Fundamentals of Fluid Mechanics

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Fundamentals of Fluid Mechanics"

Transcription

1 Sixth Edition. Fundamentals of Fluid Mechanics International Student Version BRUCE R. MUNSON DONALD F. YOUNG Department of Aerospace Engineering and Engineering Mechanics THEODORE H. OKIISHI Department of Mechanical Engineering Iowa State University Ames, Iowa, USA WADE W. HUEBSCH Department of Mechanical and Aerospace Engineering West Virginia University Morgantown, West Virginia, USA WILEY John Wiley & Sons, Inc.

2 c ontents i INTRODUCTION 1.1 Some Characteristics of Fluids 1.2 Dimensions, Dimensional Homogeneity, and Units Systems of Units 1.3 Analysis of Fluid Behavior 1.4 Measures of Fluid Mass and Weight Density Specific Weight Specific Gravity 1.5 Ideal Gas Law 1.6 Viscosity 1.7 Compressibility of Fluids Bulk Modulus Compression and Expansion of Gases Speed of Sound 1.8 Vapor Pressure 1.9 Surface Tension 1. A Brief Look Back in History 1.11 Review * 2 FLUID STATICS 2.1 Pressure at a Point 2.2 Basic for Pressure Field 2.3 'Pressure Variation in a Fluid at Rest Incompressible Fluid Compressible Fluid 2.4 Standard Atmosphere 2.5 Measurement of Pressure 2.6 Manometry Piezometer Tube U-Tube Manometer Inclined-Tube Manometer 2.7 Mechanical and Electronic Pressure Measuring Devices Hydrostatic Force on a Plane Surface Pressure Prism Hydrostatic Force on a Curved Surface Buoyancy, Flotation, and Stability Archimedes'Principle Stability Pressure Variation in a Fluid with Rigid-Body Motion Linear Motion Rigid-Body Rotation Review ELEMENTARY FLUID DYNAMICS THE BERNOULLI EQUATION 3.1 Newton's Second Law 3.2 F = ma along a Streamline 3.3 F = ma Normal to a Streamline 3.4 Physical Interpretation 3.5 Static, Stagnation, Dynamic, and Total Pressure 3.6 Examples of Use of the Bernoulli Free Jets Confined Flows Flowrate Measurement 3.7 The Energy Line and the Hydraulic Grade Line 3.8 Restrictions on Use of the Bernoulli Compressibility Effects Unsteady Effects Rotational Effects Other Restrictions 3.9 Review XVII

3 XVIII Contents FLUID KINEMATICS The Velocity Field Eulerian and Lagrangian Flow Descriptions One-, Two-, and Three- Dimensional Flows Steady and Unsteady Flows Streamlines, Streaklines, ' " and Pathlines The Acceleration Field The Material Derivative Unsteady Effects Convective Effects Streamline Coordinates Control Volume and System Representations The Reynolds Transport Theorem Derivation of the Reynolds Transport Theorem Physical Interpretation Relationship to Material Derivative Steady Effects Unsteady Effects Moving Control Volumes Selection of a Control Volume Review Application of the Moment-of- -, First Law of Thermodynamics The Energy Derivation of the Energy Application of the Energy Comparison of the Energy with the Bernoulli Application of the Energy to Nonuniform Flows Combination of the Energy and the Moment-of- Law of Thermodynamics Second Irreversible Flow Semi-infinitesimal Control Volume Statement of the Energy Semi-infinitesimal Control Volume Statement of the Second Law of Thermodynamics Combination of the s of the First and Second Laws of Thermodynamics Application of the Loss Form of the Energy Review' FINITE CONTROL VOLUME ANALYSIS ' c ' Conservation of Mass The Continuity Derivation of the Continuity Fixed, Nondeforming Control Volume Moving, Nondeforming Control Volume Deforming Control Volume 5.2 Newton's Second Law The Linear Momentum and Moment-of- s Derivation of the Linear Application of the Linear Derivation of the Moment-of DIFFERENTIAL ANALYSIS OF FLUID FLOW Fluid Element Kinematics Velocity and Acceleration Fields Revisited Linear Motion and Deformation Angular Motion and Deformation Conservation of Mass Differential Form of Continuity Cylindrical Polar Coordinates The Stream Function Conservation of Linear Momentum Description of Forces Acting on the Differential Element s of Motion Inviscid Flow Euler's s of Motion The Bernoulli 279

