Properties of Fluids by S K Mondal

8/13/2019 Properties of Fluids by S K Mondal

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Properties of Fluids

By

S K Mondal


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Definition of fluid

A fluid is a substance that deformscontinuouslyin the face of tangential or shearstress, irrespective of the magnitude of

shear stress.This continuous deformationunder the application of shear stress constitutesa flow.

In this connection fluid can also be defined asthe state of matter that cannot sustain anyshear stress.


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Fig 1.2 Shear stress on a fluid body


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Fig 1.3 Deformation of a Solid Body


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Characteristics of fluid

1. It has no definite shape of its own, but conformsto the shape of the containing vessel.

2. Even a small amount of shear force exerted on

a fluid will cause it to undergo a deformationwhich continue as long as the force continues tobe applied.

3. It is interesting to note that a solid suffers strain

when subjected to shear forces whereas a fluidsuffers Rate of Strain i.e. it flows under similarcircumstances.


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Concept of Continuum

The concept of continuum is a kind of idealization of thecontinuous description of matter where the properties ofthe matter are considered as continuous functions ofspace variables.

A dimensionless parameter known as Knudsen number, K n = / L, where isthe mean free path and L is the characteristic length. It describes the degree ofdeparture from continuum.

Usually when K n> 0.01, the concept of continuum does not hold good.

Beyond this critical range of Knudsen number, the flows are known as

slip flow (0.01 < K n < 0.1), transition flow (0.1 < K n < 10) and

free-molecule flow (Kn > 10).

However, for the flow regimes considered in this course, K n is alwaysless than 0.01 and it is usual to say that the fluid is a continuum.


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Ideal and Real Fluids

1. Ideal Fluid

An ideal fluid is one which has

no viscosity

no surface tension

and incompressible

2.Real Fluid

An Real fluid is one which hasviscosity

surface tension

and compressible

Naturally available all fluids are real fluid.


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Viscosity

Definition:Viscosity is the property of a fluid whichdetermines its resistance to shearing stresses.

Cause of Viscosity: The causes of viscosity in a

fluid are possibly attributed to two factors: (i) intermolecular force of cohesion

(ii) molecular momentum exchange

Newtons Law of Viscosity:It states that theshear stress () on a fluid element layer isdirectly proportional to the rate of shear strain.

The constant of proportionality is called the co-efficient of viscosity.


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Fig 1.7 Movement of fluid molecules betweentwo adjacent moving layers

Animation
http://localhost/var/www/apps/conversion/tmp/scratch_4/Fig%201.7%20Movement%20of%20fluid%20molecules%20between%20two%20adjacent%20moving%20layers.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_4/Fig%201.7%20Movement%20of%20fluid%20molecules%20between%20two%20adjacent%20moving%20layers.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_4/Fig%201.7%20Movement%20of%20fluid%20molecules%20between%20two%20adjacent%20moving%20layers.htmlhttp://localhost/var/www/apps/conversion/tmp/scratch_4/Fig%201.7%20Movement%20of%20fluid%20molecules%20between%20two%20adjacent%20moving%20layers.html


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Velocity Variation near a solid boundary

dy

du

dy

du

dy

du.

When two layers of fluid, at a distance dy apart,

move one over the other at different velocities,

say u and u+du

Velocity gradient =

According to Newtons law

or

Where = constant of proportionality and is known as co-efficient of Dynamic viscosityor only Viscosity

dy

du

As

Thus viscosity may also be defined as the shear stress required to

produce unit rate of shear strain


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Units of Viscosity

S.I. Units: Pa.s or N.s/m2

C.G.S Unit of viscosity is Poise= dune-sec/cm2

One Poise= 0.1 Pa.s

1/100 Poise is called centipoises.

