# I. INTRODUCTION: Phenomenology. N / m. N / m (2) kg G. Let s consider a shear force experiment on a solid cube. (Fig. 1)

Save this PDF as:

Size: px
Start display at page:

Download "I. INTRODUCTION: Phenomenology. N / m. N / m (2) kg G. Let s consider a shear force experiment on a solid cube. (Fig. 1)"

## Transcription

1 I. INTRODUCTION: Phenomenology Let s consider a shear force experiment on a solid cube. (Fig. 1) We can easily verify that for the solid not to move or rotate, all forces acting on the cube must be of equal magnitude. Let s define the tangential stress by: Fig. 1 : Shearing of a cube F t s N / m (1) If we now look at the more general case of a parallelepiped, and no longer a cube, all four stresses must be equal for the solid not to move or rotate. As a result of these stresses, the solid undergoes an angular deformation, and for small τ, we have: [G] = G N / m () This is the law of shear stress, where G is the shear modulus, and depends on the studied material. However, if we pay closer attention to the deformation, we notice that angular deformation is a function of time (Fig. ). The value established in equation () only represents the asymptotic value of the deformation. Instead, the full equation becomes: kg G avec ms (3) is called the dynamic viscosity coefficient. It depends on the studied material as well as other factors, such as temperature.

2 EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B- (t) contrainte appliquée temps temps Fig. : Dynamic viscosity Therefore, viscosity is a property of a body undergoing a deformation. It is a measure of the resistance the neighboring layers present towards sliding on one another. Viscosity is easiest to achieve and study in fluids. This is because fluids have weaker intermolecular bonds, therefore allow for one element of fluid to move around much more freely than in a solid. This results in the deformation having no asymptotic value. In other words, the shear modulus G of a fluid is 0. The stress is therefore only linked to the speed of the deformation. Viscosity is often defined by the following experiment. By maintaining the lower surface Ft stationary and giving the upper surface a speed v t (Fig. 3), we notice surface mobile that: v t e - Ft surface immobil F t Svt e Fig. 3 : Relative motion of the different layers or v t (4) e The speed profile inside the fluid presented in Fig. 4. v t z (local) z Vt (e) surface mobile e surface immobile Fig 4: Speed profile inside the fluid.

3 EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B-3 Comments: 1) Equation (4) is coherent with from (3) for small angles. ) 3 Kinematic viscosity is often defined by: v par v [ m s ], where is the density in [ kg m ]. 3) For a pure elastic deformation (i.e. 0 ), the stored potential energy during the deformation is entirely restored when the deformation is back to zero. However, viscosity implies an irreversible absorption of mechanical energy, that heats up the body through internal friction. 4) Elastic compressibility is the phenomenon the connects a isotropic compression to a volume variation. Experience shows that the volume variation isn t instantaneous when the stress is applied. This lets us * define a second viscosity coefficient,. II. OBJECTIVE OF THE EXPERIMENT The objective of this experiment is to determine the viscosity coefficient of different oils, as a function of temperature, as well as to get familiar with some technical knowledge. III. BALL VISCOMETER. Although this experiment is fundamentally simple, it isn t technically an experimentally trivial. We will use other simple phenomena to help determine. One approach consists in observing a ball falling through a fluid. In a vacuum, this would result in a uniform acceleration, but in a fluid, drag forces quickly counteract the acceleration. After a while, the ball reaches a constant speed, and in certain cases, we can use this speed to determine the viscosity coefficient. That is the principle of ball viscometer. III.1. A few definitions and results. When an object is in motion in a fluid, it undergoes a drag force. The drag force is defined by: T 1 Cx S v (5) v is the relative speed of the object to the fluid. S is the area of the projection of the object on a perpendicular plane to its speed, and C is the drag coefficient. x This drag coefficient is a function of the magical Reynolds number, Re. This dimensionless number is defined by: Re vl (6) where L is a characteristic length of the object (for example the diameter of a sphere, or the diameter of a cylindrical conduct, ). Though this is an empirical quantity, it can sometimes be determined theoretically. For a sphere with a given diameter r, we notice the following behavior:

4 EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B-4 a) Re 10 - b) Re 10 6 c) Re 0 The variation of d) Re 100 Fig. 5 : Flow around an obstacle C x as a function of Re is shown in figure 6. In the special case of a permanent flow (figure 5a), and a small Reynolds number: 0 Re 05. and by neglecting inertial forces with respect to drag forces, Stokes was able to evaluate and T. His calculations yielded: 4 Cx T 6 r v Re C x (7)

