A. Jaafar 2010

Dr Azuraien Jaafar

Mr M Faizairi M Nor

Dr Aklilu Baheta

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Course Objectives

Understand concepts and behavior

of fluids in static and flowing

condition.

Understand the concept and

applications of control volume.

Apply the knowledge of dimensional

analysis.

Apply the concepts to the design of

simple system involving fluid.

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Course Schedule

3 Lectures/wk

Lab: 8hrs/semester

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Textbook

B.R. Munson, D.F. Young, T.H.

Okiishi, W.W Huebsch, Fundamental

of Fluid Mechanics, John Wiley and

Sons, 6th edition, 2010 (Main

Textbook)

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Grading

Final Examination 50%

Coursework: 50%

Tests 20%

Assignments & Projects 20%

Lab assignments 10%

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What is Fluid Mechanics?

A study of fluids either in

motion (fluid dynamics) or at

rest (fluid statics) and the

subsequent effects of the fluid

on the boundaries.

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Chapter 1: IntroductionCharacteristics of fluids

Dimensions, Dimensional Homogeneity and Units

Analysis of Fluid Behavior

Measures of fluid mass and weight

Ideal gas law

Viscosity

Compressibility of Fluids

Vapor pressure

Surface tension

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Concept of Fluid

All matter consists of only TWO states

Solid

Fluid

Solid produces static deformation as a

reaction to applied shear stress

Fluid deforms continuously as long as

the shear stress is applied

Note : A shearing stress is created

whenever a tangential force acts on a

surface

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Types of FluidGases

widely spaced molecules with negligible

cohesive forces

All gases are true fluids

Liquid

relatively close-packed molecules with

strong cohesive forces

Common liquids are true fluids

Liquids which are not true fluids-

emulsions, colloids, high-polymer

solutions, slurries

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Fluid as a Continuum

Fluid is treated as a continuum which

means that the fluid characteristics

of interest (pressure, velocity, etc)

vary continuously throughout the

fluid

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Dimensions, Dimensional

Homogeneity, UnitsDimensions

Dimension of the fluid characteristics as

describe using the primary quantities;

the length, L, the mass, M (or the force,

F), the time, T and the temperature, .

Ex:

Velocity, V = LT-1Dimensions of a velocity

equal to length divided

by time

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Dimensions, Dimensional

Homogeneity, Units (cont.)Dimensional Homogeneity

The dimensions of the left side of all

theoretically derived equations must be

the same as those on the right side

Ex:

Equation: V = Vo + at

Dimension: LT-1 = LT-1 + LT-1

Since the dimensions on the left equal to that on the

right, the equation above is Dimensionally

Homogeneous

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Dimensions, Dimensional

Homogeneity, Units (cont.)Units

A standard used to describe fluid

characteristics

Ex:

Length : meter or foot

Time : second

Two systems commonly used

British Gravitational (BG) System

International System (SI)

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Analysis of Fluid Behavior

Fluid

Mechanics

Fluid Statics Fluid DynamicsFluid at rest Fluid is moving

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Fluid Density,

Units : slugs/ft3 (BG) or kg/m3 (SI)

Density of liquids are slightly

affected by pressure and

temperature

Density of gases are strongly

influenced by pressure and

temperature

Specific volume, v

1v

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Specific Weight,

Units : lb/ft3 (BG) or N/m3 (SI)

Defined as weight per unit volume

Related to density through

where g is the local acceleration of gravity

volume

weight

g

22 /2.32/81.9 sftsmg

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Specific Gravity, SG

Units : dimensionless

Ratio of the density of the fluid to the

density of water at some specified

temperature

COHCOH oo

SG

4@4@ 22

OR

333

4@

33

4@

/4.62/1081.9

/94.1/1000

2

2

f tlbmN

ftslugsmkg

COH

COH

o

o

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Ideal Gas Law

Also known as Perfect Gas Law or Equation of State

R is the gas constant

Note 1: Pressure in the ideal gas must be expressed as an absolute pressureAbsolute press. = Gage press. + Atmospheric press.