Dynamic viscosity of water at 200C is approx= 1 cP


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Kinematic Viscosity

It is the ratio between the dynamic

viscosity and density of fluid and denoted

by

Mathematically

Density

ityvisDynamic cos


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Units of Kinematic Viscosity

S.I units: m2/s

C.G.S units: stoke = cm2/sec

One stoke = 10-4m2/s

Thermal diffusivity and molecular diffusivity have

same dimension, therefore, by analogy, the

kinematic viscosity is also referred to as themomentum diffusivityof the fluid, i.e. the ability

of the fluid to transport momentum.


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Classification of fluids

1. Newtonian Fluids These fluids follow Newtons viscosity equation.

For such fluids viscosity does not change with rate of deformation

2. Non- Newtonian fluids These fluids does not follow Newtons viscosity equation.

Such fluids are relatively uncommon e.g. Printer ink, blood, mud,

slurries, polymer solutions.


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Effect of Temperature on Viscosity

With increase in temperature

Viscosity of liquids decrease

Viscosity of gasses increase

Note: 1. Temperature response are neglected in case of Mercury2. The lowest viscosity is reached at the critical temperature.


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Fig 1.8: Change of Viscosity of Water and Air under 1 atm


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Effect of Pressure on Viscosity

Pressure has very little effect on viscosity.

But if pressure increases intermolecular gap decreases then cohesion

increases so viscosity would be increase.


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Surface tension

Cohesion Surface tension is due to cohesion between particles

at the surface.

Adhesion Capillarity action is due to both cohesion and

adhesion.

Surface tensionThe tensile force acting on the surface of a liquid incontact with a gas or on the surface between twoimmiscible liquids such that the contact surfacebehaves like a membrane under tension.


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Figure 2.3 The intermolecular cohesive force field

in a bulk of liquid with a free surface


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Pressure Inside a curved surface

For a general curved surface with radii of

curvature r1 and r2at a point of interest

a. Pressure inside a water droplet

b. Pressure inside a soap bubble

c. Liquid jet.

21

11

rrP

dP

4

d

P 8

dP

2


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Capillarity

A general term for phenomena observed in

liquids due to inter-molecular attraction at

the liquid boundary, e.g. the rise or

depression of liquids in narrow tubes. Weuse this term for capillary action.

Capillarity rise and depression phenomena

depends upon the surface tension of theliquid as well as the material of the tube.


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Fig 2.4 Phenomenon of Capillarity


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General formula

For water and glass = 0o

For mercury and glass = 138o

(h is negative indicates capillary depression)

Note: If adhesion is more than cohesion, the wetting tendency is

more and the angle of contact is smaller.

gdh

cos4

gd

h

4

gdh

42cos4


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Bulk Modulus and Compressibility

d

dp

strainVolumetricV

dV

pressureofincreasedpKModulusBulk

)(

)(,

The pressure required to bring about a reduction in the volume of water isapproximately 15000 times the pressure required for the same percentage

reduction in the volume of air.

KilityCompressib

1

Elasticity of fluid is measured in terms of Bulk Modulus of elasticity


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Vapour Pressure

If the pressure on the liquid surface is

lower than or equal to the saturation

vapour pressure, boiling takes place.

Vapour pressure increases with the rise of

temperature.

Mercury has a very low vapour pressure

and hence, it is an excellent fluid to be

used in a barometer.


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Figure 2.5 To and fro movement of liquid molecules from an interface in a confined space as a

closed surrounding

Animation
http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/FLUID-MECHANICS/lecture-2/kkkhttp://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/FLUID-MECHANICS/lecture-2/kkkhttp://localhost/var/www/apps/conversion/tmp/scratch_4/Figure%202.5%20To%20and%20fro%20movement%20of%20liquid%20molecules%20from%20an%20interface%20in%20a%20confined%20.htmlhttp://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/FLUID-MECHANICS/lecture-2/kkkhttp://localhost/var/www/apps/conversion/tmp/scratch_4/Figure%202.5%20To%20and%20fro%20movement%20of%20liquid%20molecules%20from%20an%20interface%20in%20a%20confined%20.htmlhttp://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/FLUID-MECHANICS/lecture-2/kkk


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Discussion


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Properties of Fluids by S K Mondal

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