viscosity measuring device

VISCOSITY MEASUREMENT OF DIFFERENTFLUIDS AT SAME TEMPERATURE AND SAME

FLUID AT DIFFERENT TEMPERATURES

ByDHEERENDRA SINGH PAL (0802940033)MANU KWATRA (0802940045)PRATEEK LUMBA (0802940407)SHUBHANKUR MISHRA (0802940092)VISHAL PORWAL (0802940109)

Department of Mechanical EngineeringKrishna Institute of Engineering and Technology

13 km stone Ghaziabad - Meerut RoadGhaziabad - 201206

April, 2012

VISCOSITY MEASUREMENT OF DIFFERENTFLUIDS AT SAME TEMPERATURE AND SAME

FLUID AT DIFFERENT TEMPERATURES

ByDHEERENDRA SINGH PAL (0802940056)MANU KWATRA (0802940045)PRATEEK LUMBA (0802940407)SHUBHANKUR MISHRA (0802940092)VISHAL PORWAL (0802940109)

Submitted to the Department of Mechanical Engineeringin partial fulfillment of the requirements

for the degree ofBachelor of Technology

inMechanical Engineering

Krishna Institute of Engineering and TechnologyGautam Buddha Technical University

April, 2012

ITABLE OF CONTENTS PageDECLARATION iCERTIFICATE iiACKNOWLEDGEMENT iiiABSTRACT ivLIST OF TABLES vLIST OF FIGURES viCHAPTER 1 : INTRODUCTION 1

1.1 Properties and behavior 11.2 Types of viscosities 31.3 Viscosities coefficients 41.4 Fluidity 61.5 Effect of temperature on the viscosity of gas 71.6 Viscosity of blend of liquids 81.7 Viscosity of selected substances 91.8 Viscosity of air 91.9 Viscosity of water 101.10 Viscosity of various materials 111.11 Viscosity measurement 14

CHAPTER 2 : TYPES OF VISCOMETERS 172.1 U-tube viscometer 172.2 Falling sphere method 192.3 Oscillating piston viscometer 212.4 Stabinger viscometer 22

CHAPTER 3 : FORCE REQUIRED TO MOVE A SOLID BODY IN FLUID 24CHAPTER 4 : MODIFICATION OF FALLING SPHERE METHOD 28

4.1 Line diagram 304.2 Apparatus used 304.3 Design specification of apparatus 31

II

4.4 Mathematical calculation 324.4.1 Measurement of terminal velocity 324.4.2 Calculation of weight of ball 324.4.3 Calculation of buoyancy force 32

4.5 Calculation of viscosity of glycerin at various temperature 344.5.1 Graphical analysis 35

4.6 Calculation of viscosity of paraffin at various temperature 364.6.1 Graphical analysis 37

CHAPTER 5 : RESULTS AND DISCUSSIONS 335.1 Introduction 385.2 Analysis of result obtained 38

CHAPTER 6 : CONCLUSION 406.1 Conclusion 406.2 Scope for future work 40

REFERENCES 41

iii

DECLARATION

We hereby declare that this submission is my own work and that, to the best of myknowledge and belief, it contains no material previously published or written by anotherperson nor material which to a substantial extent has been accepted for the award of anyother degree or diploma of the university or other institute of higher learning, except wheredue acknowledgment has been made in the text.

Signature SignatureName: Dheerendra Singh Name Manu KwatraRollNo 0802940033 RollNo 08029400045Date Date

Signature SignatureName PrateekLumba Name Shubhankur Mishra

RollNo 0802940407 RollNo 0802940092Date Date

SignatureName: Vishal PorwalRollNo. 0802940109Date

iv

CERTIFICATE

This is to certify that Project Report entitled Viscosity measurement device for dfferentfluids at same temperature & same fluid at different temperatures, which is submitted byDheerendra Singh, Manu Kwatra, Prateek Lumba, Shubhankur Mishra and Vishal Porwal inpartial fulfillment of the requirement for the award of degree B. Tech. in Department ofMechanical Engineering of Gautam Buddh Technical University is a record of the candidateown work carried out under supervision of Mr. Shishir Srivastava. The matter embodied inthis thesis is original and has not been submitted for the award of any other degree.

