XI / PHYSICS FLUIDS IN MOTION 11/PA

Size: px
Start display at page:

Download "XI / PHYSICS FLUIDS IN MOTION 11/PA"

Transcription

1 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 and B. Suppose A faster than B. B would tend to retard the motion of A. On the other hand, A would try to accelerate NB. Due to these two different tendencies, a backward tangential force is set up. This force tends to destroy the relative motion between the two layers. This accounts for the viscous behavior of both liquids and gases. Newton s law of viscous drag It states that force of viscous drag between two liquid layers is 1. Directly proportional to difference in velocity of two layers 2. Directly proportional to area of two layers 3. Inversely proportional to separation between two layers Combining these three equations we get Where η is called coefficient of viscosity Negative sign shows that direction of viscous drag is opposite to relative velocity between two layers. We have Definition of coefficient of viscosity Consider modulus Putting A = 1 m 2, dv/dx = 1 s -1 we get F = η 1 1 F = η Thus coefficient of viscosity of a liquid is defined as the force of viscous drag between any two layers of liquid having unit area in contact and having unit velocity gradient. Units of η 1

2 SI unit of η is Pas (i.e. Pascal second) and cgs unit is poise 1Pas = 10 poise One poise Putting F = 1 dyne, A = 1 cm 2, and dv/dx = 1 s -1 we get 1dyne = η 1cm 2 1s -1 i.e. Therefore coefficient of viscosity of a liquid is said to be one poise if there exists a force of viscous drag of 1 dyne between any two layers of liquid having 1 cm 2 area in contact and velocity gradient 1 s A metal plate 0.02 m 2 in area is lying on a liquid layer of thickness 10-3 m and coefficient of viscosity of 12 decapoise. Calculate the horizontal force required to move the plate with a speed of ms -1. [Ans: 6 N] 2. A square plate of 0.1 m side moves parallel to another plate with a velocity of 0.1 ms -1, both the plates being immersed in water. If the viscous force is N and viscosity of water is 10-3 decapose, wthat is their distance apart? [Ans: m] 3. A metal plate of area m 2 is placed on a m thick castor oil layer. If a force of 2.25 newton is needed to move the plate with a velocity ms -1, calculate the coefficient of viscosity of castor oil. [Ans: 75 decapoise] 4. A flat plate of area 10-2 m 2 is separated from a large plate by a layer 10-3 m thick. If the coefficient of visicoty of the liquid is 10-3 decapoise, what force is required to keep the plate moving with a velocity 0.05 ms -1? [Ans: N] 5. A flat plate of area 1 m 2 is separated from a bigger flat plate of rest by a uniform layer of liquid 1 mm thick. If a tangential force of 5 N is required to move the smaller plate with a constant speed of 2.5 cm/s, what is the coefficient of viscosity of the liquid? [Ans: 0.2 Pas] Stokes Law It states that force of viscous drag experienced by a spherical body moving inside liquid at rest is 1. Directly proportional to radius of body i.e. 2. Directly proportional to velocity of body 3. Directly proportional to coefficient of viscosity of liquid Combining three factors we get This formula is called Stokes law Poiseuielle s Equation It states that rate of flow of liquid in a cylindrical tube of uniform crossection is 1. Directly proportional to the fourth power of radius of tube i.e. 2

3 2. Directly proportional to pressure difference across two ends to tube 3. Inversely proportional to length of tube 4. Inversely proportional to coefficient of viscosity of liquid Combining these four parameters we get This formula is called Poiseuielle s Formula; V has SI units m 3 / s 6. Calculate the mass of water flowing in 10 minute through a tube of radius 10-2 m, one metre in length and having a constant pressure head of 0.20 m of water. Coefficient of viscosity = decapoise, g = 9.8 ms -2. [Ans: kg] 7. A liquid flows through a pipe of 10-3 m radius and 0.1 m length under a pressure of 10 3 Nm -2. Calculate the rate of flow and the speed of the liquid coming out of the pipe. The coefficient of viscosity of the liquid is decapoise. [Ans: 1 ms -1 ] Terminal velocity It is the maximum velocity with which a body falls freely under the effect of gravity inside a liquid at rest. Consider a spherical body of radius r falling freely inside a liquid of coefficient of viscosity η. Suppose ρ is the density of body and ρ 0 is the density of liquid. When body acquires terminal velocity we observe that total upward force acting on the body is balanced by total downward force i.e. Total upward force = Total downward force i.e. F B + F V = mg Substituting values for Buoyancy, Viscous drag we get Vρ 0 g + 6πηrv = Vρg Putting for volume of spherical body we get After cancelling we get 3

