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MTV310 CHAPTER 1 – BASIC PRINCIPLES

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Introduction• Concept of fluid

• Continuumassumption

• Dimensions and units

• Eulerian vs Lagrangian

• Properties– Pressure

– Temperature

– Density

– Specific weight

– Specific gravity

– Ideal gas law

– State relations for liquids

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Viscosity

u(y)

u=0 (no slip)

Approximations:• zero acceleration• no pressure variation in flow direction• Newtonian fluid dy

du

Velocity gradient: dydu

Integrate:

Thus shear stress directly proportional to velocity gradient.Proportionality constant is dynamic viscosity.

u = V

!

h

y

00:0@ cuy

A

F

h

AVF

cyu

constdy

du

Vuhyyu :@

h

VorhV

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– Sutherland’s law

Viscosity function of temperature• Gases • Liquids

– Log-inverse quadratic law

n

T

T

00

ST

ST

T

T

0

5.1

00

2

000

ln

T

Tc

T

Tba

– Power law

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Examples

Cylindrical, linear

Cylindrical, rotational1

h1

h2

F,V

L

DF,V

a

LD

a

r

T,

AVF2

2

1

1

hh

Laminar, steady

contactAF

Torque = Shear force * armDLrT

Thin gap, linear velocity distribution

rV D/2r a

V

DLrT a

V

r

VTPowerDL

a

V

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Non-Newtonian fluids Surface tension

Shear strain rate ,dt

ddy

du

Shearstress

dy

du

m

NY

liquidgas

solid

Contact angle,

h

R

f(T)

<90°

hR2g cosR2 Y

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Thermal conductivity: Fourier’s law Tkq

Speed of sound

kRTac

Reynolds number

VDVD

Re

inertial forces

viscous forces

Kinematic viscosity

[m2.s-1]

Vapour pressure

T

pv

100kPa

100°C

pv

Cavitation

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Examples

White Ex 1.10, p.38

White Pr 1.53:

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White Pr 1.54:

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White Pr 1.56: