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Mechanics of Fluid FlowMechanics of Fluid Flow

Prof. T. I. Eldho ,Prof. T. I. Eldho ,Prof. T. I. Eldho ,Prof. T. I. Eldho ,

# De artment of Civil En ineerin# De artment of Civil En ineerin

Indian Institute of Technology Bombay.Indian Institute of Technology Bombay.

Ob ectives

• Introduce Fluid Mechanics & establish its

relevance in Civil Engg.

• Develop the fundamental principles

• Demonstrate how these are used in En .

• Course consists of 40 lectures presenting the

concepts, theory & applications



Course ContentsCourse Contents

Topics covered by the course may include:

•E uation of motion and continuit inte ral

equations of momentum and energy and controlvolume approach

•Laminar flow in pipes and channels

•Elements of boundary layer concepts,- -

•Turbulent flow in pipes and channels

• – ,dispersion in open channels, transport

mechanism & solutions



Course Contents –Contd.

•Unsteady flow in open channels, surge in

c anne s

• Transients in closed conduits, water hammer

Assessment criteria for CE 731

•The final assessment is based on end-of-semesterexamination (50%), two test papers (one each –

second week of September and end semester

examinations – last week of October course ro ect

and 4-6 assignments cum tutorials and overall class

performance. The end-of-semester examination will

.



References

•Bruce R. Munson, D.F. Young, T.H. Okiishi, Fundamentals of

Fluid Mecahnics, John Wiley, New York, 2002.

• aug er y, . ., ranz n , . ., nnemore, . . u

Mechanics with Engineering Applications, McGraw Hill, NewYork, 1985.

, . . , , . . , , . ., ,

Addison-Wesley, Harlow 1999.

•Granger, R.A., Fluid Mechanics, CBS College Publishing, New, .

•Streeter, V.L. ,Wylie, E. Benjamin , Fluid Mechanics ,

McGraw-Hill, London, 1998.

•Shames, I.H., Mecahnics of Fluids, McGraw Hill, New York,

1992.Video Course on Fluid Mechanics: Prof. T.I. Eldho, Dept.

Civil Engg., IIT Bombay

(http://www.youtube.com/course?list=PL3F50D04B70A5B935&

category=University/Engineering)(http://nptel.iitm.ac.in/video.php?subjectId=105101082)



• ec ves

– Discuss nature of fluids

– Introduce fluid properties – Discuss flow characteristics

–

– Illustrate foundations of flow analysis



Importance of FM

• Most important subject in all Sciencestreams - Physics, Chemistry, Biology,

• All Branches of Engineering – Civil,Mechanical, Chemical, Metallur , Aeros ace

• What is a Fluid?. - A Substance capable offlowing – Gases & Liquids

• Fluids – most vital for all forms of life

• or a act v t es o e – u s s requ re –water, blood, milk, air, etc.



Fluids & Fluid Mechanics

Fluid

A substance that deforms continuously when

subjected to a shear stress – gas or liquid

Branch of applied mechanics concerned withthe statics and dynamics of fluids.

The analysis of fluid behavior is based on

–mass, momentum, energy & laws ofthermodynamics



Fluids & Solids

Fluid deforms

Undergoes strain θ dueto shear stress Γ

Shear stress

Solids behavior

Solids resists shear b

Deforms

static deformation (up

to elastic limit of

Shear stress

ma er a

Deforms at elastic limit



Fluids(Liquids&Gases) Vs Solids

- inuous streams of fluid

without begin or end

individual elements in

solids

Loosely spacedmolecules

Densely spacedmolecules

Intermolecular forces

are smaller than forLarge intermolecular

so s

Fluid deforms Solid will not deform

con nuous y w enacted on by a

.



Fundamental DefinitionsSystem

Predetermined identifiable mass of fluid.

Piston Cylinder

System

System approach in FM



Control Volume

Velocity max. at centre

Control volume approach - Very useful in fluidanalysis



Secondar dimensions – Based onprimary quantities.

– .

• Coordinate system – Cartesian, Cylindrical

an n r ns c.

• Absolute velocity – v = dr/dt, u=dx/dt,v=dy/dt

• Acceleration – a = dv/dt.

• Pressure = Force/Unit area.



Lagrangian Description

Describes the history of the particles exactly.

Stud ath of fluid articles of fixed identit .

u = dx/dt a = du/dt = d2x/dt2

v = dy/dt

a = dv/dt = d2y/dt2

w = dz/dt

az = dw/dt = d2z/dt2

Rarely used in FM. due to complexities



Eulerian Description

Describes what happens at a given spatial

, ,

instant of time.

a = t

eg.ax = Du/Dt = ∂u/∂t + u ∂u/∂x + v ∂u/∂y + w ∂u/∂z.

• – behavior - advantages



Shearing Forces

When a fluid is in motion shear stresses are

develo ed if the articles of the fluid move

relative to one another.So the ad acent articles have different

velocities.

Consider water flow in a pipe. At the pipe wall the velocity of the water will

be zero.

Velocity will increase as we move towards thecenter of the pipe.