4 8. The terminal velocity of a copper ball of radius 2.0 mm falling through a tank of oil at 20 C 0 is 6.5 cms -1. Compute the viscosity of the oil at 20 C 0. Density of oil is kg m -3, density of copper is kgm -3. [Ans: 0.99 kgm -1 s -1 ] 9. A solid ball of volume V is dropped in a viscous liquid. It experiences a viscous force F. If a solid ball of volume 2V and of the same material is dropped in the same liquid, then what would be the viscous force? [Ans: 2F] 10. A rain drop of radius 0.5 mm has a terminal velocity of 2 ms -1 in air. The viscosity of air is poise. Calculate the viscous force on the rain drop. [Ans: dyne] 11. A gas bubble of diameter m rises steadily at the rate of ms -1 through a solution of density 2250 kgm -3. Calculate the coefficient of viscosity of the solution. Neglect the density of the gas. Given g = 9.8 ms -2 [Ans: 196 decapoise] 12. A drop of water of diameter m is falling through a medium of density 1.2 kgm -3 and coefficient of viscosity decapoise. Calculate the terminal velocity of the drop. [Ans: ms -1 ] 13. A solid sphere of radius 2 mm and density 10.5 gcm -3 is dropped in glycerin of coefficient of viscosity 9.8 poise and density 1.5gcm -3. Calculate the terminal velocity of the sphere. [Ans: 8 cms -1 ] 14. Two drops of equal size are falling through air with a steady velocity of 0.1 ms -1. If the drops coalesce what would be the new terminal velocity? [Ans: ms -1 ] 15. Find the radius of a small oil drop falling in air with a terminal velocity of 1 mm/s. Given specific gravity of oil = and η of air = decapoise. Neglect the density of air. [Ans: m] 16. An air bubble of 0.01 m radius is rising at a steady rate of ms -1 through a liquid of density of 800 kg m -3. Calculate the coefficient of viscosity of the liquid. Neglect the density of air. [Ans: decapoise] 17. Fine particles of sand are shaken up in water contained in a tall cylinder. If the depth of water in the cylinder is 0.3 m, calculate the size of the largest particle of sand that can remain suspended after the expiry of 40 minute. Given: density of sand = 2600 km -3 and viscosity of water = 10-3 decapoise. [Ans: m] 18. Eight rain drops of radius 10-3 m each falling down with a terminal velocity of 0.05 ms -1 coalesce to form a bigger drop. Calculate the terminal velocity of the bigger drop. [Ans: 0.2 ms -1 ] 19. A spherical ball of radius m and density 10 4 kgm -3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water, the velocity of the ball does not change, find h. The coefficient of viscosity of water is Pas. Take g = 9.8 ms -2. [Ans: 20.4 m] Streamline flow The flow of a fluid is said to be streamline if every particle of the fluid follows exactly the path of its preceding particle and has the same velocity (both in magnitude and direction) as that of its preceding particle when crossing that point. Note: 1. The fixed path followed by an orderly procession of particles in the steady flow of a liquid is called streamline. 2. A streamline may be defined as a path, straight or curved, such that tangent to it at any point indicates the direction of flow of the liquid at that point. 3. A group of streamlines is called a tube of flow. 4

