Chapter 1 Fluid Properties(1)

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FLUID MECHANICS

(CHE 203)

CHAPTER 1

FLUID PROPERTIES


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OBJECTIVE

To acquire fundamental concepts of fluid properties

LEARNING OUTCOMES

At the end of this chapter, student should be able to:

i. Define fluid

ii. State the differences between solid and fluidiii. Calculate common fluid properties when

appropriate information are given.

iv. Define Newtons Law of viscosity; relationship

between shear stress and rate of shear strain


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1.1 FLUIDS

We normally recognize 3 states of matter : Solid, Liquid and Gas.

Although differ in many respects, liquids and gases have commoncharacteristics in which they are differ from solids.

Liquid and gas are fluids: in contrast to solids, they (fluid) lack the ability toresist deformation. Because a fluid cannot resist the deformation force, itmoves, it flowsunder the action of the force. Its shape will changecontinuously as long as the force is applied.

A solid can resist a deformation force while at rest, this force may causesome displacement but the solid does not continue to move indefinitely

FLUID

Deforming continuouslyfor as long as the force

applied

Flow under the actionof such forces

Unable to retain anyunsupported shape


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What is a fluid?

A fluid is a substance in the gaseous or liquid form

Distinction between solid and fluid?

Solid: can resist an applied shear by deforming. Stress is proportionalto strain

Fluid: deforms continuously under applied shear. Stress is proportionalto strain rate

F

A

F V

A h

Solid Fluid

1.1 FLUIDS


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Stress is defined as the force perunit area.

Normal component: normal stress

In a fluid at rest, the normalstress is called pressure

Tangential component: shear stress

1.1 FLUIDS


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A liquid takes the shape of the

container it is in and forms a freesurface in the presence of gravity

A gas expands until it encountersthe walls of the container and fillsthe entire available space.Gases cannot form a free surface

Gas and vapor are often used assynonymous words

1.1 FLUIDS


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solid liquid gas

1.1 FLUIDS


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No-slip condition

No-slip condition: A fluid in direct contact with a solid``sticks' to the surface due to viscous effects

Responsible for generation of wall shear stress w, surface drag D= w dA, and the development of the

boundary layer The fluid property responsible for the no-slip condition is

viscosity


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1.1 FLUIDS

Deforming is caused by shearing forces, i.e. forces such as F(refer Figure1.1), which act tangentially to the surfaces to which they are applied and

causes the material originally occupying the space ABCD to deform ABCD.

F

DA

BB CC

y

xE

Figure 1.1: Deformation caused by shearing forces

We can then say:

A fluid is a substance which deforms continuously, or flows,when subjected to shearing forces.

On the other hand, this definition means the very importantpoint that:If a fluid is at rest, there are no shearing forces acting. All

forces must be perpendicular to the planes which they areacting.


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1.2 SHEAR STRESS IN A MOVING FLUID

Shear stresses are developed when the fluid is in motion. Ifthe particles of the fluid move relative to each other so theyhave different velocities, causing the original shape of fluidto become distorted.

If the velocity of fluid is the same at every point, no shearstresses will be produced, since the fluid particles are at

rest relative to each other. If ABCD (refer Figure 1.1) represents an element in a fluid

with thickness sperpendicular to the diagram, the force Fwill act over an area A equal to BC x s.

The force per unit area, F/A is the shear stress and the

deformation, measured by angle (the shear strain), will beproportional to the shear stress.

The shear strain will continue to increase with time andthe fluid will flow.

The rate of shear strain (or shear strain per unit time) is

directly proportional to the shear stress.


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Suppose that in time t, a particle at E (refer Figure 1.1) moves through adistance x.

If E is a distance y from AD then, for a small angles,

Revise that shear stress is proportional to shear strain, then

Eatparticletheofvelocitytheist/xuwhere

y

u

y

)t/x(

yt

xstrainshearofRate

y

x,strainShear

uconstant x Equation1.1

y



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The term u/y is the change of velocity with y and may be written in differentialform du/dy.

The constant of proportionality is known as the dynamic viscosity of the fluid.Substitute to Equation 1.1,

Equation 1.2 isNewtons law of viscosity

1.2du

Equationdy



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Fluids obeying Newtons lawof viscosity and for which has a constant value areknown as Newtonianfluids.

Most common fluids fall into

this category, for which shearstress is linearly related tovelocity gradient (refer Figure1.2)

1.3 NEWTONIAN AND NON-NEWTONIAN FLUIDS

Figure 1.2: Variation of shear stress with velocity gradient


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Fluids which do not obey obeying Newtons law of viscosity are

known as non-Newtonianfluids and fall into one or the followinggroups.