5 EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B-5 3 x c1 0 STEADYPERIO v = 0DIC t (LAMI NAR) PERIODIC "TURBULENT" TURBULENT BOUNDARY LAYER Fig. 6: Types of flow For a fluid to follow (7), it must be Newtonian, i.e. homogenous and isotropic. This is the case of water, acetone, oil, glycerin, and many more, but is not the case for most silicones, and other liquids made up of large chains of molecules. In these liquids, viscosity is anisotropic, and varies with speed. There exist many other formulae allowing to calculate the drag coefficient, but not all are valid for small Reynolds numbers. We ll mention Oseen s formula, which is applicable for 0Re 1 and accounts for inertial forces: Cx et T 3 r v r v Re 4 (8) III.. Variation of with temperature. For liquids where the molecules don t form complex groups, fluidity, defined by 1, is calculated by a Boltzmann relation (see statistical mechanics): E 1 1 kt b e (9) A where E is the activation energy, T the temperature and kb the Boltzman constant. We can make sense of the equation by looking at the microscopic scale. Microscopically, fluidity is dependent on the momentum transfer between molecules. Therefore, a molecule must be capable of overcoming a potential barrier E corresponding to the molecules. This allows us to write: E ln ln A (9 b) kt b IV. DISPOSITIF EXPERIMENTAL The experiment consists in letting a rigid ball fall in the liquid we wish to study. We know the characteristics of the ball, as well as the density of the fluid. When the ball reaches a constant speed, the drag force is easily determined by the weight of the ball, and its buoyancy. Therefore, by measuring the ball s speed, and assuming a small enough Reynolds number, we can determine the viscosity using equation (7).

6 EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B-6 b m t 1 t A a t B a liquide B réseau t éclairage pompe p chauffage liquide A chauff. autom. chauf f. réglage f in f usible s Fig. 7: Diagram of the viscometer The liquids we wish to study are contained in two glass tubes A and B, inside a basin of water. A heater inside the basin allows us to heat the water. It is operated by a thermostat. the water can also be cooled, by letting tap water flow through the system. An agitator in the water makes sure the temperature stays homogeneous. A digital thermometer indicates the water temperature. The temperatures of the liquids A and B are given by thermometers in their respective tubes. The thermometers are attached to agitators, that make the temperature more homogeneous, and can carry the ball up to the surface.

7 EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B-7 Fig 8: Experimental setup. Using the viscometer Turn the system on by pushing the main button. Then push Illumination and Pump to turn on the light, and the basin s agitator. To start the heater, hit Heating and Automatic heating up. It takes approximately 60 minutes to get from room temperature to 80 C. This generally gives the user enough time to take measurements (approximately every 5 C). However, if this is too quick, push the Automatic heating up button again to deactivate it and slow up the heating process. Once the system is at 80 C, deactivate the heater, and turn on the cooling circuit. This is done by opening the tap on the right of the setup, over the sink.

8 EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B-8 V. TRAVAIL DEMANDE 1) a. Determine the viscosity coefficient for both liquids, between 0C and 80 C (do not go over 80 C ). Do two sets of measurements for each liquid: one during the heating and one during the cooling process. b. Plot the values of log versus and E from (10). 1 T (don t forget error bars), and determine the constants A Be careful not to create air bubbles when placing the agitators back into the tubes. If the ball comes too close a bubble, the result will be faulty. Likewise, try not to let the ball fall too close to the sides of the tube. ) The error generated when using the Stokes formula increases with temperature. Please take note of that, and remember that must not exceed 0.5 ( is calculated from equation 6). 3) Please also note that the temperature can vary during a single measurement. This is particularly interesting when comparing the results of (T ) et (T ). 4) We can also study the time evolution of the drag force T(t) 6 r v(t) assuming the initial conditions x(t 0) v(t 0) 0. What is the time constant? Comments Ball diameter: ( 0.01) mm Ball mass: ( ) mg Distance between bars : 50mm The oils densities can be found on a sheet of paper in the drawer.