5 4. Tangent at any point of the streamline gives the direction of velocity of the liquid at that point. 5. Two streamlines cannot intersect. If two streamlines intersect, then it would mean two different directions of velocity at given point. This is physically impossible. Laminar flow It is a type of flow of liquid in which it flows in the form of layers. Where each layer slides on the other. Laminar flow occurs at a greater velocity than streamline flow. Turbulent flow It is that flow of liquid in which molecules of liquid moves irregularly. Flow of liquid becomes turbulent when its velocity is greater than its critical velocity. Note: 1. When velocity of a liquid exceeds the critical velocity, the paths and velocities of the liquid particles begin to change continuously flow loses all its orderliness and is called turbulent flow. 2. For example the wakes left in water by moving ships is turbulent flow. 3. Sounds produced by whistling and by wind instruments result from the turbulent flow of air. Critical velocity The critical velocity of a liquid is that velocity of liquid up to which its flow is streamlined and above which its flow becomes turbulent. It is found that critical velocity is 1. Directly proportional to coefficient of viscosity of liquid 2. Inversely proportional to radius of tube 3. Inversely proportional to density of liquid Combining 1, 2 and 3 we get Where k is constant Note: This equation can be proved using dimensional formulae as: v c (r) a (ρ) b (η) c After putting values of dimensions of various quantities we can find expression for v c Reynolds s number It is a pure number which is used to predict the type of flow of liquid in a tube It is given by: It is found that if 5

6 1. Reynolds s number is less than 2000 then flow of liquid will be streamline. 2. Reynolds s number is between 2000 and 3000 then flow of liquid will be laminar. 3. Reynolds s number is greater than 3000 then flow will be turbulent. 20. Calculate the critical velocity for air flowing through a tube of m radius. For air ρ = 1.3 kgm -3 and η = decapo9ise. [Ans: 1.39ms -1 ] 21. What should be the maximum average velocity of water in a tube of diameter 2 cm so that the flow is laminar? Given viscosity of water = 10-3 Nm -2 [Ans: 0.05 ms -1 ] 22. Water at 20 C 0 flows through a tube of diameter m with a velocity of 0.12 ms -1. Given η = 10-3 decapoise, ρ of water = kgm -3. Comment on the nature of flow. [Ans: Laminar] 23. The flow rate from a tap of diameter 1.25 cm is 3l / min. The coefficient of viscosity of water is 10-3 Pas. Characterize the flow. [Ans: turbulent] Take a Test 24. An oil drop of radius mm falls freely in air whose coefficient of viscosity is pose. Calculate its terminal velocity if the density of oil is 0.9 gcm -3 and that of air is g lt -1, g = 980 cms -2 [Ans: ] 25. A spherical ball of radius m and of density 10-4 kg m -3 fall freely under gravity through a distance before entering a tank of water. If after entering the water, the velocity of the ball does not change, find h. The coefficient of viscosity of water is Nsm -2. [Ans: Ns -1 m -1 ] 26. In Millikan s oil drop experiment, what is the terminal speed of a drop of radius m and density Nms -1. How much is the viscous force on the drop at that speed? Neglect buoyancy of the drop due to air. [Ans: N] 27. Eight spherical rain drops of equal size are falling vertically through air with a terminal velocity of 0.10 ms - 1. What should be the velocity if these drops were to combine to form one large spherical drop? [Ans: 0.4 ms -1 ] 28. A plate of metal 10 cm 2 rests on a layer of castor oil 2mm thick whose coefficient of viscosity is 15.5 poise. Calculate the horizontal force required to move the plate with a speed of 3 cms -1. [Ans: dyne.] 29. What should be the average velocity of water in a tube of diameter 2.0 cm so that the flow is laminar? The viscosity of water is Nm -2 s. [Ans: 0.1ms -1 ] 6

FLUID FLOW STREAMLINE LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER

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

More information

Dimensional Analysis

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

More information

Aids needed for demonstrations: viscous fluid (water), tubes (pipes), injections, paper, stopwatches, vessels,, weights

Aids needed for demonstrations: viscous fluid (water), tubes (pipes), injections, paper, stopwatches, vessels,, weights 1 Viscous and turbulent flow Level: high school (16-17 years) hours (2 hours class teaching, 2 hours practical excercises) Content: 1. Viscous flow 2. Poiseuille s law 3. Passing from laminar to turbulent

More information

The Viscosity of Fluids

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

More information

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

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

More information

Fluids and Solids: Fundamentals

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.

