intruduction to fluid dynamics

7/29/2019 Intruduction to Fluid Dynamics

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SME 1313 Fluid Mechanics I

CHAPTER 1INTRODUCTION

By

Ummikalsom Abidin

C24-316FKM, UTM


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Introduction

Fluid Mechanics

Fluid Statics- fluid at rest

- deals with forcesapplied by fluids at rest

Fluid Dynamics

- fluid in motion

Hydrostatic forceson submerged bodies

e.g dam, tanksstoring fluid,automation actuators

Buoyant forceapplied by fluids onsubmerged orfloating bodies

e.g ships,

submarines

Hydrodynamics

e.g liquid flow inpipes and openchannel(hydraulics),pumps,hydroturbine

s, water coolingsystem

Gas dynamics

e.g gas turbines,flow of air over abody(aerodynamics) aircraft, rockets,

automobiles


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Introduction

Naturally occuring flows Meteorology

Oceanography

Hydrology


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What is fluid?

Fluid is a substance that deforms continuously underthe application of a shear (tangential) stress nomatter how small the shear stress may be.

t1 t2

F F

t0

t2>t1>t0

(a) (b)

Behavior of (a) solid and (b) fluid, under the action of a constantshear


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What is fluid?

Fluids comprise the liquid and gas (orvapor) phases

Distinction between solid,liquid and gas

StrongestMolecules are relatively

fixed position

Solid

WeakestMolecules move about atrandom in the gas phaseGas

ModerateGroups of molecules moveabout each other in theliquid phase

Liquid

Intermolecularbonds

Atom Arrangement


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What is fluid?Normal to surface

Force acting on areadA

Tangent to surface

Fn

dA Ft

Normal stress: = Fn/dA

Shear stress: = 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


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No-slip Condition 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

velocity, V

Relative velocities of

fluid layers

Zero velocity atthe surface

Plate

A fluid flowing over stationary surface comes to a complete stopat the surface because of the no-slip condition


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Classification of Fluid Flows

Viscous vs. Inviscid Regions of Flow

Viscous Flow Region flows in which the frictional effect issignificant

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 theplate on both sides) and inviscid flow (away from the plate)


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Internal vs. External Flow Internal flow flows in which the fluid is completely

bounded by solid surface

e.g flow in a pipe or duct

Dominated by the influence of viscosity throughout the flowfield

External flow flows in which the fluid is unbounded over

solid surfaces e.g flow over a plate, wire, sphere object

Viscous effects are limited to boundary layers near solidsurfaces and to wake regions downstream of bodies

* Open-channel flow the flow of liquids in a duct in which the liquid ispartially filled and there is a free surface e.g rivers, irrigation channels


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Classification of Fluid Flows Compressible vs. Incompressible Flow

Incompressible Flow density of the fluid remains nearly

constant throughout

liquids, gases at low speeds

density changes of gas flows are under 5% or when Ma0.3 Mach number,

Ma = V = Speed of flow

c Speed of sound Ma=1 (Sonic), Ma1(Supersonic), Ma>>1

(Hypersonic)

(Speed of sound=346 m/s)


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Laminar vs. Turbulent Flow

In 1880s, Osborn Reynolds conducted an experiment to seeflow patterns

Tank arranged as above with a pipe taking water from the centre into which dye is injected through aneedle


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Classification of Fluid FlowsFilament of dye

Laminar (viscous)

Transitional

Turbulent


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Reynolds number,Re=ud

Laminar flow Re


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Natural (or unforced) vs. Forced Flow

Forced Flow fluid is forced to flow over a surface or in apipe 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) fluidrises and cooler (and thus denser) fluid falls

Schlieren image of a hot water (left) and ice water (right)in a glass


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Steady vs. Unsteady Flow

Steady Flow no change of fluid properties (velocity,pressure) at a point with time

Devices that are intended for continuous operation e.g

turbines, pumps, boilers, condensers

Unsteady Flow fluid properties change at a point with time

Transient used for developing flows

t1=5 s

V1=10 m/s

t2=10 s

V2=10 m/s

t1=5 s

V1=10 m/s

t2=10 sV2=11 m/s


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Uniform vs. Non-uniform Flow

Uniform Flow no change of fluid properties with locationover a specified region

Non-uniform Flow if at a given instant, fluid propertieschange with location over a specified region

V1=10 m/s V2=10 m/s

V1=10 m/s V2=11 m/s

or V=10 m/s

orV1=10 m/s

V2=10 m/s

1

2

2

1


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Classification of Fluid Flows Steady uniform flow

Conditions do not change with position and with time e.g flow ofwater in a pipe of constant diameter at constant velocity

