
CV
(a nozzle)
Imaginary
boundary
CV
Real
boundary SME 1313 Fluid Mechanics I
Imaginary
boundary
Dimensions and Units
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Any physical quantity can be characterized by dimensions
Magnitude assigned to the dimensions are called units
Primary or fundamental dimensions
Dimension
Unit
Length
meter (m)
Mass
kilogram (kg)
Time
second (s)
Temperature
kelvin (K)
Electric of current
ampere (A)
Amount of light
candela (cd)
Amount of matter
mole (mol)
The seven fundamental (or primary) dimensions and their units in SI
SME 1313 Fluid Mechanics I
Dimensions and Units
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Derived or secondary dimensions are dimensions obtained from
combination of primary dimensions
SME 1313 Fluid Mechanics I
Most used derived dimensions
SI Units
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Metric SI (from Le Systeme International d’Unites) or
International System
SI system was produced by General Conference of Weights and
Measures in 1960
SI is a simple and logical system and widely being used for
scientific and engineering work in most of the industrialized
nations
SME 1313 Fluid Mechanics I
SI Units
Multiple
Prefix
1012
tera, T
109
giga, G
106
mega, M
103
Kilo, k
102
hecto, h
101
deka, da
10-1
deci, d
10-2
centi, c
10-3
milli, m
10-6
micro, µ
10-9
nano, n
10-12
pico, p
Standard
in SI units
SME
1313 prefixes
Fluid Mechanics
I
Dimensional Homogeneity
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In engineering, all equations must be dimensionally
homogeneous where every term in an equation must
have the same unit
SME 1313 Fluid Mechanics I
Problem-Solving Technique
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Step 1:Problem Statement
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Step 2:Schematic
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State briefly and concisely (in your own words) the
information given and the quantities to be found
Draw a schematic of the system or control volume to be
used in the analysis.
Indicate any energy and mass interactions with the
surroundings
Listing the given information on sketch
Step 3:Assumptions and Approximations
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State any assumptions and approximations made to simplify
the problem to make it possible to obtain a solution
SME 1313 Fluid Mechanics I
Problem-Solving Technique
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Step 4:Physical Laws
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Step 5:Properties
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Apply all the relevant basic physical laws and principle and
reduce them to their simplest form by utilizing the
assumptions made
Determine the unknown properties at known states
necessary to solve the problem from property relations or
tables
Step 6:Calculations
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Substitute the known quantities into the simplified relations
and perform the calculations to determine the unknown
Pay attention to the units and unit cancellations
Give appropriate number of significant digits
SME 1313 Fluid Mechanics I
Problem-Solving Technique
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Step 7:Reasoning, Verification, and Discussion
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Check to make sure that the results obtained are reasonable
and intuitive and verify the validity of the questionable
assumptions
Repeat the calculations that resulted in unreasonable values
SME 1313 Fluid Mechanics I