More information

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

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

More information

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

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

More information

Basic Principles in Microfluidics

Basic Principles in Microfluidics Basic Principles in Microfluidics 1 Newton s Second Law for Fluidics Newton s 2 nd Law (F= ma) : Time rate of change of momentum of a system equal to net force acting on system!f = dp dt Sum of forces

More information

For Water to Move a driving force is needed

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

More information

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. 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

More information

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

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,

More information

Fluid Mechanics: Static s Kinematics Dynamics Fluid

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

More information

Diffusion and Fluid Flow

Diffusion and Fluid Flow Diffusion and Fluid Flow What determines the diffusion coefficient? What determines fluid flow? 1. Diffusion: Diffusion refers to the transport of substance against a concentration gradient. ΔS>0 Mass

More information

Viscosity: The Fluids Lab Teacher Version

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,

More information

MEASUREMENT OF VISCOSITY OF LIQUIDS BY THE STOKE S METHOD

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.

More information

01 The Nature of Fluids

01 The Nature of Fluids 01 The Nature of Fluids WRI 1/17 01 The Nature of Fluids (Water Resources I) Dave Morgan Prepared using Lyx, and the Beamer class in L A TEX 2ε, on September 12, 2007 Recommended Text 01 The Nature of

More information

Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE

Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE 1 P a g e Motion Physics Notes Class 11 CHAPTER 3 MOTION IN A STRAIGHT LINE If an object changes its position with respect to its surroundings with time, then it is called in motion. Rest If an object

More information

VISUAL PHYSICS School of Physics University of Sydney Australia. Why do cars need different oils in hot and cold countries?

VISUAL PHYSICS School of Physics University of Sydney Australia. Why do cars need different oils in hot and cold countries? VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW VISCOSITY POISEUILLE'S LAW? Why do cars need different oils in hot and cold countries? Why does the engine runs more freely as

More information

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

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.

More information

Notes on Polymer Rheology Outline

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

More information

Applied Fluid Mechanics

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

More information

OUTCOME 3 TUTORIAL 5 DIMENSIONAL ANALYSIS

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

More information

The ratio of inertial to viscous forces is commonly used to scale fluid flow, and is called the Reynolds number, given as:

The ratio of inertial to viscous forces is commonly used to scale fluid flow, and is called the Reynolds number, given as: 12.001 LAB 3C: STOKES FLOW DUE: WEDNESDAY, MARCH 9 Lab Overview and Background The viscosity of a fluid describes its resistance to deformation. Water has a very low viscosity; the force of gravity causes

More information

The Viscosity of Fluids

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

More information

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 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

More information

Natural Convection. Buoyancy force

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

More information

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

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

More information

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam

Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry

More information

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 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

More information

Viscosity. Desmond Schipper Andrew R. Barron. 1 Introduction

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

More information

Lecture 24 - Surface tension, viscous flow, thermodynamics

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

More information

Teil I. Student Laboratory Manuals

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

More information

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

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

More information

Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.

Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc. Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular

More information

CHAPTER 3: FORCES AND PRESSURE

CHAPTER 3: FORCES AND PRESSURE CHAPTER 3: FORCES AND PRESSURE 3.1 UNDERSTANDING PRESSURE 1. The pressure acting on a surface is defined as.. force per unit. area on the surface. 2. Pressure, P = F A 3. Unit for pressure is. Nm -2 or

More information

Millikan Oil Drop Experiment Matthew Norton, Jurasits Christopher, Heyduck William, Nick Chumbley. Norton 0

Millikan Oil Drop Experiment Matthew Norton, Jurasits Christopher, Heyduck William, Nick Chumbley. Norton 0 Millikan Oil Drop Experiment Matthew Norton, Jurasits Christopher, Heyduck William, Nick Chumbley Norton 0 Norton 1 Abstract The charge of an electron can be experimentally measured by observing an oil

More information

2After completing this chapter you should be able to

2After completing this chapter you should be able to After completing this chapter you should be able to solve problems involving motion in a straight line with constant acceleration model an object moving vertically under gravity understand distance time

More information

INTRODUCTION TO FLUID MECHANICS

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

More information

Forces. Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy

Forces. Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy Forces Definition Friction Falling Objects Projectiles Newton s Laws of Motion Momentum Universal Forces Fluid Pressure Hydraulics Buoyancy Definition of Force Force = a push or pull that causes a change