9 EPFL-TRAVAUX PRATIQUES DE PHYSIQUE B-9 VI. APPENDIX : A BIT OF TECHNICAL KNOWLEDGE ABOUT OILS 1) Units The CGS units for dynamic viscosity are the poise : centipoises : cpo), and for kinematic viscosity, the stokes: commonly used : cst). 1Po 1g cm s 1 1 (or the more commonly used 1 1St 1cm s (again, the centistokes is more In Switzerland, we tend to use conventional Engler viscosity for industrial lubricants. (time it takes for 00 cm 3 of oil to flow divided by the time the same quantity of water takes, at 0 o C). ) Classification of SAE oils The most widely used system to classify vehicle oils as a function of their viscosity is that of the American Society of Automotive Engineers. This system was elaborated to replace unspecific terminology such as light or heavy. SAE 5W, SAE 10W, and SAE 0W all correspond to a give viscosity at 0 o F (-17,8 o C). These limits were established to ensure reliable vehicle starting in winter (W stands for Winter) and an effective lubricant at the operating temperature. SAE 0 and SAE 50 oils correspond to specific viscosities at 10 o F (98,9 o C). Please note that SAE ratings do not ensure quality, since it is only a viscosity indicator. SAE specifications being based on only temperatures( -17,8 o C and 98,9 o C), we can use an appropriate oil to make an oil that satisfy two or more SAE grades. This is called a multigrade oil. For instance, a motor oil that has a viscosity of '000 cst at a temperature of C (SAE 10W) and a viscosity of 15cSt at 98.9 C (SAE 40) will be graded as an SAE 10W/40 oil, and will therefore cover 4 different SAE ranks: SAE 10W, SAE 0W, SAE 30 and SAE 40, depending on the oil s temperature. This improved viscosity index (low variation of the viscosity with temperature) is generally achieved by adding long chained polymers. The advantage of multigrade oils is that they can be used at a wide range of temperatures. Oil viscosity indices The viscosity index is a good indicator of the viscosity s variation with temperature. This notion (VI=viscosity index) was created by Dean and Darvis in 199. They used two different types of oil as a reference: Those that vary a lot with temperature (VI=0) and those that don t (VI=100). The viscosity index is given by comparing the Fig. 9 : Viscosity index oil with the reference oils. (figure 8) Supposing we have an oil whose viscosity varies like the dashed line on figure 8, the viscosity index is calculated according to equation (11): L U VI 100 L H (11) This process allows any oil to be characterized with respect to the two reference oils. The bigger VI, the closer the curve will be to H (strong paraffinic property), and therefore the less it will vary with temperature.

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### Swissmetro travels at high speeds through a tunnel at low pressure. It will therefore undergo friction that can be due to:

I. OBJECTIVE OF THE EXPERIMENT. Swissmetro travels at high speeds through a tunnel at low pressure. It will therefore undergo friction that can be due to: 1) Viscosity of gas (cf. "Viscosity of gas" experiment)

### Lubricants' measurements

Lubricants' measurements Aims of the practice: measurement of lubricants' viscosity, familiarization of the viscosity index and its calculation from the data measured during the practice. Notion, determination,

### XI / PHYSICS FLUIDS IN MOTION 11/PA

Viscosity It is the property of a liquid due to which it flows in the form of layers and each layer opposes the motion of its adjacent layer. Cause of viscosity Consider two neighboring liquid layers A

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA. PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 13 NQF LEVEL 3

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA PRINCIPLES AND APPLICATIONS of FLUID MECHANICS UNIT 13 NQF LEVEL 3 OUTCOME 1 - PHYSICAL PROPERTIES AND CHARACTERISTIC BEHAVIOUR OF FLUIDS TUTORIAL 1 - SURFACE TENSION

### 1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids

1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids - both liquids and gases.

### Chapter (1) Fluids and their Properties

Chapter (1) Fluids and their Properties Fluids (Liquids or gases) which a substance deforms continuously, or flows, when subjected to shearing forces. If a fluid is at rest, there are no shearing forces

### TYPES OF FLUID FLOW. Laminar or streamline flow. Turbulent flow

FLUID DYNAMICS We will deal with Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID

### SIZE OF A MOLECULE FROM A VISCOSITY MEASUREMENT

Experiment 8, page 1 Version of April 25, 216 Experiment 446.8 SIZE OF A MOLECULE FROM A VISCOSITY MEASUREMENT Theory Viscous Flow. Fluids attempt to minimize flow gradients by exerting a frictional force,

### Fluids and Solids: Fundamentals

Fluids and Solids: Fundamentals We normally recognize three states of matter: solid; liquid and gas. However, liquid and gas are both fluids: in contrast to solids they lack the ability to resist deformation.

