CE-205: Fluid Mechanics Lecture -1 CE-205: Fluid Mechanics Lecture -1

CE-205: Fluid MechanicsLecture - 1CE-205: Fluid MechanicsLecture - 1

Deepashree Raje

Dept of Civil Engineering, IIT Bombay

FLUID MECHANICS: CE 205(1st Semester 2013-2014), LCC 11

Course Instructors: 1. Prof. B.S. Pani (Section S1, Roll No. 120040001 to 40060)

2. Prof. Deepashree Raje (Section S2, Roll No. 120040061 to 40120) Room no 11, Ground Floor, Civil EngineeringPhone-7337 (office), Email- [email protected]

Mon: 8.30-9.25 am, Tue: 9.30-10.25 pm, Thu: 10.30-11.25 am

Evaluation scheme:i. 2 Quizzes, 10 marks eachii. Mid-term examination- 30 marksiii. End-sem examination- 50 marksNO re-exams will be given.Attendance: Strictly compulsory as per the institute norms. DX grades will

be awarded to those whose attendance is below 80%. Biometric attendance

Deepashree Raje CE-205

mailto:[email protected]

Course content• Fundamental Concepts of Fluid Flow: Fundamental definitions, Flowcharacteristics, Classification of fluids, Fluid properties• Fluid Statics: Fluid pressure, Forces on solid surfaces, Buoyant forces.• Kinematics of Fluid Flow: Equations for acceleration, Continuityequation, Irrotational and rotational flow, Potential and stream functions.• Dynamics of Fluid Flow: Finite control volume analysis, Euler andBernoulli’s theorems, Impulse momentum theory, Applications of energyand momentum equations.• Laminar and Turbulent Flows: Types of flow, Reynolds experiment,Laminar flow between parallel plates, Laminar flow in pipes, Turbulentflow in pipes.• Navier-Stokes Equations: Introduction to Navier-Stokes equations,Exact solutions for simple cases of flow, Plane Poiseuille flow, Coute flow,Stokes flow and porous media flow.• Boundary Layer Theory: Concepts of boundary layer, Flowseparation, Circulation, Drag and lift on immersed bodies.


Texts / References• V.L. Streeter and E.B. Wylie, Fluid Mechanics, McGrawHill, 1998.• V.Gupta and S.K. Gupta, Fluid Mechanics and itsapplications, New Age Publishers,2011• Granger, R.A., Fluid Mechanics, Publishing, , 1985.• J.F. Douglas, J.M. Gasiorek, and J.A. Swaffield, FluidMechanics, Addison-Wesley, 1999.• I.H. Shames, Mecahnics of Fluids, , 1992.• R.L. Daugherthy, J.B. Franzini and E.J. Finnemore, FluidMechanics with Engineering Applications, , 1985.• A.K. Jain, Fluid Mechanics, Khanna Publishers, , 1998.• L.P.N. Modi and S.M. Seth, Hydraulics and FluidMechanics, Standard Book House, , 2002.


Expectations from students

• Class attendance

• Punctuality

• Student participation (raise hands and wait to be called on)

• Seek help when needed – after class / email appt

• Offer feedback


How to do well in FM• Statistics show UG students find FM among the most

difficult subjects

• Keep up with what is being covered in class

• FM is a visual subject by nature

– Try to make use of visual aids in learning

– Interactive web tutorials, figures, graphs

• Notes are not enough - read a few of the referencetexts• each book differs in the way the material is presented

• Solve as many practice problems, tutorial sheets asyou can


Why study Fluid Mechanics?• Direct or indirect involvement in nearly all areas of Civil

Engineering• Fluids are directly handled in

– Water distribution / sewerage networks; – Hydraulic design of water/sewage treatment works– Dams– Irrigation canals– Pumps and Turbines– Sea and river flood defences

• Analysis of fluid mechanics required in – Flow of air around buildings– Air pollution dispersion and control – Bridge piers in rivers– Ground-water flow


Contents

• Introduction

• Examples

• History

• Fluid properties : viscosity


Introduction

• Fluid mechanics is a study of the behavior offluids, either at rest (fluid statics) or in motion(fluid dynamics).

• Analysis is based on the fundamental laws ofmechanics

– Continuity of mass and energy, relation with forceand momentum.

• Understanding of the properties and behaviorof fluids at rest and in motion is veryimportant in engineering.


Fluid mechanics in real life

• This is a satellite picture of ahurricane

• The atmospheric flow fieldis modeled as a “Rankinevortex”

• The Rankine vortex model isa circular wind flow inwhich– an inner circular region

about the origin is in solidrotation (a forced vortex inthe central core)

– the outer region is free ofvorticity, the speed beinginversely proportional tothe distance from the origin(a free vortex).



• This is a visualisation of blood flow through the brain

• To model this flow we use equations from fluid mechanics incomputational fluid dynamics (CFD)– predict the likelihood of stroke in the short term

– risk associated with surgical procedures such as carotid endarterectomy



• Laminar and turbulent flows



• Flow field around an airfoil – aeroplane wing

• How do we determine the thrust needed to be generatedby the aircraft engine?


Why study fluid mechanics

• Understanding flow patterns in tornadoes andhurricanes

• Predicting flow rates in rivers

• Fluid mechanics of blood flow through heart

• Design of aircraft or sailboat

• And several other..