More information

CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS

CHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change

More information

Fluid Dynamics. AP Physics B

Fluid Dynamics. AP Physics B Fluid Dynamics AP Physics B Fluid Flow Up till now, we hae pretty much focused on fluids at rest. Now let's look at fluids in motion It is important that you understand that an IDEAL FLUID: Is non iscous

More information

A Guide to Calculate Convection Coefficients for Thermal Problems Application Note

A Guide to Calculate Convection Coefficients for Thermal Problems Application Note A Guide to Calculate Convection Coefficients for Thermal Problems Application Note Keywords: Thermal analysis, convection coefficients, computational fluid dynamics, free convection, forced convection.

More information

Chapter 3.8 & 6 Solutions

Chapter 3.8 & 6 Solutions Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled

More information

Three Methods for Calculating the Buoyant Force Gleue: Physics

Three Methods for Calculating the Buoyant Force Gleue: Physics Three Methods for Calculating the Buoyant Force Gleue: Physics Name Hr. The Buoyant Force (F b ) is the apparent loss of weight for an object submerged in a fluid. For example if you have an object immersed

More information

Chapter 13 - Solutions

Chapter 13 - Solutions = Chapter 13 - Solutions Description: Find the weight of a cylindrical iron rod given its area and length and the density of iron. Part A On a part-time job you are asked to bring a cylindrical iron rod

More information

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

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)

More information

p atmospheric Statics : Pressure Hydrostatic Pressure: linear change in pressure with depth Measure depth, h, from free surface Pressure Head p gh

p atmospheric Statics : Pressure Hydrostatic Pressure: linear change in pressure with depth Measure depth, h, from free surface Pressure Head p gh IVE1400: n Introduction to Fluid Mechanics Statics : Pressure : Statics r P Sleigh: P..Sleigh@leeds.ac.uk r J Noakes:.J.Noakes@leeds.ac.uk January 008 Module web site: www.efm.leeds.ac.uk/ive/fluidslevel1

More information

Applied Fluid Mechanics

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

More information

Lecture L2 - Degrees of Freedom and Constraints, Rectilinear Motion

Lecture L2 - Degrees of Freedom and Constraints, Rectilinear Motion S. Widnall 6.07 Dynamics Fall 009 Version.0 Lecture L - Degrees of Freedom and Constraints, Rectilinear Motion Degrees of Freedom Degrees of freedom refers to the number of independent spatial coordinates

More information

Experiment 3 Pipe Friction

Experiment 3 Pipe Friction EML 316L Experiment 3 Pipe Friction Laboratory Manual Mechanical and Materials Engineering Department College of Engineering FLORIDA INTERNATIONAL UNIVERSITY Nomenclature Symbol Description Unit A cross-sectional

More information

CE 204 FLUID MECHANICS

CE 204 FLUID MECHANICS CE 204 FLUID MECHANICS Onur AKAY Assistant Professor Okan University Department of Civil Engineering Akfırat Campus 34959 Tuzla-Istanbul/TURKEY Phone: +90-216-677-1630 ext.1974 Fax: +90-216-677-1486 E-mail:

More information

Collision of a small bubble with a large falling particle

Collision of a small bubble with a large falling particle EPJ Web of Conferences 67, 212 (214) DOI: 1.11/ epjconf/ 21467212 C Owned by the authors, published by EDP Sciences, 214 Collision of a small bubble with a large falling particle Jiri Vejrazka 1,a, Martin

More information

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

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

More information

Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION

Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION 1 P a g e Inertia Physics Notes Class 11 CHAPTER 5 LAWS OF MOTION The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line its own, is

More information

THIS IS A NEW SPECIFICATION

THIS IS A NEW SPECIFICATION THIS IS A NEW SPECIFICATION ADVANCED SUBSIDIARY GCE PHYSICS A Mechanics G481 *CUP/T63897* Candidates answer on the question paper OCR Supplied Materials: Data, Formulae and Relationships Booklet Other

More information

Unit 1 INTRODUCTION 1.1.Introduction 1.2.Objectives

Unit 1 INTRODUCTION 1.1.Introduction 1.2.Objectives Structure 1.1.Introduction 1.2.Objectives 1.3.Properties of Fluids 1.4.Viscosity 1.5.Types of Fluids. 1.6.Thermodynamic Properties 1.7.Compressibility 1.8.Surface Tension and Capillarity 1.9.Capillarity