1. Plastic: Shear stress must reach a certain minimum before flowcommences. Thereafter, shear stress increases with the rate ofshear according to the relationship in Equation 1.3, where A, B

and n are constants. If n=1, the material is known as Binghamplastic, e.g. sewage sludge.

2. Pseudo-plastic:Dynamic viscosity decreases as therate of shear increases, e.g. colloidial substances likeclay, milk and cement.


1.3

n

A B Equationdu

dy


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3. Dilatant substances:Dynamic viscosity increases as the rate of shear

increase, e.g. quicksand.4. Thixotropic substances:Dynamic viscosity decreases with the time for

which shearing force is applied, e.g. Thixotropic jelly paints.5. Rheopectic substances:Dynamic viscosity increases with the time for

which shearing force is applied.6. Viscoelastic materials:Behavesimilar to Newtonian fluids but if there

is a sudden large change in shear stress, they behave like plastic.

The above is a classification of actual fluids. There is also one more - which is not real, it does

not exist - known as the ideal fluid. This is a fluidwhich is assumed to have no viscosity ( = 0). This

is a useful concept when theoretical solutions arebeing considered - it does help achieve somepractically useful solutions in analyzing some of theproblems arising in fluid mechanics.


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1.4 DENSITY

The density of a substance is that quantity of matter contained in unitvolume of the substance. It can be expressed in three different ways.

1.4.1 MASS DENSITY

Mass density is defined as the mass of substance per unitvolume. Units: kilogram per cubic meter (kgm-3) Dimensions: ML-3

Typical values at p=1.013 x 105 Nm-2, T=288.15 K, massdensity of water is 1000 kgm-3 and air is 1.23 kgm-3.


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1.4 DENSITY

1.4.2 SPECIFIC WEIGHT

Specific weight w is defined as the weight per unit volume. Since weight is dependent on gravitational attraction, the specific

weight will vary from point to point, according to the local value ofgravitational acceleration g.

The relationship between w and can be deduced from Newtonssecond law where,

Weight per unit volume = Mass per unit volume x g = g

Units: newtons per cubic meter (Nm-3) Dimensions: ML-2T-2

Typical values for water is 9.81 x 103 Nm-3and air is 12.07 Nm-3.


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1.4 DENSITY

1.4.3 RELATIVE DENSITY

Relative density or specific gravity (SG) is defined as the ratio ofthe mass density of a substance to some standard mass density.

For solids and liquids, the standard mass density chosen is themaximum density of water (which occur at 4C at atmosphericpressure).

The relationship between is represented by,

C4atwater

cetansubs

=

For gases, the standard density may be that air orhydrogen at a specified temperature and pressure,but the term is not used frequently.

Units: since relative density is a ratio of twoquantities of the same kind, it is a pure numberhaving no units.

Dimensions: as a pure number, its dimension areM0L0T0=1.

Typical values for water is 1.0 and oil is 0.9.


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1.5 VISCOSITY

1.5.1 DYNAMIC VISCOSITY

The coefficient of dynamic viscosity can be defined as the shearforce per unit area (or shear stress ) required to drag one layer of fluidwith unit velocity past another layer a unit distance away from it in thefluid.

Rearranging Equation 1.2,

TimexLenght

Massor

Area

TimexForce=

Distance

Velocity

Area

Force

=

dy

du

=

Unit: newtons seconds per square meter (Nsm-2

)or kilograms per meter per second (kgm-1s-1). Butnote that the coefficient of viscosity is oftenmeasures in poise (P) where 10 P = 1 kgm-1s-1.

Dimension: ML-1T-1

Typical values for water is 1.14 x 10-3 kgm-1s-1

and air is 1.78 x 10-5 kgm-1s-1.


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1.5 VISCOSITY

1.5.2 KINEMATIC VISCOSITY

The kinematic viscosity, is defined as ratio of dynamicviscosity, to mass density, .

Unit: square meters per second (m2s-1) but note that thekinematic viscosity is often measures in stokes (St)where 10 St = 1 m2s-1.

Dimension: L2T-1

Typical values for water is 1.14 x 10-6 m2s-1 and air is1.46 x 10-5 m2s-1.

=


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1.6 UNIT AND CONVERSION FACTORS

In the United States most measurements use the English system of units

(based on the foot, pound and F), but most of the world uses the metric(or SI) units (based on the meter, kilogram and C).

Chapter 1 Fluid Properties(1)

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