Steady non-uniform flow Conditions change from point to point in the stream but do not

change with time e.g flow in tapering pipe with constant velocity atinlet, but velocity change along the length of the pipe toward theexit

Unsteady uniform flow At a given instant of time, the conditions at every point are the

same, but will change with time e.g pipe of constant diameterconnected to a pump pumping at a constant rate which is thenswitched off

Unsteady non-uniform flow Every condition of the flow may change from point to point and

with time at every point e.g waves in channel


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Classification of Fluid Flows One-, Two-, and Three-Dimensional Flows

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

The development of the velocity profile in a circular pipe, V=V(r,z) and thus theflow is 2-D in the entrance region, and becomes 1-D downstream when the velocity

profile fully develops and remain unchanged in the flow direction, V=V(r)

z

Developing velocity profile,V(r,z)

Fully developed velocityprofile, V(r)

r


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Classification of Fluid Flows The dimensionality of the flow also depends on the choice of

coordinate system and its orientation Rectangular coordinates, V(x,y,z)

Cylindrical coordinates, V(r,,z)

Higher dimensionality should be considered if only very highaccuracy is required


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Application Areas of Fluid Mechanics

Human body (Bio-fluid Mechanics) Cardiovascular system

Artificial heart

Pulmonary system Breathing machine

Building Water supply system

Sewerage system

Heating and air-conditioning

Aerodynamics forces and flow fields aroundstructure


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Automobiles Hydraulic brakes, power steering, automatic

transmission

Fuels line, fuel pump, fuel injectors

Lubrication systems

Cooling systems

Air-conditioning

Aerodynamics design

Aircraft Aerofoil design

Gas turbine


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Ship, submarines, hovercraft Hydrodynamics design

Buoyancy and stability

Industry Cooling of electronics

Automation system

Recreational Badminton shuttle and golf ball aerodynamics

Geophysical fluid dynamics Meteorology Oceanography


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System and Control Volumes 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)

SYSTEM

SURROUNDINGS

BOUNDARY


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System and Control Volumes Closed System (Control Mass)

Consists of a fixed amount of mass, and no work, can cross theboundary

Energy in the form of heat and work can cross the boundary

E.g piston-clinder device Open System (Control Volume)

Both mass and energy can cross the boundary

E.g compressor, turbine, nozzle, car radiator

Imaginaryboundary

Realboundary

CV

(a nozzle) CV

Imaginaryboundary

Imaginaryboundary


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Dimensions and Units Any physical quantity can be characterized by dimensions

Magnitude assigned to the dimensions are called units

Primary or fundamental dimensions

mole (mol)Amount of matter

candela (cd)Amount of light

ampere (A)Electric of current

kelvin (K)Temperature

second (s)Time

kilogram (kg)Mass

meter (m)Length

UnitDimension

The seven fundamental (or primary) dimensions and their units in SI


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Dimensions and Units Derived or secondary dimensions are dimensions obtained from

combination of primary dimensions

Most used derived dimensions


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SI Units Metric SI (from Le Systeme International dUnites) 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 forscientific and engineering work in most of the industrializednations


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SI Units

pico, p10-12

nano, n10-9

micro, 10-6

milli, m10-3

centi, c10-2

deci, d10-1

deka, da101hecto, h102

Kilo, k103

mega, M106

giga, G109tera, T10

12

PrefixMultiple

Standard prefixes in SI units


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Dimensional Homogeneity In engineering, all equations must be dimensionally

homogeneouswhere every term in an equation musthave the same unit


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Problem-Solving Technique Step 1:Problem Statement

State briefly and concisely (in your own words) theinformation given and the quantities to be found

Step 2:Schematic

Draw a schematic of the system or control volume to beused in the analysis.

Indicate any energy and mass interactions with thesurroundings

Listing the given information on sketch Step 3:Assumptions and Approximations

State any assumptions and approximations made to simplifythe problem to make it possible to obtain a solution


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Problem-Solving Technique Step 4:Physical Laws

Apply all the relevant basic physical laws and principle andreduce them to their simplest form by utilizing theassumptions made

Step 5:Properties Determine the unknown properties at known states

necessary to solve the problem from property relations ortables

Step 6:Calculations

Substitute the known quantities into the simplified relationsand perform the calculations to determine the unknown Pay attention to the units and unit cancellations Give appropriate number of significant digits


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Problem-Solving Technique Step 7:Reasoning, Verification, and Discussion

Check to make sure that the results obtained are reasonableand intuitive and verify the validity of the questionableassumptions

Repeat the calculations that resulted in unreasonable values

intruduction to fluid dynamics

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