### Journal bearings/sliding bearings

Journal bearings/sliding bearings Operating conditions: Advantages: - Vibration damping, impact damping, noise damping - not sensitive for vibrations, low operating noise level - dust tight (if lubricated

### CHBE 363: Rotary Viscometer

CHBE 363: Rotary Viscometer Objectives 1. To illustrate the use of a rotary viscometer in the characterization of different types of fluids. 2. To determine the viscosity of Newtonian liquids. 3. To investigate

### The Viscosity of Fluids

Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et

### The Viscosity of Fluids

Experiment #11 The Viscosity of Fluids References: 1. Your first year physics textbook. 2. D. Tabor, Gases, Liquids and Solids: and Other States of Matter (Cambridge Press, 1991). 3. J.R. Van Wazer et

### Fluid Mechanics: Static s Kinematics Dynamics Fluid

Fluid Mechanics: Fluid mechanics may be defined as that branch of engineering science that deals with the behavior of fluid under the condition of rest and motion Fluid mechanics may be divided into three

### Notes on Polymer Rheology Outline

1 Why is rheology important? Examples of its importance Summary of important variables Description of the flow equations Flow regimes - laminar vs. turbulent - Reynolds number - definition of viscosity

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

Vol. XX 2012 No. 4 28 34 J. ŠIMIČEK O. HUBOVÁ NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES Jozef ŠIMIČEK email: jozef.simicek@stuba.sk Research field: Statics and Dynamics Fluids mechanics

### Viscosity. Desmond Schipper Andrew R. Barron. 1 Introduction

OpenStax-CNX module: m50215 1 Viscosity Desmond Schipper Andrew R. Barron This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution License 4.0 Abstract This module discusses

### Lecture 24 - Surface tension, viscous flow, thermodynamics

Lecture 24 - Surface tension, viscous flow, thermodynamics Surface tension, surface energy The atoms at the surface of a solid or liquid are not happy. Their bonding is less ideal than the bonding of atoms

### Ch 2 Properties of Fluids - II. Ideal Fluids. Real Fluids. Viscosity (1) Viscosity (3) Viscosity (2)

Ch 2 Properties of Fluids - II Ideal Fluids 1 Prepared for CEE 3500 CEE Fluid Mechanics by Gilberto E. Urroz, August 2005 2 Ideal fluid: a fluid with no friction Also referred to as an inviscid (zero viscosity)

### Viscosity: The Fluids Lab Teacher Version

Viscosity: The Fluids Lab Teacher Version California Science Content Standards: 1. Motion and Forces: Newton's laws predict the motion of most objects. 1b. Students know that when forces are balanced,

### Dimensional Analysis

Dimensional Analysis An Important Example from Fluid Mechanics: Viscous Shear Forces V d t / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Ƭ = F/A = μ V/d More generally, the viscous

### For Water to Move a driving force is needed

RECALL FIRST CLASS: Q K Head Difference Area Distance between Heads Q 0.01 cm 0.19 m 6cm 0.75cm 1 liter 86400sec 1.17 liter ~ 1 liter sec 0.63 m 1000cm 3 day day day constant head 0.4 m 0.1 m FINE SAND

### Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

### Basic Fluid Mechanics. Prof. Young I Cho

Basic Fluid Mechanics MEM 220 Prof. Young I Cho Summer 2009 Chapter 1 Introduction What is fluid? Give some examples of fluids. Examples of gases: Examples of liquids: What is fluid mechanics? Mechanics

### Practice Problems on Viscosity. free surface. water. y x. Answer(s): base: free surface: 0

viscosity_01 Determine the magnitude and direction of the shear stress that the water applies: a. to the base b. to the free surface free surface U y x h u water u U y y 2 h h 2 2U base: yx y 0 h free

### PHYSICS FUNDAMENTALS-Viscosity and flow

PHYSICS FUNDAMENTALS-Viscosity and flow The origin of viscosity When a force is applied to a solid, it will yield slightly, and then resist further movement. However, when we apply force to a fluid, it

### SURFACE TENSION. Definition

SURFACE TENSION Definition In the fall a fisherman s boat is often surrounded by fallen leaves that are lying on the water. The boat floats, because it is partially immersed in the water and the resulting

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 6. Flow of Fluid and Bernoulli s Equation 7.