4 6.4.3 Irrotational Flow The Bernoulli for Irrotational Flow The Velocity Potential 6.5 Some Basic, Plane Potential Flows Uniform Flow Source and Sink Vortex Doublet 6.6 Superposition of Basic, Plane Potential Flows Source in a Uniform Stream Half-Body Rankine Ovals Flow around a Circular Cylinder 6.7 Other Aspects of Potential Flow Analysis 6.8 Viscous Flow Stress-Deformation Relationships The Naiver-Stokes s 6.9 Some Simple Solutions for Viscous, Incompressible Fluids Steady, Laminar Flow between Fixed Parallel Plates Couette Flow Steady, Laminar Flow in Circular Tubes Steady, Axial, Laminar Flow in an Annulus 6. Other Aspects of Differential Analysis 6..1 Numerical Methods 6.11 Review 7 DIMENSIONAL ANALYSIS, SIMILITUDE, AND MODELING 7.1 Dimensional Analysis 7.2 Buckingham Pi Theorem 73 ' Determination of Pi Terms 7.4 Some Additional Comments About Dimensional Analysis Selection of Variables Determination of Reference Dimensions Uniqueness of Pi Terms 7.5 Determination of Pi Terms by Inspection 7.6 Common Dimensionless Groups in Fluid Mechanics 7.7 Correlation of Experimental Data with One Pi Term Contents with Two or More Pi Terms Modeling and Similitude Theory of Models Model Scales Practical Aspects of 288 Using Models Some Typical Model Studies Flow through Closed Conduits Flow around Immersed Bodies Flow with a Free Surface 7. Similitude Based on Governing Differential s Review VISCOUS FLOW IN PIPES 8.1 General Characteristics of Pipe Flow Laminar or Turbulent Flow Entrance Region and Fully Developed Flow Pressure and Shear Stress 8.2 Fully Developed Laminar Flow From F = ma Applied to a Fluid Element From the Navier-Stokes s From Dimensional Analysis Energy Considerations 8.3 Fully Developed Turbulent Flow Transition from Laminar to Turbulent Flow Turbulent Shear Stress Turbulent Velocity Profile Turbulence Modeling Chaos and Turbulence 8.4 Dimensional Analysis of Pipe Flow Major Losses Minor Losses Noncircular Conduits 8.5 Pipe Flow Examples Single Pipes Multiple Pipe Systems 8.6 Pipe Fkwrate Measurement Pipe Flowrate Meters Volume Flow Meters 8.7 Review XIX

