chapter1_me2134

1-1ME2134 Fluid Mechanics I

1 Introduction

ME2134 Fluid Mechanics I

1 Introduction


1 Introduction

Organisation

• This 4-MC module will be taught by– Nhan Phan-Thien, 11 Aug – 19 Sept (6 weeks) (called me Nhân)

• Rm EA-02-01 Tel: 6601-2054• [email protected] (email is the best source of getting help)

– TT Lim, 22 Sept – end of Sem 1– 3 hrs of lectures per week, Monday 10-12pm (45 mins + 10 mins break +

45 min), Tues 12-1pm, cells mob devices off please – Tutorials start from 2nd week, 25 Aug, every 2nd week, Tutors: Nhan

Phan-Thien, TT Lim, Yao Jie, Chia Poo Hiang, group allocation from Department

– 2 labs from 2nd week, 25 Aug, Coordinators: Shu Chang & R Jaiman (20% final mark) – time table & group allocation from Department

– Final exam (80%)– Lab reports (20%) are VERY important! They MUST be handed in at

the end of the relevant Lab sessions – no exception allowed


1 Introduction

Is there any fun in 2nd year?• Best time of your life!• Life is exploring, enquiring,

experiencing and learning

• ME2134 is traditionally a 2nd year filter, along with Thermo

• You are an engineering in-training – have some self discipline, time management and keep an eye on your target!


1 Introduction

Outline of Contents• Introduction• Fluid Properties• Fluid Statics• Fluid Dynamics• Equilibrium of Moving Fluids• Momentum and its Applications• Dimensional Analysis and Similitude• Analysis of Pipe Flows

• Main Ideas Will Be Tagged “KEY IDEA”


1 Introduction

References

Lots of suitable references, take your pick:

• M.C. Potter and D.C. Wiggert Mechanics of Fluids, 2nd ed., Prentice-Hall International, 1997

• A.J. Smits A Physical Introduction to Fluid Mechanics, John Wiley, 2000

• V.L. Streeter, E.B. Wylie and K.W. Bedford Fluid Mechanics, 9th ed., McGraw Hill, 1998

• F.M. White Fluid Mechanics, 6th ed., McGraw Hill, 2008• Supplied lecture notes & tutorials may be sufficient, and can be

downloaded from IVLE• Lab manuals are also downloadable from IVLE


1 Introduction

Learning Objectives in this Chapter:

To understand:

• the concept of a fluid

• the wide scope of fluid mechanics

• the concept of a continuum and the continuum assumption

• The concept of a Newtonian fluid

1 Introduction


1 Introduction

Introductory Remarks

• What is a fluid?– Solid can support a (shear) stress acting on its surfaces – fluid

or gas deform (flow) continuously and permanently

– Solid can hold its shape independently of its container – a fluid will occupy a definite volume in the container, whereas a gas fills up the whole container volume; when there are gases & liquids present the surfaces separate the two phases are called free surfaces

KEY IDEAS: fluids cannot support a shear stress


1 Introduction

• Fluid Mechanics is the study of the behaviour of fluids at rest (fluid statics) or in motion (fluid dynamics)

• Fluid Mechanics can be divided into several categories:Hydrodynamics: study of flows of incompressible fluids (water,

gases at low speeds)Hydraulics: study of liquid flows in pipes and open channelsGas dynamics: study of flows of gasesAerodynamics: study of flow of gases (air) over bodies (aircraft,

rockets, automobiles) at low and high speeds

MeteorologyOceanographyHydrology

Rheology or viscoelastic fluid mechanics: study of flows and deformation – the focus is on non-Newtonian fluids, or fluids with microstructures

1.1 Introductory Remarks

Naturally occurring flows


1 Introduction

• Why study Fluid Mechanics?– Fluids are essential to our everyday lives– Air and water are two very important fluids:

• ~70% of human body is made up of water• ~70% of earth’s surface is covered by

water• ~90% of earth’s atmosphere extends to an

altitude of 16 km above earth’s surface• Laid in one single line, our capillaries and

veins could be ~100000 km!

1.2 Applications of Fluid Mechanics

Earth Earth’s atmopshereRed Blood Cells


1 Introduction

• Flight Vehicle Aerodynamics ME4231


Aircraft water tunnel dye flow visualization


1 Introduction

• Low Speed Aerodynamics ME42311.2 Applications of Fluid Mechanics

Aerofoil at low angle of attack Aerofoil at high angle of attack

Smoke flow visualization of wing tip vortices Wing tip vortices

/M U c

Ernst Mach (1838–1916)


1 Introduction

• High Speed Aerodynamics ME3232, ME4231

Bullet at Mach 1.5

F/A-18 Hornet

Airplane model at Mach 1.1

Sphere (Mach 5.7)Sphere (Mach 1.53)