Atmospheric press. = 14.7 psi or 101 kPa

Note 2: Temperature too must be in absolute unit

RTp

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Example 1

A compressed air tank contains 8 kg of air at a temperature of 80oC. A

gage on the tank reads 300 kPa. Determine the volume of the tank.

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Pressure

Unit : lb/ft2 or psf (BG) or N/m2 or Pascal (SI)

A static fluid exerts only normal force on a contacting surface

A moving fluid exerts both normal and shear forces on the surface in contact with the fluid

Normal force is called pressure force

Shear force is called friction force

Zero pressure means vacuum

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Viscosity,

Units : lbs/ft2 (BG) or N-s/m2 (SI)

Also called absolute viscosity or dynamic viscosity

Very sensitive to temperature changes

Mildly change with pressure

For Newtonian fluid

Kinematic viscosity,

dy

du

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Viscosity, (cont.)

Fluids for which the shearing stress

is linearly related to the rate of

shearing strain are designated as

Newtonian Fluids.

Fluids for which the shearing stress

is not linearly related to the rate of

shearing strain are designated as

non-Newtonian Fluid.

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Example 2

The kinematic viscosity of oxygen at 20oC and a pressure of 150 kPa

(abs) is 0.104 stokes. Determine the dynamic viscosity of oxygen

at this temperature and pressure.

(From table A1, 1 stokes = 1.00E-4 m2/s)

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Newtonian and

NonNewtonian Fluids

Not a fluid

because

require some

amount of

stress before

start flowing

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Compressibility: Bulk

Modulus, Ev

Units : lb/in2 (BG) or N/m2 (SI)

Indicates how easily can the volume of a

given mass of the fluid be changed when

there is a change in pressure

Given as

Also known as bulk modulus of elasticity

// d

dp

VdV

dpEv

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Compressibility

If compression or expansion takes place under constant temperature conditions (isothermal)

If compression or expansion is frictionless and no heat is exchanged with the surrounding (isentropic)

Note : pressure in both must be expressed as an absolute pressure

k = ratio of specific heats =

constantp

constantp

k

vp cc /

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Example 3

Natural gas at 70oF and standard atmospheric pressure of 14.7 psi is

compressed isentropically to a new absolute pressure of 60 psi.

Determine the final density and temperature of the gas.

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Compressibility: Speed of

Sound, cVelocity at which small disturbances

propagate in a fluid

Given as

Since disturbances is small, process

is assumed to be isentropic where

Hence

vE

ddp

c

kpEv

kRTkp

c For Ideal Gas

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Vapor Pressure

Evaporation takes place because some liquid molecules at the surface have sufficient momentum to overcome the intermolecular cohesive forces and escape into the atmosphere.

When an equilibrium condition is reached so that the number of molecules leaving the liquid surface is equal to the number entering, the fluid is said to be saturated and the pressure the vapor exerts on the liquid surface is termed the vapor pressure.

When vapor bubbles are formed in a flowing fluid, they are swept along into regions of higher pressure when they suddenly collapse with sufficient intensity to actually cause structural damage. The formation and subsequent collapse of vapor bubbles in a flowing fluid is called cavitation.

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Example 4

A partially filled closed tank contains ethyl alcohol at 68oF. If the air

above the alcohol is evacuated, what is the minimum absolute

pressure that develops in the evacuated space?

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Surface Tension,

Units : lb/ft (BG) or N/m (SI)

It is the intensity of the molecular

attraction per unit length along any

line in the surface

Depends on

Temperature ( as T)

Fluid/surface it is in contact with

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Surface Tension, (cont.)

Figure 1 : Effect of capillary action in small tubes (a) Rise of column for a liquid that

wets the tube. (b) Free-body diagram for calculating column height. (c) Depression of

column for a nonwetting liquid.

The height of the column is given as

The angle of contact, , is a function of

both the liquid and the surface

Rh

cos2

Open to atmosphere

130

0

mercury

water

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Example 5

An open, clean glass tube, having a diameter of 3 mm, is inserted

vertically into a dish of mercury at 20oC. How far will the column of

mercury in the tube be depressed?