### VISCOSITY OF A LIQUID. To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied.

VISCOSITY OF A LIQUID August 19, 004 OBJECTIVE: EQUIPMENT: To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied. Viscosity apparatus

### 15. The Kinetic Theory of Gases

5. The Kinetic Theory of Gases Introduction and Summary Previously the ideal gas law was discussed from an experimental point of view. The relationship between pressure, density, and temperature was later

### HW Set VI page 1 of 9 PHYSICS 1401 (1) homework solutions

HW Set VI page 1 of 9 10-30 A 10 g bullet moving directly upward at 1000 m/s strikes and passes through the center of mass of a 5.0 kg block initially at rest (Fig. 10-33 ). The bullet emerges from the

### Boundary Conditions in Fluid Mechanics

Boundary Conditions in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University The governing equations for the velocity and pressure fields are partial

### Higher Technological Institute Civil Engineering Department. Lectures of. Fluid Mechanics. Dr. Amir M. Mobasher

Higher Technological Institute Civil Engineering Department Lectures of Fluid Mechanics Dr. Amir M. Mobasher 1/14/2013 Fluid Mechanics Dr. Amir Mobasher Department of Civil Engineering Faculty of Engineering

### Experiment: Viscosity Measurement B

Experiment: Viscosity Measurement B The Falling Ball Viscometer Purpose The purpose of this experiment is to measure the viscosity of an unknown polydimethylsiloxiane (PDMS) solution with a falling ball

RHEOLOGY RHEOLOGY Science describing the flow and deformation of matter under stress. Rheo = the flow Viscosity (η) is the resistance of a fluid material to flow under stress. The higher the viscosity,

### Viscous Flow in Pipes

Viscous Flow in Pipes Excerpted from supplemental materials of Prof. Kuang-An Chang, Dept. of Civil Engin., Texas A&M Univ., for his spring 2008 course CVEN 311, Fluid Dynamics. (See a related handout

### A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension

A drop forms when liquid is forced out of a small tube. The shape of the drop is determined by a balance of pressure, gravity, and surface tension forces. 2 Objectives Have a working knowledge of the basic

### We will study the temperature-pressure diagram of nitrogen, in particular the triple point.

K4. Triple Point of Nitrogen I. OBJECTIVE OF THE EXPERIMENT We will study the temperature-pressure diagram of nitrogen, in particular the triple point. II. BAKGROUND THOERY States of matter Matter is made

### Lecture 5 Hemodynamics. Description of fluid flow. The equation of continuity

1 Lecture 5 Hemodynamics Description of fluid flow Hydrodynamics is the part of physics, which studies the motion of fluids. It is based on the laws of mechanics. Hemodynamics studies the motion of blood

### Teil I. Student Laboratory Manuals

Teil I Student Laboratory Manuals 1 IR1 5. Fluid friction in liquids 5.1 Introduction Generally the term fluid is understood to be matter either in the gaseous or liquid state. The physics involved on

### Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture No. # 36 Pipe Flow Systems

Fluid Mechanics Prof. T. I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture No. # 36 Pipe Flow Systems Welcome back to the video course on Fluid Mechanics. In today

### Air Resistance: Distinguishing Between Laminar and Turbulent Flow 0.1 Introduction

Air Resistance: Distinguishing Between Laminar and Turbulent Flow 0.1 Introduction You have probably heard that objects fall (really, accelerate) at the same rate, independent of their mass. Galileo demonstrated

### 1. Introduction, fluid properties (1.1, and handouts)

1. Introduction, fluid properties (1.1, and handouts) Introduction, general information Course overview Fluids as a continuum Density Compressibility Viscosity Exercises: A1 Applications of fluid mechanics

### Viscosity Measurement Guide

Viscosity Measurement Guide For using Viscotester 3-20-41 Higashimotomachi, Kokubunji, Tokyo 185-8533, Japan http://www.rion.co.jp/english/ Contents Introduction...1 What is viscosity?...2 Viscosity unit:

### Applied Fluid Mechanics

Applied Fluid Mechanics Sixth Edition Robert L. Mott University of Dayton PEARSON Prentkv Pearson Education International CHAPTER 1 THE NATURE OF FLUIDS AND THE STUDY OF FLUID MECHANICS 1.1 The Big Picture

### CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology

CBE 6333, R. Levicky 1 Review of Fluid Mechanics Terminology The Continuum Hypothesis: We will regard macroscopic behavior of fluids as if the fluids are perfectly continuous in structure. In reality,

### VISCOSITY. Aslı AYKAÇ, PhD. NEU Faculty of Medicine Department of Biophysics

VISCOSITY Aslı AYKAÇ, PhD. NEU Faculty of Medicine Department of Biophysics DEFINITION A fluid s ability to flow is called viscosity. Viscosity arises from the mutual COHESIVE FORCES between molecules

### Basic Concepts of Thermodynamics

Basic Concepts of Thermodynamics Every science has its own unique vocabulary associated with it. recise definition of basic concepts forms a sound foundation for development of a science and prevents possible

### OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS

Unit 41: Fluid Mechanics Unit code: T/601/1445 QCF Level: 4 Credit value: 15 OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS 3 Be able to determine the behavioural characteristics and parameters of real fluid

### Sinking Bubble in Vibrating Tanks Christian Gentry, James Greenberg, Xi Ran Wang, Nick Kearns University of Arizona

Sinking Bubble in Vibrating Tanks Christian Gentry, James Greenberg, Xi Ran Wang, Nick Kearns University of Arizona It is experimentally observed that bubbles will sometimes sink to the bottom of their

### Steven Burian Civil & Environmental Engineering March 27, 2015

Fundamentals of Engineering (FE) Exam Mechanics Steven Burian Civil & Environmental Engineering March 27, 2015 s and FE Morning ( Mechanics) A. Flow measurement 7% of FE Morning B. properties Session C.

### HEAVY OIL FLOW MEASUREMENT CHALLENGES

HEAVY OIL FLOW MEASUREMENT CHALLENGES 1 INTRODUCTION The vast majority of the world s remaining oil reserves are categorised as heavy / unconventional oils (high viscosity). Due to diminishing conventional

### PUMPS STEAM TURBINES BUILDING & FIRE WASTEWATER SERVICE PUMP CLINIC 22 VISCOSITY

PUMP CLINIC 22 VISCOSITY The viscosity of a fluid is that property which tends to resist a shearing force. It can be thought of as the internal friction resulting when one layer of fluid is made to move

### AP2 Fluids. Kinetic Energy (A) stays the same stays the same (B) increases increases (C) stays the same increases (D) increases stays the same

A cart full of water travels horizontally on a frictionless track with initial velocity v. As shown in the diagram, in the back wall of the cart there is a small opening near the bottom of the wall that

### LAB #2: Forces in Fluids

Princeton University Physics 103/105 Lab Physics Department LAB #2: Forces in Fluids Please do NOT attempt to wash the graduated cylinders once they have oil in them. Don t pour the oil in the graduated

### 4 The strength of the lithosphere

4 The strength of the lithosphere Constitutive equations specify the relations between stress and strain or the time derivatives of strain and thus can be used in conjunction with the equations of motion

### INTRODUCTION TO FLUID MECHANICS

INTRODUCTION TO FLUID MECHANICS SIXTH EDITION ROBERT W. FOX Purdue University ALAN T. MCDONALD Purdue University PHILIP J. PRITCHARD Manhattan College JOHN WILEY & SONS, INC. CONTENTS CHAPTER 1 INTRODUCTION

### FLUID DYNAMICS. Intrinsic properties of fluids. Fluids behavior under various conditions

FLUID DYNAMICS Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID FLOW Laminar or

### ENSC 283 Introduction and Properties of Fluids

ENSC 283 Introduction and Properties of Fluids Spring 2009 Prepared by: M. Bahrami Mechatronics System Engineering, School of Engineering and Sciences, SFU 1 Pressure Pressure is the (compression) force

### Rheology. Definition of viscosity. Non-newtonian behaviour.

Rheology. Definition of viscosity. Non-newtonian behaviour. Rheology Rheology is the science of the flow and deformation of matter (liquid or soft solid) under the effect of an applied force Deformation

### CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK PART - A

CE 6303 MECHANICS OF FLUIDS L T P C QUESTION BANK 3 0 0 3 UNIT I FLUID PROPERTIES AND FLUID STATICS PART - A 1. Define fluid and fluid mechanics. 2. Define real and ideal fluids. 3. Define mass density

### Rheological Properties of Topical Formulations

Rheological Properties of Topical Formulations Hemi Nae, PhD Hydan Technologies, Inc. Key Words Complex Modulus, Creep/Recovery, Dilatant Flow, Dynamic Viscosity, Flow, Flow Curve, Flow Models, Frequency

### HWR 431 / 531 HYDROGEOLOGY LAB SECTION LABORATORY 2 DARCY S LAW

HWR 431 / 531 HYDROGEOLOGY LAB SECTION LABORATORY 2 DARCY S LAW Introduction In 1856, Henry Darcy, a French hydraulic engineer, published a report in which he described a series of experiments he had performed

### Dimensional analysis is a method for reducing the number and complexity of experimental variables that affect a given physical phenomena.