Velocity

Center linevelocity



Equal

Ma nitude

v



Viscosity(μ)

Shear stress is directly proportional to rateof shear strain (velocity gradient)

Γ α θ = rate of strain ; Γ = μθ

μ = coefficient of viscosity (Experiment)

Fluids for which the shearing stress is

directly proportional to the rate of shearingstrain are designated as Newtonian fluids.

Non Newtonian fluid

linearly related to the rate of shearingstrain are designated as non-Newtonianu s.



Newton’s Law of ViscosityShearing

orce

Shear

Fluid element

of sizeδx,δy,δz

Shear force acted on a fluid element



Shear strain Φ = x/y

u/y

=

E.Shear stress is proportional to rate of shearstrain.

Γ = Constant X (u/y).u y s e c ange n ve oc y w y.

It may be written in the differential form.

The constant of proportionality is known asthe d namic viscosit .

Newton’s law of viscosity Γ = µ(du/dy).



Г = Shear stress => M L-1 T-2

µ = Coefficient of dynamic viscosity=> M L-1 T-1

γ = Kinematic Viscosity(µ/ρ) => L2 T-1

µ for water = 1.14×10-3 Kg m-1 s-1

µ for air = 1.78×10-5 Kg m-1 s-1

Γ for water = 1.14×10-6 m2 s-1

-5 2 -1 .



Variation of shearing

stress with rate of

shearing strain for

several types of fluids

Figure – Types of

Viscosity



Dilatant – μ increases as the rate of shear

.Eg. – Paint, Printer’s ink

Thixotropic – μ decreases with time for which.

Eg. Mud gels used in drilling

– shearing forces are applied.

Visco-elastic – Similar to Newtonian fluids

changes suddenly behave as elastic.



Temperature => 0C

Surface Tension(σ) – Phenomena occurs due

to the unbalanced cohesive forcesactin on different surfaces such as air and

water.

Surface tension σ => N/mThe intensity of the molecular attraction per

σ = dF/dl F = Force

.



Capillary Rise

It is either due to Cohesion or due to Adhesion.

Non wettin t e li uidwetting type liquid

RiseFall



h = 2бcosθ/γR

Vapor Pressure

When a liquid is in a closed container small air

space, a pressure will develop in the space as

a resu o vapor a s orme y escap ng

molecules.

When equilibrium is reached so that number of

mo ecu es eav ng e sur ace s equa onumber entering – Vapor is said to be saturated

termed as vapor pressure.



Basic Flow Analysis Techniques

Three basic ways to approach Fluid flow

.

. on ro o ume or n egra ana ys s.

2. Infinitesimal System (or) Differential

analysis.

3. Ex erimental Stud or Dimensional

analysis.



Foundation of Flow Analysis

In all cases flow must satisfy three basic

law of mechanics plus a thermodynamic

state relation and associated boundarycondition.

I. Conservation of Mass (Continuity).

II. Linear momentum Newton’s second law .III. First law of Thermodynamics

Conservation of ener .

IV. A state relation like ρ = ρ (P,T).

.

surfaces, interfaces, inlets and exists).



2. Surface powder or Flakes or Liquid flows.

3. Floats or Neutral – Density Neutral.

4. Optical techniques – Detect densitychan es.

5. Evaporate coatings on boundary surfaces.

6. Luminescent fluids, additives or bio-

luminescence.

. ar c e mage ve oc y.



Flow Patterns

• Stream lines- Line every where tangent to the

velocit vector at a iven instant.

P th li



Path-line

Actual path traversed by a given fluid particle

Streak line



Streak line

Locus of particles that passed through aprescribed point

Timeline

Set of fluid particle that form a line at a given instant.

Cl ifi ti f Fl id Fl



Classification of Fluid Flows

Rhelogical

Considerations Dilational

Tensor Temporal

Type

Motion

CharacteristicsS atial

Dimensions



1 Gases Vs Liq ids



1. Gases Vs Liquids

2. Continuum Vs Discrete fluids

on nuum – n v ua mo ecu ar proper es

are negligible.

Discrete fluids – Each molecule treated

separately.

3. Perfect Vs Real fluids

Real fluids – Does not slip past a solid wall.

4. Newton Vs Non Newton fluidsNewton - constant for fixed fluid

temperature and pressure. Eg. water



7 1 2 3D Flow



7. 1, 2, 3D Flow

–direction.

–

directions.3D Flow – S atial variations are in threedirections.

8. Rotational Vs Irrotational flowIrrotational flow – No rate of angulardeformation of any fluid particle.

eg. Potential flowRotational flow – Rate of angulardeformation.

Solution of Fluid Flow Problem



Solution of Fluid Flow Problem

2

Theoretical Investigation Experimental Investigation

Physical Analysis

Force Concept Energy Concept

Mathematical Analysis

Force Concept Energy Concept Dimensional Analysis



Dr. T. I.Dr. T. I. EldhoEldho

Professor,Professor,

Department of Civil Engineering,Department of Civil Engineering,

Indian Institute of Technology Bombay,Indian Institute of Technology Bombay,

Mumbai, India, 400 076.Mumbai, India, 400 076.

ma :ma : e o .ac. ne o .ac. n

Phone: (022)Phone: (022) –– 25767339; Fax: 2576730225767339; Fax: 25767302

http://www.http://www.civil.iitb.ac.incivil.iitb.ac.in

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