More information

CHAPTER 15 FORCE, MASS AND ACCELERATION

CHAPTER 15 FORCE, MASS AND ACCELERATION CHAPTER 5 FORCE, MASS AND ACCELERATION EXERCISE 83, Page 9. A car initially at rest accelerates uniformly to a speed of 55 km/h in 4 s. Determine the accelerating force required if the mass of the car

More information

Pipe Flow-Friction Factor Calculations with Excel

Pipe Flow-Friction Factor Calculations with Excel Pipe Flow-Friction Factor Calculations with Excel Course No: C03-022 Credit: 3 PDH Harlan H. Bengtson, PhD, P.E. Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980

More information

(a) Calculate the voidage (volume fraction occupied by voids) of the bed.

(a) Calculate the voidage (volume fraction occupied by voids) of the bed. SOLUTIONS TO CAPTER 6: FLOW TROUG A PACKED BED OF PARTICLES EXERCISE 6.1: A packed bed of solid particles of density 500 kg/m 3, occupies a depth of 1 m in a vessel of cross-sectional area 0.04 m. The

More information

Chapter 8 Fluid Flow

Chapter 8 Fluid Flow Chapter 8 Fluid Flow GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions Define each of the following terms, and use it in an operational

More information

Millikan Oil Drop. Introduction

Millikan Oil Drop. Introduction Millikan Oil Drop Introduction Towards the end of the 19th century a clear picture of the atom was only beginning to emerge. An important aspect of this developing picture was the microscopic nature of

More information

FREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES

FREESTUDY HEAT TRANSFER TUTORIAL 3 ADVANCED STUDIES FREESTUDY HEAT TRANSFER TUTORIAL ADVANCED STUDIES This is the third tutorial in the series on heat transfer and covers some of the advanced theory of convection. The tutorials are designed to bring the

More information

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics

UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics UNIVERSITY OF SASKATCHEWAN Department of Physics and Engineering Physics Physics 111.6 MIDTERM TEST #4 March 15, 2007 Time: 90 minutes NAME: (Last) Please Print (Given) STUDENT NO.: LECTURE SECTION (please

More information

Chapter 9: The Behavior of Fluids

Chapter 9: The Behavior of Fluids Chapter 9: The Behavior of Fluids 1. Archimedes Principle states that A. the pressure in a fluid is directly related to the depth below the surface of the fluid. B. an object immersed in a fluid is buoyed

More information

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur

Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Fluid Mechanics Prof. S. K. Som Department of Mechanical Engineering Indian Institute of Technology, Kharagpur Lecture - 20 Conservation Equations in Fluid Flow Part VIII Good morning. I welcome you all

More information

FLUID MECHANICS. Problem 2: Consider a water at 20 0 C flows between two parallel fixed plates.

FLUID MECHANICS. Problem 2: Consider a water at 20 0 C flows between two parallel fixed plates. FLUID MECHANICS Problem 1: Pressures are sometimes determined by measuring the height of a column of liquid in a vertical tube. What diameter of clean glass tubing is required so that the rise of water

More information

AS COMPETITION PAPER 2008

AS COMPETITION PAPER 2008 AS COMPETITION PAPER 28 Name School Town & County Total Mark/5 Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question

More information

AS CHALLENGE PAPER 2014

AS CHALLENGE PAPER 2014 AS CHALLENGE PAPER 2014 Name School Total Mark/50 Friday 14 th March Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question

More information

4.What is the appropriate dimensionless parameter to use in comparing flow types? YOUR ANSWER: The Reynolds Number, Re.

4.What is the appropriate dimensionless parameter to use in comparing flow types? YOUR ANSWER: The Reynolds Number, Re. CHAPTER 08 1. What is most likely to be the main driving force in pipe flow? A. Gravity B. A pressure gradient C. Vacuum 2.What is a general description of the flow rate in laminar flow? A. Small B. Large

More information

Chapter 2. Derivation of the Equations of Open Channel Flow. 2.1 General Considerations

Chapter 2. Derivation of the Equations of Open Channel Flow. 2.1 General Considerations Chapter 2. Derivation of the Equations of Open Channel Flow 2.1 General Considerations Of interest is water flowing in a channel with a free surface, which is usually referred to as open channel flow.