Dimensional Analysis and Similarity Dimensional analysis is very useful for planning, presentation, and interpretation of experimental data. As discussed previously, most practical fluid mechanics problems

### 1.4 Review. 1.5 Thermodynamic Properties. CEE 3310 Thermodynamic Properties, Aug. 26,

CEE 3310 Thermodynamic Properties, Aug. 26, 2011 11 1.4 Review A fluid is a substance that can not support a shear stress. Liquids differ from gasses in that liquids that do not completely fill a container

### du u U 0 U dy y b 0 b

BASIC CONCEPTS/DEFINITIONS OF FLUID MECHANICS (by Marios M. Fyrillas) 1. Density (πυκνότητα) Symbol: 3 Units of measure: kg / m Equation: m ( m mass, V volume) V. Pressure (πίεση) Alternative definition:

### FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER

VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER? What type of fluid flow is observed? The above pictures show how the effect

### Min-218 Fundamentals of Fluid Flow

Excerpt from "Chap 3: Principles of Airflow," Practical Mine Ventilation Engineerg to be Pubished by Intertec Micromedia Publishing Company, Chicago, IL in March 1999. 1. Definition of A Fluid A fluid

### Solution for Homework #1

Solution for Homework #1 Chapter 2: Multiple Choice Questions (2.5, 2.6, 2.8, 2.11) 2.5 Which of the following bond types are classified as primary bonds (more than one)? (a) covalent bonding, (b) hydrogen

### Chapter 12 Elasticity

If I have seen further than other men, it is because I stood on the shoulders of giants. Isaac Newton 12.1 The Atomic Nature of Elasticity Elasticity is that property of a body by which it experiences

### Department of Mechanical Engineering

Department of Mechanical Engineering AMEE 401/ AUTO 400 Aerodynamics Instructor: Marios M. Fyrillas Email: m.fyrillas@frederick.ac.cy QUESTION 1 HOMEWORK ASSIGNMENT #1 SOLUTION a. Explain the meaning of

### Characteristics of a fluid

Characteristics of a fluid Fluids are divided into liquids and gases. A liquid is hard to compress and as in the ancient saying Water takes the shape of the vessel containing it, it changes its shape according

### Fig. 1. The velocity distribution will be linear over the distance dx, and experiments show that the velocity

Viscosity The viscosity of a fluid is that property which tends to resist a shearing force. It can be thought of as the internal friction resulting when one layer of fluid is made to move in relation to

### Chapter Six. Non-Newtonian Liquid

Chapter Six Non-Newtonian Liquid For many fluids a plot of shear stress against shear rate does not give a straight line. These are so-called Non-Newtonian Fluids. Plots of shear stress against shear rate

### Physics for the Life Sciences: Fall 2008 Lecture #25

Physics for the Life Sciences: Fall 2008 Lecture #25 Real fluids: As we have mentioned several times, real fluids are more complex than the ideal fluids described by the continuity equation and Bernoulli

### Rheology of multigrade engine oils

Indian Journal of Chemical Technology Vol. 13, March 2006, pp. 180-184 Rheology of multigrade engine oils Sabiha Tanveer, Umesh Chandra Sharma & Ram Prasad* Department of Chemical Engineering, H.B.Technological

### Experiments on the Viscosity and Freezing Point of a Starch Water Mixture

Experiments on the Viscosity and Freezing Point of a Starch Water Mixture Chunyang Ding Physics Department, Interlake High School, Washington 988 Alice Huang Physics Department, Interlake High School,

### CHAPTER 2: LIQUID VISCOSITY MEASUREMENT

CHAPTER 2: LIQUID VISCOSITY MEASUREMENT Objective Calculate viscosity (dynamic or absolute, and kinematic) and determine how this property varies with changes in temperature for a constant-composition