Date Mr. Shishir SrivastavaAssistant ProfessorMechanical Engineering DepartmentKIET, Ghaziabad

vACKNOWLEDGEMENT

It gives us a great sense of pleasure to present the report of the B. Tech Project undertakenduring B. Tech. Final Year. We owe special debt of gratitude to Assistant Professor Mr.Shishir Srivastava, Department of Mechanical Engineering, College, KIET Ghaziabad for hisconstant support and guidance throughout the course of our work. His sincerity,thoroughness and perseverance have been a constant source of inspiration for us. It is onlyhis cognizant efforts that our endeavors have seen light of the day.We also take the opportunity to acknowledge the contribution of Dr.K.L.A. Khan, Head,Department of Mechanical Engineering, College, KIET Ghaziabad for his full support andassistance during the development of the project.We also do not like to miss the opportunity to acknowledge the contribution of all facultymembers of the department for their kind assistance and cooperation during the developmentof our project. Last but not the least, we acknowledge our friends for their contribution in thecompletion of the project.

Signature SignatureName: Dheerendra Singh Name Manu KwatraRollNo 0802940033 RollNo 08029400045Date Date

Signature SignatureName PrateekLumba Name Shubhankur MishraRollNo 0802940407 RollNo 0802940092Date Date

SignatureName: Vishal PorwalRollNo. 0802940109Date

vi

Abstract

The increase in uncertainty throughout the viscosity scale being the principal disadvantage of capillaryviscometry.. Now we decided to develop an absolute falling-ball viscometer making it possible to cover a widerange of viscosity while keeping a weak uncertainty. The measurement of viscosity then rests on the speed limitmeasurement of falling ball, corrected principal identified effects (edge effects, inertial effects, etc.). Anexperimental bench was developed in order to reach a relative uncertainty of the order of 10-3 to the measure ofviscosity. This bench must allow to observe the trajectory of the ball inside a cylindrical tube filled with liquidfor which the viscosity is to be measured, and to obtain the variations in speed throughout the fall in order todetermine the area where the speed limit is reached.Viscosity is a property of fluid by virtue of which it resistthemotion between two fluid layers.Here we are using Stokes Lawfor the measurement of viscosity. It gives arelation among the net drag force on spherical steel ball , buoyancy force and weight of the ball when it isimmersed in a fluid.

vii

LIST OF TABLES

1.1 Some absolute properties of gases 61.2 Viscosity of water at various temperature 71.3 Viscosity of Newtonian fluids 91.4 Viscosity of Non Newtonian fluid 101.5 Specification of fluid used 281.6 Comparison of calculated value of viscosities 33

viii

LIST OF FIGURES

1.1.Shear stress v/s velocity gradient 21.2.Shear stress v/s velocity gradient (all type fluids) 31.3.Dynamic viscosity v/s temperature 81.4.U-tube viscometer 131.5.Falling sphere viscometer 141.6.oscillatory piston viscometer 171.7.Drag force v/s Reynoldss no 211.8. Images of Project made 241.9.Line diagram of apparatus 251.10 Equilibrium condition of steel ball 261.11 Viscosity v/s temperature for glycerin 301.12 Viscosity v/s temperature for paraffin 32

1

CHAPTER 1

INTRODUCTION

Viscosity is a measure of the resistance of a fluid which is being deformed by

either shear or tensile stress. In everyday terms (and for fluids only), viscosity is "thickness"

or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick",

having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of

movement.

Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of

fluid friction. For example, high-viscosity felsic magma will create a tall, steep stratovolcano,

because it cannot flow far before it cools, while low-viscosity mafic lava will create a wide,

shallow-sloped shield volcano. With the exception of super fluids, all real fluids have some

resistance to stress and therefore are viscous, but a fluid which has no resistance to shear

stress is known as an ideal fluid or inviscid fluid.[1]

1.1 Properties and behaviour

In general, in any flow, layers move at different velocities and the fluid's viscosity arises from

the shear stress between the layer that ultimately opposes any applied force. The relationship

between the shear stress and the velocity gradient can be obtained by considering two plates

closely spaced at a distance y, and separated by a homogeneous substance. Assuming that the

plates are very large, with a large area A, such that edge effects may be ignored, and that the

lower plate is fixed, let a force F be applied to the upper plate. If this force causes the

substance between the plates to undergo shear flow with a velocity gradient u/y (as opposed to

just shearing elastically until the shear stress in the substance balances the applied force), the

substance is called a fluid. The applied force

in the fluid:

Where: - is the proportionality factor called

This equation can be expressed in terms of shear stress

Thus as expressed in differential

flow, the shear stress between layers is proportional to the

direction perpendicular to the layers:

Hence, through this method, the relation between the shear stress and the velocity gradient

can be obtained .James Clerk Maxwell

analogy that elastic deformation opposes shear stress in

stress is opposed by rate of deformation

substance is called a fluid. The applied force is proportional to the area and velocity gradient

is the proportionality factor called dynamic viscosity.

This equation can be expressed in terms of shear stress

.

differential form by Isaac Newton for straight, parallel

flow, the shear stress between layers is proportional to the velocity

to the layers:


James Clerk Maxwell called viscosity fugitive elasticity

analogy that elastic deformation opposes shear stress in solids, while in viscous

stress is opposed by rate of deformation.[18]

2

is proportional to the area and velocity gradient

parallel and uniform

velocity gradient in the


fugitive elasticity because of the

, while in viscous fluids, shear

1.2 Types of viscosities

Newton's law of viscosity, given above, is a

law, Ohm's law).A It is not a fundamental law of nature but an approximation that holds in

some materials and fails in others.

Non-Newtonian fluids exhibit a more complicated relationship between shear stress and

velocity gradient than simple linearity. Thus there exist

Newtonian: fluids, such as

Shear thickening

Shear thinning

are very commonly, but misleadingly, described as thixotropic.

Thixotropic: materials which become

agitated, or otherwise stressed.

Figure:-1.1 Shear stress diagram [1]

1.2 Types of viscosities

viscosity, given above, is a constitutive equation (like Hooke's law

).A It is not a fundamental law of nature but an approximation that holds in

some materials and fails in others.

exhibit a more complicated relationship between shear stress and

velocity gradient than simple linearity. Thus there exist a number of forms of viscosity.[4]

: fluids, such as water and most gases which have a c

Shear thickening: viscosity increases with the rate of shear.

Shear thinning: viscosity decreases with the rate of shear. Shear thinning liquids


: materials which become less viscous over time when shaken,


3

Hooke's law, Ficks

).A It is not a fundamental law of nature but an approximation that holds in

exhibit a more complicated relationship between shear stress and

a number of forms of viscosity.[4]

which have a constant viscosity.

with the rate of shear. Shear thinning liquids


time when shaken,

Rheopectic: materials which become


A Bingham plastic

as a viscous fluid at high stresses.

Figure 1.2 Shear stess variation with shea

1.3 Viscosity Coefficients

Viscosity coefficients can be defined in two ways:

Dynamic viscosity, also

Poise, P)

Kinematic viscosity

cm2/s, Stokes, St).

: materials which become more viscous over time when shaken,


Bingham plastic is a material that behaves as a solid at low stresses but flows

as a viscous fluid at high stresses.

Shear stess variation with shear strain for all type of fluids [3]

Viscosity Coefficients

Viscosity coefficients can be defined in two ways:

, also absolute viscosity, the more usual one (typical units Pas,

Kinematic viscosity is the dynamic viscosity divided by the density (typical units

4

viscous over time when shaken,

is a material that behaves as a solid at low stresses but flows

r strain for all type of fluids [3]

, the more usual one (typical units Pas,

divided by the density (typical units

5

Viscosity is a tensorial quantity that can be decomposed in different ways into two

independent components. The most usual decomposition yields the following viscosity

coefficients:

Shear viscosity, the most important one, often referred to as simply viscosity, describing the

reaction to applied shear stress; simply put, it is the ratio between the pressure exerted on the

surface of a fluid, in the lateral or horizontal direction, to the change in velocity of the fluid as

you move down in the fluid (this is what is referred to as a velocity gradient).