/M U c


1 Introduction

• Ground Vehicle Aerodynamics


Wind tunnel testing of car

Flow pattern behind car Flow pattern around bus


1 Introduction

• Sports Aerodynamics


Flow over cricket ball Flow over tennis ball

Flow over golf ball Flow over bicycle Flow over swimmer


1 Introduction

• Building Aerodynamics


Wind tunnel testing of buildings

Flow past circular cylinder


1 Introduction

• Marine / Ocean Engineering, Naval Architecture, Hydrodynamics


Ships and water wavesComputer simulations

Submarine

Cargo ship


1 Introduction

• Fluid Machinery ME21351.2 Applications of Fluid Mechanics

Pump impellers Turbine

Pelton wheel Wind turbine


1 Introduction

• Aerospace Propulsion ME42311.2 Applications of Fluid Mechanics

Jet engine for commercial aircraft Rocket propulsion

Jet engine for fighter aircraft SR-71


1 Introduction

• Marine Propulsion1.2 Applications of Fluid Mechanics

Marine propeller Computer simulation of marine propeller

Cavitation in marine propellers


1 Introduction


Flames

Flame structure Detonation waves

• Chemically Reacting Flows and Combustion


1 Introduction

• Civil Engineering Applications


Canals Aqueducts

Dams Drainage Systems


1 Introduction

• Geophysical Fluid Dynamics: Atmosphere / Weather


WaterspoutTornado

Hurricane

Global climate


1 Introduction

• Geophysical Fluid Dynamics: Ocean circulation, Tsunamis


Circulation system of the ocean

Tsunamis

Ocean surface wind


1 Introduction

1.2 Applications of Fluid Mechanics• Environmental Fluid Mechanics

Atmospheric pollution

Plume dispersion

River pollution and sedimentation

Pollutant sedimentation and dispersion


1 Introduction

• Bio-Fluid Mechanics1.2 Applications of Fluid Mechanics

Carotid bifurcation models with stenosis Flow through a bifurcation model

Blood flow through damaged artery Computer simulation of blood flow


1 Introduction

1.2 Applications of Fluid Mechanics• Animal Locomotion: Flight of Birds, Bats

Wing tunnel testing of birds

Wind tunnel testing of bat Formation flight of birds


1 Introduction

• Animal Locomotion: Insect Flight1.2 Applications of Fluid Mechanics

Tethered fly

Robotic fly Computer simulation of insect flight

Wind tunnel testing of dragonfly


1 Introduction

• Animal Locomotion: Swimming1.2 Applications of Fluid Mechanics

Animal locomotion

Fish swimming

Robo-tuna


1 Introduction

• Piping Systems and other Industrial Applications ME2134


Pipe network Oil refinery

Water pipeline Computer simulation of pipe flow


1 Introduction

• Microfluidics1.2 Applications of Fluid Mechanics

Integrated microfluidic bioprocessor

Microengine Microrocket

Inkjet printer


1 Introduction

Key Idea: Shear stressis force tangential

to surface

• Recall: Stress force per unit area• Fluid at rest normal stress is called pressure

1.3 State of stresses on a fluid surface

n

nn

tn

Key Idea: Pressure is force normal to surface


1 Introduction

• What distinguishes a solid from a fluid?A fluid is a substance which deforms continuously when

acted on by a shear stress of any magnitude

1.3 What is a Fluid?

; :shear modulustn G G


1 Introduction

1.3 A SolidRobert Hooke (1635-1703)

Ut tensio sic vis

; :shear modulustn G G


1 Introduction

1.3 What is a Fluid?

FLUID

Continuousdeformation

: viscosity

tn

d

dt

Sir Isaac Newton1642–1727)


1 Introduction

• A solid deforms when a shear stress is applied, but its deformation does not continue to increase with respect to time

• Deformation of fluid element continues to increase as long as shear force is applied to upper plate

Key Idea: Hookean solids: (G: shear modulus)

Key Idea: Newtonian fluids:

is known as the rate of shearing strain or strain rate

• Any fluid that does not obey the Newtonian law is called non-Newtonian fluid (or simply viscoelastic fluid)

1.3 Summary

tn G

, : viscositytn

d

dt

d d x dx u

dt dt y y dt y


1 Introduction

Non-Newtonian Fluids

A fluid deforms continuously and permanently under the application of a shearing stress, however small

• This definition does not address how fast the shearing force is applied, relative to the response time (relaxation time) of the fluid

• varies from ~10-13 s (water) to ~103 s (polymer solutions and melts). With this new physical constant one has a new dimensionless group, called the Deborah number

T is the observation time scale (experimental time span)• “The mountains flowed before the Lord” – Prophetess Deborah (Old

Testament)• “Everything is in the state of flux” - Confucius

De T


1 Introduction

Non-Newtonian Fluids

• There is no clear distinction between fluids and solids – it’s a matter of time scales

• When De<<1, one has a (Newtonian) liquid-like behaviour• When De>>1, a solid-like behaviour• A non-Newtonian, or viscoelastic fluid for 0 < De <

Key Idea: Low De: fluid-like, large De: solid-like behaviour

• When one must walk on water, one has to walk very, very fast!

• Rheology is the study of flow and deformation

De T


1 Introduction

• In almost all Fluid Mechanics applications, it is convenient to disregard the molecular nature of the fluid; instead we consider the fluid to be a continuous, homogeneous medium (continuum assumption), capable of infinitely sub-division

• A fluid volume V can be shrunk down to infinitesimally small in size, and yet the fluid in this volume still have a definite property, down to a mathematical point

Key Idea: Continuum assumption

– Each fluid property is assumed to have a definite value at every point in space

– Breaks down when size of system is comparable to mean free path of molecules

1.4 Fluid as a Continuum


1 Introduction

• Density


m

V


1 Introduction

• δV < δV* too few molecules to yield statistically meaningful value for ρ

• δV must be sufficiently large to yield statistically meaningful and reproducible result for ρ and yet small enough to be regarded as a “point”

• δV* 10-9 mm3 for all liquids and for all gases at atmospheric pressure (mean free path of typical gases)

• Density at “point” C thus defined as


*limV V

m

V


1 Introduction

• Physical volumes much larger than 10-9 mm3 in most engineering problems density is essentially a point function fluid properties assumed to vary continuously throughout fluid continuum assumption

• Continuum assumption is valid as long as characteristic length of system is much larger than mean free path of molecules

• With continuum assumption, the variations in fluid properties are smooth so that differential calculus can be used

• A fluid particle is a collection of a sufficiently large number of fluid molecules such that the continuum assumption is valid, but it is also small enough to be regarded as a “point”


https://engineering.purdue.edu/~wassgren/applet/java/continuum/Index.html

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