More information

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

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

More information

Solution: (a) For a positively charged particle, the direction of the force is that predicted by the right hand rule. These are:

Solution: (a) For a positively charged particle, the direction of the force is that predicted by the right hand rule. These are: Problem 1. (a) Find the direction of the force on a proton (a positively charged particle) moving through the magnetic fields as shown in the figure. (b) Repeat part (a), assuming the moving particle is

More information

Problem 1. 12ft. Find: Velocity of truck for both drag situations. Equations: Drag F Weight. For force balance analysis: Lift and Drag: Solution:

Problem 1. 12ft. Find: Velocity of truck for both drag situations. Equations: Drag F Weight. For force balance analysis: Lift and Drag: Solution: Problem 1 Given: Truck traveling down 7% grade Width 10ft m 5 tons 50,000 lb Rolling resistance on concrete 1.% weight C 0.96 without air deflector C 0.70 with air deflector V 100 7 1ft Find: Velocity

More information

2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration.

2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. 2.1 Force and Motion Kinematics looks at velocity and acceleration without reference to the cause of the acceleration. Dynamics looks at the cause of acceleration: an unbalanced force. Isaac Newton was

More information

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22

Practice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22 BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =

More information

Applied Fluid Mechanics

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

More information

ME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts

ME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts ME 305 Fluid Mechanics I Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey csert@metu.edu.tr

More information

oil liquid water water liquid Answer, Key Homework 2 David McIntyre 1

oil liquid water water liquid Answer, Key Homework 2 David McIntyre 1 Answer, Key Homework 2 David McIntyre 1 This print-out should have 14 questions, check that it is complete. Multiple-choice questions may continue on the next column or page: find all choices before making

More information

Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion

Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Physics: Principles and Applications, 6e Giancoli Chapter 4 Dynamics: Newton's Laws of Motion Conceptual Questions 1) Which of Newton's laws best explains why motorists should buckle-up? A) the first law

More information

Chapter 18 Electric Forces and Electric Fields. Key Concepts:

Chapter 18 Electric Forces and Electric Fields. Key Concepts: Chapter 18 Lectures Monday, January 25, 2010 7:33 AM Chapter 18 Electric Forces and Electric Fields Key Concepts: electric charge principle of conservation of charge charge polarization, both permanent

More information

Dynamics in nanoworlds

Dynamics in nanoworlds Dynamics in nanoworlds Interplay of energy, diffusion and friction in (sub)cellular world 1 NB Queste diapositive sono state preparate per il corso di Biofisica tenuto dal Dr. Attilio V. Vargiu presso

More information

Fluid Mechanics Definitions

Fluid Mechanics Definitions Definitions 9-1a1 Fluids Substances in either the liquid or gas phase Cannot support shear Density Mass per unit volume Specific Volume Specific Weight % " = lim g#m ( ' * = +g #V $0& #V ) Specific Gravity

More information

SURFACE TENSION. Definition

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

More information

Viscosity (VIS) Topic: Mechanics. Laminar and turbulent flow, Reynolds number, Hagen-Poiseuille s law, Stokes law

Viscosity (VIS) Topic: Mechanics. Laminar and turbulent flow, Reynolds number, Hagen-Poiseuille s law, Stokes law Seite 1 Viscosity Topic: Mechanics 1 Key words Laminar and turbulent flow, Reynolds number, Hagen-Poiseuille s law, Stokes law 2 Literatur L. Bergmann, C. Schäfer, Lehrbuch der Experimentalphysik, Band

More information

Vatten(byggnad) VVR145 Vatten. 2. Vätskors egenskaper (1.1, 4.1 och 2.8) (Föreläsningsanteckningar)

Vatten(byggnad) VVR145 Vatten. 2. Vätskors egenskaper (1.1, 4.1 och 2.8) (Föreläsningsanteckningar) Vatten(byggnad) Vätskors egenskaper (1) Hydrostatik (3) Grundläggande ekvationer (5) Rörströmning (4) 2. Vätskors egenskaper (1.1, 4.1 och 2.8) (Föreläsningsanteckningar) Vätska som kontinuerligt medium

