II. Properties of II. Properties of FluidsFluids

ContentsContents

1.1. Definition of FluidsDefinition of Fluids

2.2. Continuum HypothesisContinuum Hypothesis

3.3. Density and CompressibilityDensity and Compressibility

4.4. ViscosityViscosity

5.5. Surface TensionSurface Tension

6.6. VaporizationVaporization

7.7. Forces Acting on FluidsForces Acting on Fluids

1. Definition of Fluids1. Definition of Fluids

Definition of FluidsDefinition of Fluids

A fluid is a substance that deforms

continuously when subjected to a shear stress, no

matter how small that the shear stress may be

Flows

Solid Fluid

Fixed Plate

F U

Fluid

Definition of FluidsDefinition of Fluids

A fluid is a substance that cannot support

any shear stress in static state

Fluids

Liquids (water)

Gases (air)

Classification of FluidsClassification of Fluids

Liquids and GasesLiquids and Gases

Liquid has definite volume;

gas has no definite volume.

2. Continuum Hypothesis2. Continuum Hypothesis

The Sensitive VolumeThe Sensitive Volume

The minimal volume in which the

number of fluid molecule is big

enough so that the average of any

physical quantity over this volume is

essentially independent of the volume

itself

V

B

V 0

Physical quantity

Sensitive volume

Micro effect

Macro effect

The Sensitive VolumeThe Sensitive Volume

FACT: There are 2.71016

molecules in 1 mm3 air of 0 C at 1

atm

The sensitive volume is usually

very small (infinitesimally small)

from a macroscopic view

Fluid ParticleFluid Particle

A mass of fluid that has a

spatial dimension equivalent

to the sensitive volume

Mathematical point of view:

Fluid particle = Moving point

with no size

with no

orientation

Continuum HypothesisContinuum Hypothesis

At any point in a fluid we can find a

fluid particle which occupies that

point

The fluid is a continuum

formed by fluid particles

3. Density and Compressibility3. Density and Compressibility

DensityDensity

Vm 0

limV

mV

rD ®

D=

D

DensityDensity

Density is the mass per unit

volume

Unit: kg / m3

Specific WeightSpecific Weight

Unit: N / m3

W mg=

gg r=

( )29.8m sg =

Specific VolumeSpecific Volume

1v

r=

Specific Volume is the volume

occupied by a unit mass of fluid

Compressibility of FluidCompressibility of Fluid

vp K

vD

D = -

pK

vvD

= -D

(Bulk modulus)

Compressibility of WaterCompressibility of Water

0

0. 5

1

1. 5

2

2. 5

3

0 10 20 30 40 50 60 70 80 90 100

K

T

910´

Incompressible FluidIncompressible Fluid

pK

vvD

= - ® ¥D

Incompressible FluidIncompressible Fluid

The bulk modulus of liquid is usually

very large, or the compressibility of

liquid is usually very small

Water can be assumed as

incompressible fluid in hydraulics

Incompressible FluidIncompressible Fluid

A fluid can be assumed to be

incompressible if the variation of

density within the flow is not large

Air can be assumed as

incompressible fluid when

velocity is much smaller than the

speed of sound

4. Viscosity 4. Viscosity

ViscosityViscosity

EXPERIMENTEXPERIMENT

A measurement on stickiness of

fluids

ViscosityViscosity

A measurement on the ability

of a fluid to resist shearing

F U

u

y

x

Fixed Plate

Moving Plate

Measured ResultsMeasured Results

The flow is nearly parallelThe flow is nearly parallel

The fluid near the lower plate does not moveThe fluid near the lower plate does not move

The fluid near the upper plate moves with the plateThe fluid near the upper plate moves with the plate

The velocity distribution in The velocity distribution in yy direction is linear direction is linear

F

UAd

µ

F U

u

y

x

ViscosityViscosity

F U duA dy

td

= µ =

dudy

t m=

Viscosity

Shear stress

Rate of strain

Udtd Udt

ViscosityViscosity

Coefficient of ViscosityCoefficient of Viscosity

Absolute ViscosityAbsolute Viscosity

Dynamic ViscosityDynamic Viscosity

du dyt

m=

Unit of : N s /

m2

Dynamic Viscosity of FluidsDynamic Viscosity of Fluids

Viscosity is a function of temperatureViscosity is a function of temperature

T

G a s e s

Liq

uid

s

Newtonian and Non-Newtonian FluidNewtonian and Non-Newtonian Fluid

I d e a l F l u id

N e w t o n i a n F l u i d

I de a

l Pl a

s ti c

N o n - Ne w

t o n i a n Fl u i d

Inviscid Fluid ( Inviscid Fluid ( ) )

The viscosity of water is very small

and may be omitted depends on the

problem of interest

Water can be assumed as

inviscid fluid in many

situations

Kinematic ViscosityKinematic Viscosity

mn

r=

Unit of : m2 / s

Kinematic Viscosity of FluidsKinematic Viscosity of Fluids

ProblemProblem

A journal bearing consists of a shaft and a sleeve as

shown in the following figure. The clearance space is filled

with oil. The sleeve is fixed. The shaft turns at a known

speed. Calculate the rate of heat generation at the

bearing.

Diameter of shaft: d (m)

Diameter of sleeve: d

(m)

Length of sleeve: l (m)

Viscosity of oil: (N s/m2)

Speed of shaft: n (rpm)Shaft

Sleeve

Oil

SolutionSolution

Angular velocity of the shaft:

Shear stress on the surface of the shaft:

Torque to keep rotation of the shaft:

Heat generation rate (= Power):

2 60nv p=

( )12 60

U d n dv pmt m m

d d d= = =

2 2 60T A n l dt mp d= =

( )2 3 2 1800 J sQ T n l dv mp d= =

5. Surface Tension 5. Surface Tension

Capillary RiseCapillary Rise

h

Surface TensionSurface Tension

= Surface tension per unit length

Unit of : N / m

6. Vaporization6. Vaporization

ICE

WATER VAPOR

Te m p e ra t u re

Pre

ss

ure

T P

C P

S o l i d L iq u i d

G a s

S u b l i m a t i o n

Va po r i za ti o

nFusio n

Vapor PressureVapor Pressure

hp

Water

Vapor

Vapor PressureVapor Pressure

0

2000

4000

6000

8000

10000

0 20 40 60 80 100

2kg m

Co

6. Forces Acting on Fluids6. Forces Acting on Fluids

Two Types of ForcesTwo Types of Forces

• Body forceBody force

Forces acting on fluid mass, e.g. gravity Forces acting on fluid mass, e.g. gravity

forceforce

• Surface forceSurface force

Contact force acting on fluid surfaceContact force acting on fluid surface

Description of Body ForceDescription of Body Force

Vm

0limV

Ff

mD ®

D=

D

rr

FDr

(Force per unit mass)

In case of gravity,

f gk= -r r

Description of Surface ForceDescription of Surface Force

0limA

nn

Pp

AD ®

D=

D

rr

Fr

(Force per unit area = Stress)

nPDr

nr

AD• Normal stress

• Shear Stress

END OF CHAPTER IIEND OF CHAPTER II