Volume viscosity (also called bulk viscosity or second viscosity) becomes important only for

such effects where fluid compressibility is essential. Examples would include shock

waves and sound propagation. It appears in the Stokes' law (sound attenuation) that describes

propagation of sound in Newtonian liquid.

Alternatively,

Extensional viscosity, a linear combination of shear and bulk viscosity, describes the reaction

to elongation, widely used for characterizing polymers. For example, at room temperature,

water has a dynamic shear viscosity of about1.0103 Pas and motor oil of

about 250103 Pas.[4] [5] [6]

1.3.1 Dynamic viscosity

The usual symbol for dynamic viscosity used by mechanical and chemical engineers as well

as fluid dynamicists is the Greek letter mu ().The symbol is also used by chemists,

physicists, and the IUPAC.The SI physical unit of dynamic viscosity is the pascal-

second (Pas), (equivalent to Ns/m2, or kg/(ms)). If a fluid with a viscosity of one Pas is

placed between two plates, and one plate is pushed sideways with a shear stress of one pascal,

it moves a distance equal to the thickness of the layer between the plates in one second. Water

at 20 C has a viscosity of 0.001002 Pas .

The cgs physical unit is more commonly expressed, particularly in ASTM standards,

as centipoises (cP). Water at 20 C has a viscosity of 1.0020 cP.

1 P = 0.1 Pas,

1 cP = 1 mPas = 0.001 Pas.

1.3.2 Kinematic viscosity

In many situations, we are concerned

(i.e.) the Reynolds number

the fluid density .

This ratio is characterized by the

The SI unit of is m2/s. The SI unit of

The cgs physical unit for kinematic viscosity is sometimes expressed in terms

of centistokes (cSt). In U.S. usage,

1 St = 1 cm2s1 = 10

1 cSt = 1 mm2s1 = 10

Water at 20 C has a kinematic viscosity of about 1 cSt.The kinematic viscosity is sometimes

referred to as diffusivity of momentum

heat and diffusivity of mass

ratio of the diffusivities.[10][13][21]

1.4 Fluidity

The reciprocal of viscosity is

on the convention used, measured in

the rhe. Fluidity is seldom used in

determine the viscosity of an

when a and b are mixed is

1 cP = 1 mPas = 0.001 Pas.

In many situations, we are concerned with the ratio of the inertial force to the viscous force

Reynolds number (, ), the former character

This ratio is characterized by the kinematic viscosity (Greek letter nu, ), defined as follows:

/s. The SI unit of is kg/m3.


(cSt). In U.S. usage, stoke is sometimes used as the singular form.

= 104 m2s1.

= 106m2s1.


diffusivity of momentum, because it is analogous to

diffusivity of mass. It is therefore used in dimensionless numbers which

[10][13][21]

of viscosity is fluidity, usually symbolized by = 1 / or F

on the convention used, measured in reciprocal poise (cmsg1), sometimes called

is seldom used in engineering practice. The concept of fluidity can be used to

determine the viscosity of an ideal solution. For two components

6

force to the viscous force

), the former characterized by

), defined as follows:


is sometimes used as the singular form.


, because it is analogous to diffusivity of

less numbers which compare the

F = 1 / , depending

), sometimes called

practice. The concept of fluidity can be used to

and , the fluidity

which is only slightly simpler than the equivalent equation in terms of viscosity:

where:-

a and b is the mole fraction of component

components pure viscosities.

1.5 Effect of temperature on the viscosity of a gas

Sutherland's formula can be used to derive the dynamic viscosity of an

of the temperature:

This in turn is equal to

where is a constant for the gas. I

= dynamic viscosity in (Pas) at input temperature

0 = reference viscosity in (Pas) at reference temperature

T0 = reference temperature in kelvins,

C = Sutherland's constant for the gaseous material in question.

Valid for temperatures between 0

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viscosity measuring device