More information

SIZE OF A MOLECULE FROM A VISCOSITY MEASUREMENT

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,

More information

CE 3500 Fluid Mechanics / Fall 2014 / City College of New York

CE 3500 Fluid Mechanics / Fall 2014 / City College of New York 1 Drag Coefficient The force ( F ) of the wind blowing against a building is given by F=C D ρu 2 A/2, where U is the wind speed, ρ is density of the air, A the cross-sectional area of the building, and

More information

Lesson 29: Newton's Law of Universal Gravitation

Lesson 29: Newton's Law of Universal Gravitation Lesson 29: Newton's Law of Universal Gravitation Let's say we start with the classic apple on the head version of Newton's work. Newton started with the idea that since the Earth is pulling on the apple,

More information

Measurement of the viscosities of He, Ne and Ar for the determination of their gas kinetic diameters.

Measurement of the viscosities of He, Ne and Ar for the determination of their gas kinetic diameters. American Journal of Engineering Research (AJER) e-issn: 2320-0847 p-issn : 2320-0936 Volume-4, Issue-11, pp-57-62 www.ajer.org Research Paper Measurement of the viscosities of He, Ne and Ar for the determination

More information

These slides contain some notes, thoughts about what to study, and some practice problems. The answers to the problems are given in the last slide.

These slides contain some notes, thoughts about what to study, and some practice problems. The answers to the problems are given in the last slide. Fluid Mechanics FE Review Carrie (CJ) McClelland, P.E. cmcclell@mines.edu Fluid Mechanics FE Review These slides contain some notes, thoughts about what to study, and some practice problems. The answers

More information

When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.

When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs

More information

CH-205: Fluid Dynamics

CH-205: Fluid Dynamics CH-05: Fluid Dynamics nd Year, B.Tech. & Integrated Dual Degree (Chemical Engineering) Solutions of Mid Semester Examination Data Given: Density of water, ρ = 1000 kg/m 3, gravitational acceleration, g

More information

EXPERIMENT 10 CONSTANT HEAD METHOD

EXPERIMENT 10 CONSTANT HEAD METHOD EXPERIMENT 10 PERMEABILITY (HYDRAULIC CONDUCTIVITY) TEST CONSTANT HEAD METHOD 106 Purpose: The purpose of this test is to determine the permeability (hydraulic conductivity) of a sandy soil by the constant

More information

du u U 0 U dy y b 0 b

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:

More information

CHAPTER: 6 FLOW OF WATER THROUGH SOILS

CHAPTER: 6 FLOW OF WATER THROUGH SOILS CHAPTER: 6 FLOW OF WATER THROUGH SOILS CONTENTS: Introduction, hydraulic head and water flow, Darcy s equation, laboratory determination of coefficient of permeability, field determination of coefficient

More information

HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case.

HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. HW6 Solutions Notice numbers may change randomly in your assignments and you may have to recalculate solutions for your specific case. Tipler 22.P.053 The figure below shows a portion of an infinitely

More information

2.2.1 Pressure and flow rate along a pipe: a few fundamental concepts

2.2.1 Pressure and flow rate along a pipe: a few fundamental concepts 1.1 INTRODUCTION Single-cell organisms live in direct contact with the environment from where they derive nutrients and into where they dispose of their waste. For living systems containing multiple cells,

More information

Archimedes. F b (Buoyant Force) DEMO. Identical Size Boxes Which has larger F B. Which is heavier. styrofoam (1 cm 3 ) steel ( 1 cm 3 )

Archimedes. F b (Buoyant Force) DEMO. Identical Size Boxes Which has larger F B. Which is heavier. styrofoam (1 cm 3 ) steel ( 1 cm 3 ) Fluids Density 1 F b (Buoyant Force) DEMO Archimedes Identical Size Boxes Which has larger F B Which is heavier styrofoam (1 cm 3 ) steel ( 1 cm 3 ) steel ( 1 cm 3 ) styrofoam (1 cm 3 ) 2 Finding the Weight

More information