5 XX Contents FLOW OVER IMMERSED BODIES 9.1 General External Flow Characteristics Lift and Drag Concepts Characteristics of Flow Past an Object 9.2 Boundary Layer Characteristics Boundary Layer Structure _and Thickness on a Flat Plate * Prandtl/Blasius Boundary Layer Solution Momentum Integral Boundary Layer for a Flat Plate Transition from Laminar to Turbulent Flow Turbulent Boundary Layer Flow Effects of Pressure Gradient Momentum-Integral Boundary Layer with Nonzero Pressure Gradient Drag Lift Friction Drag Pressure Drag Drag Coefficient Data and Examples Surface Pressure Distribution Circulation Review OPEN-CHANNEL.1 General Characteristics of Open- Channel Flow.2 Surface Waves.2.1 Wave Speed '.2.2 Froude Number Effects.3 Energy Considerations.3.1 Specific Energy.3.2 Channel Depth Variations.4 Uniform Depth Channel Flow.4.1 Uniform Flow Approximations.4.2 The Chezy and Manning s.4.3 Uniform Depth Examples.5 Gradually Varied Flow.5.1 Classification of Surface Shapes.5.2 Examples of Gradually Varied Flows Rapidly Varied Flow.6.1 The Hydraulic Jump.6.2 Sharp-Crested Weirs.6.3 Broad-Crested Weirs.6.4 Underflow Gates.7 Review COMPRESSIBLE FLOW 11.1 Ideal Gas Relationships 11.2 Mach Number and Speed of Sound 11.3 Categories of Compressible Flow 11.4 Isentropic Flow of an Ideal Gas Effect of Variations in Flow Cross-Sectional Area Converging-Diverging Duct Flow Constant-Area Duct Flow 11.5 Nonisentropic Flow of an Ideal Gas Adiabatic Constant-Area Duct Flow with Friction (Fanno Flow) Frictionless Constant-Area Duct Flow with Heat Transfer (Rayleigh Flow) Normal Shock Waves 11.6 Analogy between Compressible and Open-Channel Flows 11.7 Two-Dimensional Compressible Flow 11.8 Review 12 TURBOMACHINES 12.1 Introduction 12.2 Basic Energy Considerations 12.3 Basic Angular Momentum Considerations 12.4 The Centrifugal Pump Theoretical Considerations Pump Performance Characteristics Net Positive Suction Head (NPSH) System Characteristics and Pump Selection 12.5 Dimensionless Parameters and Similarity Laws Special Pump Scaling Laws Specific Speed Suction Specific Speed

6 Contents xxi 12.6 Axial-Flow and Mixed-Flow Pumps 12.7 Fans 12.8 Turbines Impulse Turbines Reaction Turbines 12.9 Compressible Flow Turbomachines Compressors Compressible Flow Turbines 12. Review COMPUTATIONAL FLUID DYNAMICS AND FLOWLAB B PHYSICAL PROPERTIES OF FLUIDS C PROPERTIES OF THE U.S. STANDARD ATMOSPHERE D COMPRESSIBLE FLOW DATA FOR AN IDEAL GAS ONLINE APPENDIX LIST,1l COMPREHENSIVE TABLE OF CONVERSION FACTORS VIDEO LIBRARY REVIEW PROBLEMS H LABORATORY PROBLEMS I CFD DRIVEN CAVITY EXAMPLE J FLOWLAB TUTORIAL AND USER'S GUIDE K FLOWLAB PROBLEMS ANSWERS ANS-1 INDEX 1-1 VIDEO INDEX VI-1

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

Distinguished Professor George Washington University. Graw Hill

Distinguished Professor George Washington University. Graw Hill Mechanics of Fluids Fourth Edition Irving H. Shames Distinguished Professor George Washington University Graw Hill Boston Burr Ridge, IL Dubuque, IA Madison, Wl New York San Francisco St. Louis Bangkok

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

FLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS - CB0235 2014_1

FLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS - CB0235 2014_1 COURSE CODE INTENSITY PRE-REQUISITE CO-REQUISITE CREDITS ACTUALIZATION DATE FLUID MECHANICS IM0235 3 LECTURE HOURS PER WEEK 48 HOURS CLASSROOM ON 16 WEEKS, 32 HOURS LABORATORY, 112 HOURS OF INDEPENDENT

More information

E 490 Fundamentals of Engineering Review. Fluid Mechanics. M. A. Boles, PhD. Department of Mechanical & Aerospace Engineering

E 490 Fundamentals of Engineering Review. Fluid Mechanics. M. A. Boles, PhD. Department of Mechanical & Aerospace Engineering E 490 Fundamentals of Engineering Review Fluid Mechanics By M. A. Boles, PhD Department of Mechanical & Aerospace Engineering North Carolina State University Archimedes Principle and Buoyancy 1. A block

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

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

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

Textbook: Introduction to Fluid Mechanics by Philip J. Pritchard. John Wiley & Sons, 8th Edition, ISBN-13 9780470547557, -10 0470547553

Textbook: Introduction to Fluid Mechanics by Philip J. Pritchard. John Wiley & Sons, 8th Edition, ISBN-13 9780470547557, -10 0470547553 Semester: Spring 2016 Course: MEC 393, Advanced Fluid Mechanics Instructor: Professor Juldeh Sesay, 226 Heavy Engineering Bldg., (631)632-8493 Email: Juldeh.sessay@stonybrook.edu Office hours: Mondays