### Ch 6 Forces. Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79

Ch 6 Forces Question: 9 Problems: 3, 5, 13, 23, 29, 31, 37, 41, 45, 47, 55, 79 Friction When is friction present in ordinary life? - car brakes - driving around a turn - walking - rubbing your hands together

### Material Types and Properties

Material Types and Properties 1 Material Types There are many kinds of materials, but most of them can be divided into four groups: Metals - Metals are composed of one or more metallic elements and often

### Fluids in Motion Supplement I

Fluids in Motion Supplement I Cutnell & Johnson describe a number of different types of flow: Compressible vs incompressible (most liquids are very close to incompressible) Steady vs Unsteady Viscous or

### Applied Fluid Mechanics

Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and

### CHE 253M Experiment No. 3 LIQUID FLOW MEASUREMENT

Rev 8/15 AW/GW CHE 253M Experiment No. 3 LIQUID FLOW MEASUREMENT The objective of this experiment is to familiarize the student with several types of flow-measuring devices commonly used in the laboratory

### Differential Relations for Fluid Flow. Acceleration field of a fluid. The differential equation of mass conservation

Differential Relations for Fluid Flow In this approach, we apply our four basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of

### Natural Convection. Buoyancy force

Natural Convection In natural convection, the fluid motion occurs by natural means such as buoyancy. Since the fluid velocity associated with natural convection is relatively low, the heat transfer coefficient

### Surface Tension. the surface tension of a liquid is the energy required to increase the surface area a given amount

Tro, Chemistry: A Molecular Approach 1 Surface Tension surface tension is a property of liquids that results from the tendency of liquids to minimize their surface area in order to minimize their surface

### www.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x

Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity

### 4 Microscopic dynamics

4 Microscopic dynamics In this section we will look at the first model that people came up with when they started to model polymers from the microscopic level. It s called the Oldroyd B model. We will

### Chapter 1. Governing Equations of Fluid Flow and Heat Transfer

Chapter 1 Governing Equations of Fluid Flow and Heat Transfer Following fundamental laws can be used to derive governing differential equations that are solved in a Computational Fluid Dynamics (CFD) study

### SAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 1 STRESS AND STRAIN

SAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 1 STRESS AND STRAIN 1.1 Stress & Strain Stress is the internal resistance offered by the body per unit area. Stress is represented as force per unit area. Typical

### c) Give two integral expressions that relate the time dependent modulus, G(t), to J e 0 and η 0.

Final Polymer Physics (Dynamics) Fall 2000 12/5/00 1) In polymers the viscosity is often measured using a cone and plate viscometer where the zero shear rate viscosity, η 0 and coefficient of the first

### Predicting and Measuring Viscosity of Crude Oil Blends

June 20 22, 2012 Kananaskis, Alberta Predicting and Measuring Viscosity of Crude Oil Blends Branko Banjac Joint CCQTA/COQA Meetings TABLE OF CONTENTS Viscosity measurement techniques Predicting viscosity

### Fluid Dynamics Viscosity. Dave Foster Department of Chemical Engineering University of Rochester Email: dafoster@che

Fluid Dynamics Viscosity Dave Foster Department of Chemical Engineering University of Rochester Email: dafoster@che che.rochester.eduedu 1 Chemical Engineering What do Chemical Engineers Do? Manufacturing

### Chapter 4 Strain and Material Relations

CIVL 222 STRENGTH OF MATERIALS Chapter 4 Strain and Material Relations Terminology 1. Displacement 2. Deformation 3. Strain 4. Average Axial Strain 5. Shearing Strain 6. Poisson s Ratio 7. Mechanical Properties

### MEASUREMENT OF VISCOSITY OF LIQUIDS BY THE STOKE S METHOD

130 Experiment-366 F MEASUREMENT OF VISCOSITY OF LIQUIDS BY THE STOKE S METHOD Jeethendra Kumar P K, Ajeya PadmaJeeth and Santhosh K KamalJeeth Instrumentation & Service Unit, No-610, Tata Nagar, Bengaluru-560092.

### LAB 6: GRAVITATIONAL AND PASSIVE FORCES

55 Name Date Partners LAB 6: GRAVITATIONAL AND PASSIVE FORCES And thus Nature will be very conformable to herself and very simple, performing all the great Motions of the heavenly Bodies by the attraction