• Almost all fields of engineering require knowledge offluid mechanics


History of fluid mechanics• Archimedes (250 BC): Buoyancy principle, Principles of hydrostatics

• Leonardo da Vinci (1452-1519): Derived the equation of conservation of mass in 1D steady flow

• Isaac Newton (1643-1727): Postulated his laws of motion and the law of viscosity of linear fluids (now called Newtonian)

• Bernoulli, Euler, Lagrange, Laplace (18th century mathematicians): Solutions of frictionless-flow problems

• Chézy, Pitot, Hagen, Poiseuille, Darcy, Manning and Weisbach : Experimentalists who produced data on a variety of flows- open channels, ship resistance, pipe flows, waves, and turbines

• Lord Rayleigh (1842-1919) : Dimensional analysis

• Osborne Reynolds (1842-1912): Classic pipe experiment which showed the importance of the dimensionless Reynolds number

• Navier (1785-1836) and Stokes (1819-1903): Viscous-flow theory, successfully added viscous terms to the governing equations of motion.

• Ludwig Prandtl (1904): Boundary layer theory


IntroductionWhat is “Fluid Mechanics”?

- Study of fluids and forces acting on that fluid

- Fluid statics : fluids at rest, fluid dynamics : fluids in motion

What is a fluid?

- A substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress.

- Solids acquire an equilibrium deformation under shear stress

- Fluid resists shear force by acquiring an equilibrium rate of deformation


Fluid properties• Viscosity

– Property which characterizes resistance to shear forces

– The resistance is caused by intermolecular friction exertedwhen layers of fluids attempt to slide by one another.

– Shear stress developed is proportional to the rate of shear strain

• This is in contrast to solids, where shear stress ∝ shear strain

– Shear stresses developed if particles of fluid move relative toone another, i.e. adjacent particles have different velocities.

– If fluid velocity is the same at every point then there is no shearstress produced: the particles have zero relative velocity.


t

Fluid properties

• No-slip condition : Presence of solid surfaceaffects fluid flow

– Exptl measurements show that fluid in directcontact with a solid has zero velocity relative tothe surface

– This is caused due to viscosity of the fluid

– Leads to development of a velocity profile as afluid flows over a solid surface

• Boundary layer formed adjacent to wall

• Viscous effects in BL, large velocity gradient


Fluid properties


Fluid properties : viscosity

• Consider flow between two parallel plates

• The lower plate is stationary while the upper moves withvelocity U.

• No-slip condition: Fluid particles in contact with solid surfacemove with velocity of surface

• The fluid velocity u is then a function of y.


0 at 0

at

u y

u U y h

Fluid properties : viscosity• Rate of deformation/shear strain rate:

• Newton’s law of viscosity: Shear stress which opposes shear of fluid is proportional to rate of shear strain


(tan )

1( )

t t

duu y t u t

t y dy

du

dy

du

t dy

du

dy

Fluid properties : viscosity• μ is called the dynamic viscosity of the fluid.

• Newtonian fluids: Shear stress varies linearly with rate of shear strain– Eg. Water, milk, sugar solution, petrol

• Non-Newtonian fluids: Shear stress does not vary linearly with rate of shear strain– Eg. Blood, grease, colloids, paint


Fluid properties : viscosity• Plastic: At low stresses, behaves as rigid body. Beyond

yield shear stress, flows as viscous fluid.– Bingham plastic: Ideal plastic , beyond yield stress, the

shear stress is directly proportional to shear rate as forNewtonian fluids e.g. mud flow, toothpaste, mayonnaise.

• Pseudo-plastic (shear thinning) : Viscosity decreaseswith increased shear rate e.g. colloidial substances likepaint, slurries like cement, ketchup, quicksand.

• Dilatant substances (shear thickening) : Viscosityincreases with increased shear rate e.g. wet sand,starch suspension.

• Ideal fluid: A fluid which is assumed to have noviscosity.


Fluid properties : viscosity

Depending on how viscosity changes with time the flowbehaviour is also characterised as:

• Thixotropic (time thinning) : Viscosity decreases withlength of time shear force is applied e.g. paint,yoghurt.

• Rheopectic substances (time thickening) : Viscosityincreases with length of time shear force is appliede.g. gypsum paste


Dynamic Viscosity

• Units of dynamic viscosity:

– SI system : N-s/m2, Pa-s or kg/m-s

– CGS system: 1 poise (P) = 1 g/cm-s = 100 centipoise (cP)


LiquidAbsolute Viscosity at Room Temperature(Pa s)

Air 10-5

Water 10-3

Olive Oil 10-1

Glycerol 100

Liquid Honey 101

Golden Syrup 102

Glass 1040

Kinematic viscosity• Kinematic viscosity is the ratio of absolute or dynamic

viscosity to density of fluid

• In the SI-system the theoretical unit is m2/s or Stoke (St)1 St = 10-4 m2/s

• Viscosity of a fluid is almost indep of pressure, but highlytemperature dependent

• For a liquid - the kinematic viscosity decreases with highertemperature (why?)

• For a gas - the kinematic viscosity increases with highertemperature (why?)

• Typical values: Water =1.14 x 10-6 m2/s , Air =1.46 x10-5 m2 /s


CE-205: Fluid Mechanics Lecture -1 CE-205: Fluid Mechanics Lecture -1

Documents

Transcript of CE-205: Fluid Mechanics Lecture -1 CE-205: Fluid Mechanics Lecture -1