More information

NCEES Fundamentals of Engineering (FE) Examination Review Fluid Mechanics, Hydraulics and Hydrologic Systems

NCEES Fundamentals of Engineering (FE) Examination Review Fluid Mechanics, Hydraulics and Hydrologic Systems NCEES Fundamentals of Engineering (FE) Examination Review Fluid Mechanics, Hydraulics and Hydrologic Systems Instructor: Dr. Marcio H. Giacomoni 1 Introduction The FE examination is an 8-hour suppliedreference

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

Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS

Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Chapter 5 MASS, BERNOULLI AND ENERGY EQUATIONS Lecture slides by Hasan Hacışevki Copyright

More information

Fundamentals of THERMAL-FLUID SCIENCES

Fundamentals of THERMAL-FLUID SCIENCES Fundamentals of THERMAL-FLUID SCIENCES THIRD EDITION YUNUS A. CENGEL ROBERT H. TURNER Department of Mechanical JOHN M. CIMBALA Me Graw Hill Higher Education Boston Burr Ridge, IL Dubuque, IA Madison, Wl

More information

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

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

More information

1.Name the four types of motion that a fluid element can experience. YOUR ANSWER: Translation, linear deformation, rotation, angular deformation.

1.Name the four types of motion that a fluid element can experience. YOUR ANSWER: Translation, linear deformation, rotation, angular deformation. CHAPTER 06 1.Name the four types of motion that a fluid element can experience. YOUR ANSWER: Translation, linear deformation, rotation, angular deformation. 2.How is the acceleration of a particle described?

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 13 OPEN-CHANNEL FLOW

Chapter 13 OPEN-CHANNEL FLOW Fluid Mechanics: Fundamentals and Applications, 2nd Edition Yunus A. Cengel, John M. Cimbala McGraw-Hill, 2010 Lecture slides by Mehmet Kanoglu Copyright The McGraw-Hill Companies, Inc. Permission required

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

Open channel flow Basic principle

Open channel flow Basic principle Open channel flow Basic principle INTRODUCTION Flow in rivers, irrigation canals, drainage ditches and aqueducts are some examples for open channel flow. These flows occur with a free surface and the pressure

More information

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur

High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur High Speed Aerodynamics Prof. K. P. Sinhamahapatra Department of Aerospace Engineering Indian Institute of Technology, Kharagpur Module No. # 01 Lecture No. # 06 One-dimensional Gas Dynamics (Contd.) We

More information

Fundamentals of Aerodynamics

Fundamentals of Aerodynamics Fundamentals of Aerodynamics Fourth Edition John D. Anderson, Jr.; Curator of Aerodynamics National Air arid Space Museum Smithsonian Institution * and Professor Emeritus University of Maryland Mc Graw

More information

Fundamentals of Heat and Mass Transfer

Fundamentals of Heat and Mass Transfer 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. SIXTH EDITION Fundamentals of Heat and Mass Transfer FRANK P. INCROPERA

More information

Chapter 8 Steady Incompressible Flow in Pressure Conduits

Chapter 8 Steady Incompressible Flow in Pressure Conduits Chapter 8 Steady Incompressible Flow in Pressure Conduits Outline 8.1 Laminar Flow and turbulent flow Reynolds Experiment 8.2 Reynolds number 8.3 Hydraulic Radius 8.4 Friction Head Loss in Conduits of

More information

NUMERICAL ANALYSIS OF THE EFFECTS OF WIND ON BUILDING STRUCTURES

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

More information

Urban Hydraulics. 2.1 Basic Fluid Mechanics

Urban Hydraulics. 2.1 Basic Fluid Mechanics Urban Hydraulics Learning objectives: After completing this section, the student should understand basic concepts of fluid flow and how to analyze conduit flows and free surface flows. They should be able

