chapter1_me2134
DESCRIPTION
Fluid Mechanics NUSTRANSCRIPT
1-1ME2134 Fluid Mechanics I
1 Introduction
ME2134 Fluid Mechanics I
1 Introduction
1-2ME2134 Fluid Mechanics I
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
1-3ME2134 Fluid Mechanics I
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!
1-4ME2134 Fluid Mechanics I
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”
1-5ME2134 Fluid Mechanics I
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
1-6ME2134 Fluid Mechanics I
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
1-7ME2134 Fluid Mechanics I
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
1-8ME2134 Fluid Mechanics I
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
1-9ME2134 Fluid Mechanics I
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
1-10ME2134 Fluid Mechanics I
1 Introduction
• Flight Vehicle Aerodynamics ME4231
1.2 Applications of Fluid Mechanics
Aircraft water tunnel dye flow visualization
1-11ME2134 Fluid Mechanics I
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)
1-12ME2134 Fluid Mechanics I
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)
1.2 Applications of Fluid Mechanics
/M U c
1-13ME2134 Fluid Mechanics I
1 Introduction
• Ground Vehicle Aerodynamics
1.2 Applications of Fluid Mechanics
Wind tunnel testing of car
Flow pattern behind car Flow pattern around bus
1-14ME2134 Fluid Mechanics I
1 Introduction
• Sports Aerodynamics
1.2 Applications of Fluid Mechanics
Flow over cricket ball Flow over tennis ball
Flow over golf ball Flow over bicycle Flow over swimmer
1-15ME2134 Fluid Mechanics I
1 Introduction
• Building Aerodynamics
1.2 Applications of Fluid Mechanics
Wind tunnel testing of buildings
Flow past circular cylinder
1-16ME2134 Fluid Mechanics I
1 Introduction
• Marine / Ocean Engineering, Naval Architecture, Hydrodynamics
1.2 Applications of Fluid Mechanics
Ships and water wavesComputer simulations
Submarine
Cargo ship
1-17ME2134 Fluid Mechanics I
1 Introduction
• Fluid Machinery ME21351.2 Applications of Fluid Mechanics
Pump impellers Turbine
Pelton wheel Wind turbine
1-18ME2134 Fluid Mechanics I
1 Introduction
• Aerospace Propulsion ME42311.2 Applications of Fluid Mechanics
Jet engine for commercial aircraft Rocket propulsion
Jet engine for fighter aircraft SR-71
1-19ME2134 Fluid Mechanics I
1 Introduction
• Marine Propulsion1.2 Applications of Fluid Mechanics
Marine propeller Computer simulation of marine propeller
Cavitation in marine propellers
1-20ME2134 Fluid Mechanics I
1 Introduction
1.2 Applications of Fluid Mechanics
Flames
Flame structure Detonation waves
• Chemically Reacting Flows and Combustion
1-21ME2134 Fluid Mechanics I
1 Introduction
• Civil Engineering Applications
1.2 Applications of Fluid Mechanics
Canals Aqueducts
Dams Drainage Systems
1-22ME2134 Fluid Mechanics I
1 Introduction
• Geophysical Fluid Dynamics: Atmosphere / Weather
1.2 Applications of Fluid Mechanics
WaterspoutTornado
Hurricane
Global climate
1-23ME2134 Fluid Mechanics I
1 Introduction
• Geophysical Fluid Dynamics: Ocean circulation, Tsunamis
1.2 Applications of Fluid Mechanics
Circulation system of the ocean
Tsunamis
Ocean surface wind
1-24ME2134 Fluid Mechanics I
1 Introduction
1.2 Applications of Fluid Mechanics• Environmental Fluid Mechanics
Atmospheric pollution
Plume dispersion
River pollution and sedimentation
Pollutant sedimentation and dispersion
1-25ME2134 Fluid Mechanics I
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
1-26ME2134 Fluid Mechanics I
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
1-27ME2134 Fluid Mechanics I
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
1-28ME2134 Fluid Mechanics I
1 Introduction
• Animal Locomotion: Swimming1.2 Applications of Fluid Mechanics
Animal locomotion
Fish swimming
Robo-tuna
1-29ME2134 Fluid Mechanics I
1 Introduction
• Piping Systems and other Industrial Applications ME2134
1.2 Applications of Fluid Mechanics
Pipe network Oil refinery
Water pipeline Computer simulation of pipe flow
1-30ME2134 Fluid Mechanics I
1 Introduction
• Microfluidics1.2 Applications of Fluid Mechanics
Integrated microfluidic bioprocessor
Microengine Microrocket
Inkjet printer
1-31ME2134 Fluid Mechanics I
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
1-32ME2134 Fluid Mechanics I
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
1-33ME2134 Fluid Mechanics I
1 Introduction
1.3 A SolidRobert Hooke (1635-1703)
Ut tensio sic vis
; :shear modulustn G G
1-34ME2134 Fluid Mechanics I
1 Introduction
1.3 What is a Fluid?
FLUID
Continuousdeformation
: viscosity
tn
d
dt
Sir Isaac Newton1642–1727)
1-35ME2134 Fluid Mechanics I
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
1-36ME2134 Fluid Mechanics I
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
1-37ME2134 Fluid Mechanics I
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
1-38ME2134 Fluid Mechanics I
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
1-39ME2134 Fluid Mechanics I
1 Introduction
• Density
1.4 Fluid as a Continuum
m
V
1-40ME2134 Fluid Mechanics I
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
1.4 Fluid as a Continuum
*limV V
m
V
1-41ME2134 Fluid Mechanics I
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”
1.4 Fluid as a Continuum
https://engineering.purdue.edu/~wassgren/applet/java/continuum/Index.html