Properties of Fluids: Pressure, Density, Viscosity, and Surface Tension, Summaries of Engineering

Download Properties of Fluids: Pressure, Density, Viscosity, and Surface Tension and more Summaries Engineering in PDF only on Docsity!

ENSC

Introduction

and

Properties

of

Fluids

Spring

Prepared by:Prepared

by:

M.

Bahrami

Mechatronics

System

Engineering,

School

of

Engineering

and

Sciences,

SFU

M.

Bahrami

ENSC

283

Spring

2009

Pressure

•^

Pressure

is

the

(compression)

force

exerted

by

a

fluid

per

unit

area.

•^

Stress

vs.

pressure?

•^

In fluids gases and liquids we speak of pressure; in solids this is normal

-^

In

fluids

,^ gases

and

liquids

,^ we

speak

of

pressure;

in

solids

this

is

normal

stress.

For

a

fluid

at

rest,

the

pressure

at

a

given

point

is

the

same

in

all

directions. Differences

or

gradients

in

pressure

drive

a

fluid

flow,

especially

in

ducts

and

ipipes.

M.

Bahrami

ENSC

283

Spring

2009

Specific

weight

The

specific

weight

of

a

fluid

is

its

weight,

,^

per

unit

volume.

Density

and

specific

weight

are

related

by

g

ravity:

y^

p

g^

y g

y

M.

Bahrami

ENSC

283

Spring

2009

Specific

gravity

Specific

gravity

is

the

ratio

of

a

fluid

density

to

a

standard

reference

fluid,

typically

water

at

˚C

(for

liquids)

and

air

(for

gases):

•^

For

example,

the

specific

gravity

of

mercury

is

SG

Hg

M.

Bahrami

ENSC

283

Spring

2009

Energy

Note:

internal

energy,

u

,^ is

a

function

of

temperature

and

pressure

for

the

single

‐phase

substance,

whereas

KE

and

PE

are

kinematic

quantities.

M.

Bahrami

ENSC

283

Spring

2009

Specific

heat

•^

Specific

heat

capacity:

is

the

measure

of

the

heat

energy

required

to

increase

the

temperature

of

a

unit

mass

of

a

substance

by

one

degree

temperature.

-^

caluminum

(kJ/kg.K)

and

c

water

(kJ/kg.K)

•^

There

are

two

types

of

specific

heats,

constant

volume

c^ v

and

constant

yp

p^

,^

v

pressure

c

. p

Atmospheric

Gas with

const. volume

Heat

Rigid

tank

Heat

pressure

Cylinder

‐ piston

transfer

transfer

Gas with

const. pressure

c^ v

c^ p

M.

Bahrami

ENSC

283

Spring

2009

Properties

of

ideal

gas

For

an

ideal

gas,

internal

energy

is

only

a

function

of

temperature;

thus

constant

volume

specific

heat

is

only

a

function

of

temperature:

•^

For

an

ideal

gas,

enthalpy

is

only

a

function

of

temperature;

h=

u

pv

•^

The

constant

pressure

specific

heat

can

be

defined

as:

•^

The

specific

heat

ratio

is

an

important

dimensionless

parameter:

M.

Bahrami

ENSC

283

Spring

2009

Incompressible

fluids

Liquids

are

(almost)

incompressible

and

thus

have

a

single

constant

specific

heat:

M.

Bahrami

ENSC

283

Spring

2009

Viscosity

A^

Newtonian

fluid has

a

linear

relationship

between

shear

stress

and

velocity

gradient:

u(y)

y^

Velocity

profile No

‐slip

at

wall

•^

The

no

‐slip condition

: at the wall velocity is zero relative to the wall This is

The

no

slip

condition

:^ at

the

wall

velocity

is

zero

relative

to

the

wall

.^ This

is

a^

characteristic

of

all

viscous

fluid.

•^

The

shear

stress

is

proportional

to

the

slope

of

the

velocity

profile

and

is

greatest at the wallgreatest

at

the

wall

M.

Bahrami

ENSC

283

Spring

2009

The

Reynolds

number

The

Reynolds

number,

Re

,^ is

a

dimensionless

number

that

gives

a

measure

of

the

ratio

of

inertial

forces

to

viscous

forces

Laminar flow,

Re

moderate

Creeping

flow,

Re

is

very

low

Turbulent flow,

Re

high

M.

Bahrami

ENSC

283

Spring

2009

Flow

between

parallel

plates

•^

It^

is^

the

flow

induced

between

a

fixed

lower

plate

and

upper

plate

moving

steadily

at

velocity

V

•^

Shear

stress

is

constant

throughout

the

fluid:

•^

After

integration

and

applying

boundary

conditions:

M.

Bahrami

ENSC

283

Spring

2009

Surface

tension

A^

liquid,

being

unable

to

expand

freely,

will

form

an

interface

with

a

second

liquid

or

gas.

•^

The

cohesive

forces

between

liquid

molecules

are

responsible

for

the

phenomenon

known

as

surface

tension.

-^

Surface

tension

Υ

(pronounced

upsilon)

has

the

dimension

of

force

per

unit

length

( N/m

)^ or

of

energy

per

unit

area

( J/m

2 ).

-^

Υair

‐water

= 0.

N/m;

Υ

air

‐mercury

= 0.

N/m

M.

Bahrami

ENSC

283

Spring

2009

Vapor

pressure

and

cavitation

•^

Vapor pressure:

the

pressure

at

which

a

liquid

boils

and

is

in

equilibrium

with

its

own

vapor.

•^

When

the

liquid

pressure

is

dropped

below

the

vapor pressure

due

to

a

flow

phenomenon,

we

call

the

process

cavitation

The

dimensionless

parameter

describing

flow

‐induced

boiling

is

called

cavitation

number:

M.

Bahrami

ENSC

283

Spring

2009

Cavitation

Bubble

formation

due

to

high

velocity

(flow

‐induced

boiling).

•^

Damage

(erosion)

due

to

cavitation

on

a

marine

propeller.

M.

Bahrami

ENSC

283

Spring

2009