More information

Min-218 Fundamentals of Fluid Flow

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

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

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

ENSC 283 Introduction and Properties of Fluids

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

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

Chapter 1. Governing Equations of Fluid Flow and Heat Transfer

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

More information

CHAPTER 1 PROPERTIES OF FLUID

CHAPTER 1 PROPERTIES OF FLUID FLUID MECHANICS (2141906) CHAPTER 1 PROPERTIES OF FLUID Theory 1. Explain following terms in brief: a) Density or Mass density f) Kinematic viscosity b) Specific weight or Weight density g) Viscosity or

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

Gas Turbine Engine Performance Analysis. S. Jan

Gas Turbine Engine Performance Analysis. S. Jan Gas Turbine Engine Performance Analysis S. Jan Jul. 21 2014 Chapter 1 Basic Definitions Potential & Kinetic Energy PE = mgz/g c KE = mv 2 /2g c Total Energy Operational Envelopes & Standard Atmosphere

More information

Contents. Microfluidics - Jens Ducrée Physics: Navier-Stokes Equation 1

Contents. Microfluidics - Jens Ducrée Physics: Navier-Stokes Equation 1 Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors

More information

Introduction to Fluid Mechanics. Chapter 9 External Incompressible Viscous Flow. Pritchard

Introduction to Fluid Mechanics. Chapter 9 External Incompressible Viscous Flow. Pritchard Introduction to Fluid Mechanics Chapter 9 External Incompressible Viscous Flow Main Topics The Boundary-Layer Concept Boundary-Layer Thicknesses Laminar Flat-Plate Boundary Layer: Exact Solution Momentum

More information

MODULE SPECIFICATION FORM

MODULE SPECIFICATION FORM MODULE SPECIFICATION FORM Module Title: Thermo-fluid and Propulsion Level: 5 Credit Value: 20 Module code: (if known) ENG538 Cost Centre: GAME JACS2 code: H141/H311/ H450 Semester(s) in which to be offered:

More information

ENSC 283 Introduction and Properties of Fluids

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 Introduction A fluid cannot resist a shear stress

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

Open Channel Flow. M. Siavashi. School of Mechanical Engineering Iran University of Science and Technology

Open Channel Flow. M. Siavashi. School of Mechanical Engineering Iran University of Science and Technology M. Siavashi School of Mechanical Engineering Iran University of Science and Technology W ebpage: webpages.iust.ac.ir/msiavashi Email: msiavashi@iust.ac.ir Landline: +98 21 77240391 Fall 2013 Introduction

More information

Abaqus/CFD Sample Problems. Abaqus 6.10

Abaqus/CFD Sample Problems. Abaqus 6.10 Abaqus/CFD Sample Problems Abaqus 6.10 Contents 1. Oscillatory Laminar Plane Poiseuille Flow 2. Flow in Shear Driven Cavities 3. Buoyancy Driven Flow in Cavities 4. Turbulent Flow in a Rectangular Channel

More information

Experiment (13): Flow channel

Experiment (13): Flow channel Introduction: An open channel is a duct in which the liquid flows with a free surface exposed to atmospheric pressure. Along the length of the duct, the pressure at the surface is therefore constant and

More information

Basic Equations, Boundary Conditions and Dimensionless Parameters

Basic Equations, Boundary Conditions and Dimensionless Parameters Chapter 2 Basic Equations, Boundary Conditions and Dimensionless Parameters In the foregoing chapter, many basic concepts related to the present investigation and the associated literature survey were

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

ME 305 Fluid Mechanics I. Part 4 Integral Formulation of Fluid Flow

ME 305 Fluid Mechanics I. Part 4 Integral Formulation of Fluid Flow ME 305 Fluid Mechanics I Part 4 Integral Formulation of Fluid Flow These presentations are prepared by Dr. Cüneyt Sert Mechanical Engineering Department Middle East Technical University Ankara, Turkey

More information

Contents. Microfluidics - Jens Ducrée Physics: Fluid Dynamics 1

Contents. Microfluidics - Jens Ducrée Physics: Fluid Dynamics 1 Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. Ink-Jet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors

More information

220103 - Fluid Mechanics

220103 - Fluid Mechanics Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2016 205 - ESEIAAT - Terrassa School of Industrial, Aerospace and Audiovisual Engineering 729 - MF - Department of Fluid Mechanics

More information

Introduction to basic principles of fluid mechanics

Introduction to basic principles of fluid mechanics 2.016 Hydrodynamics Prof. A.H. Techet Introduction to basic principles of fluid mechanics I. Flow Descriptions 1. Lagrangian (following the particle): In rigid body mechanics the motion of a body is described

More information

CBE 6333, R. Levicky 1. Potential Flow

CBE 6333, R. Levicky 1. Potential Flow CBE 6333, R. Levicky Part I. Theoretical Background. Potential Flow Potential Flow. Potential flow is irrotational flow. Irrotational flows are often characterized by negligible viscosity effects. Viscous

More information

This chapter deals with three equations commonly used in fluid mechanics:

This chapter deals with three equations commonly used in fluid mechanics: MASS, BERNOULLI, AND ENERGY EQUATIONS CHAPTER 5 This chapter deals with three equations commonly used in fluid mechanics: the mass, Bernoulli, and energy equations. The mass equation is an expression of

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

Heat Transfer From A Heated Vertical Plate

Heat Transfer From A Heated Vertical Plate Heat Transfer From A Heated Vertical Plate Mechanical and Environmental Engineering Laboratory Department of Mechanical and Aerospace Engineering University of California at San Diego La Jolla, California

More information

MASTER OF SCIENCE IN MECHANICAL ENGINEERING

MASTER OF SCIENCE IN MECHANICAL ENGINEERING MASTER OF SCIENCE IN MECHANICAL ENGINEERING Introduction There are over 22 schools in Mindanao that offer Bachelor of Science in Mechanical Engineering and majority of their faculty members do not have

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

Viscous Flow in Pipes

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

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

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 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

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

جامعة البلقاء التطبيقية

جامعة البلقاء التطبيقية AlBalqa Applied University تا سست عام 997 The curriculum of associate degree in Air Conditioning, Refrigeration and Heating Systems consists of (7 credit hours) as follows: Serial No. Requirements First

More information

Commercial CFD Software Modelling

Commercial CFD Software Modelling Commercial CFD Software Modelling Dr. Nor Azwadi bin Che Sidik Faculty of Mechanical Engineering Universiti Teknologi Malaysia INSPIRING CREATIVE AND INNOVATIVE MINDS 1 CFD Modeling CFD modeling can be

More information

Practice Problems on Bernoulli s Equation. V car. Answer(s): p p p V. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Sep 15

Practice Problems on Bernoulli s Equation. V car. Answer(s): p p p V. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Sep 15 bernoulli_0 A person holds their hand out of a car window while driving through still air at a speed of V car. What is the maximum pressure on the person s hand? V car 0 max car p p p V C. Wassgren, Purdue

More information

Appendix 4-C. Open Channel Theory

Appendix 4-C. Open Channel Theory 4-C-1 Appendix 4-C Open Channel Theory 4-C-2 Appendix 4.C - Table of Contents 4.C.1 Open Channel Flow Theory 4-C-3 4.C.2 Concepts 4-C-3 4.C.2.1 Specific Energy 4-C-3 4.C.2.2 Velocity Distribution Coefficient

More information

Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics

Lecture 6 - Boundary Conditions. Applied Computational Fluid Dynamics Lecture 6 - Boundary Conditions Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.

More information

GATE Syllabus for Chemical Engineering

GATE Syllabus for Chemical Engineering 2017 YOUR CAREER QUEST ENDS HERE GATE Syllabus for Chemical Engineering Section 1: Engineering Mathematics Linear Algebra: 1. Matrix algebra, 2. Systems of linear equations, 3. Eigen values and eigenvectors.

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 11 Boundary Layers and Separation. Applied Computational Fluid Dynamics

Lecture 11 Boundary Layers and Separation. Applied Computational Fluid Dynamics Lecture 11 Boundary Layers and Separation Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (2002-2006) Fluent Inc. (2002) 1 Overview Drag. The boundary-layer

More information

Macroscopic Balances for Nonisothermal Systems

Macroscopic Balances for Nonisothermal Systems Transport Phenomena Macroscopic Balances for Nonisothermal Systems 1 Macroscopic Balances for Nonisothermal Systems 1. The macroscopic energy balance 2. The macroscopic mechanical energy balance 3. Use

More information

Lecture 4 Classification of Flows. Applied Computational Fluid Dynamics

Lecture 4 Classification of Flows. Applied Computational Fluid Dynamics Lecture 4 Classification of Flows Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (00-006) Fluent Inc. (00) 1 Classification: fluid flow vs. granular flow

More information

AA200 Chapter 9 - Viscous flow along a wall

AA200 Chapter 9 - Viscous flow along a wall AA200 Chapter 9 - Viscous flow along a wall 9.1 The no-slip condition 9.2 The equations of motion 9.3 Plane, Compressible Couette Flow (Review) 9.4 The viscous boundary layer on a wall 9.5 The laminar

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

Fluent Software Training TRN Boundary Conditions. Fluent Inc. 2/20/01

Fluent Software Training TRN Boundary Conditions. Fluent Inc. 2/20/01 Boundary Conditions C1 Overview Inlet and Outlet Boundaries Velocity Outline Profiles Turbulence Parameters Pressure Boundaries and others... Wall, Symmetry, Periodic and Axis Boundaries Internal Cell

More information

Chapter 5. Microfluidic Dynamics

Chapter 5. Microfluidic Dynamics Chapter 5 Thermofluid Engineering and Microsystems Microfluidic Dynamics Navier-Stokes equation 1. The momentum equation 2. Interpretation of the NSequation 3. Characteristics of flows in microfluidics

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

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

Airflow through Mine Openings and Ducts Chapter 5

Airflow through Mine Openings and Ducts Chapter 5 Airflow through Mine Openings and Ducts Chapter 5 Fundamentals of Airflow Ventilation the application of the principles of fluid mechanics & thermodynamics to the flow of air in underground openings Fluid

More information

THE EVOLUTION OF TURBOMACHINERY DESIGN (METHODS) Parsons 1895

THE EVOLUTION OF TURBOMACHINERY DESIGN (METHODS) Parsons 1895 THE EVOLUTION OF TURBOMACHINERY DESIGN (METHODS) Parsons 1895 Rolls-Royce 2008 Parsons 1895 100KW Steam turbine Pitch/chord a bit too low. Tip thinning on suction side. Trailing edge FAR too thick. Surface

More information

Chapter 4. Dimensionless expressions. 4.1 Dimensional analysis

Chapter 4. Dimensionless expressions. 4.1 Dimensional analysis Chapter 4 Dimensionless expressions Dimensionless numbers occur in several contexts. Without the need for dynamical equations, one can draw a list (real or tentative) of physically relevant parameters,

More information

df dt df dt df ds df ds

df dt df dt df ds df ds Principles of Fluid Mechanics Fluid: Fluid is a substance that deforms or flows continuously under the action of a shear stress (force per unit area). In fluid mechanics the term fluid can refer to any

More information

ANALYSIS OF FULLY DEVELOPED TURBULENT FLOW IN A PIPE USING COMPUTATIONAL FLUID DYNAMICS D. Bhandari 1, Dr. S. Singh 2

ANALYSIS OF FULLY DEVELOPED TURBULENT FLOW IN A PIPE USING COMPUTATIONAL FLUID DYNAMICS D. Bhandari 1, Dr. S. Singh 2 ANALYSIS OF FULLY DEVELOPED TURBULENT FLOW IN A PIPE USING COMPUTATIONAL FLUID DYNAMICS D. Bhandari 1, Dr. S. Singh 2 1 M. Tech Scholar, 2 Associate Professor Department of Mechanical Engineering, Bipin

More information

Advanced Hydraulics Prof. Dr. Suresh. A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati

Advanced Hydraulics Prof. Dr. Suresh. A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati Advanced Hydraulics Prof. Dr. Suresh. A. Kartha Department of Civil Engineering Indian Institute of Technology, Guwahati Module - 6 Turbines Lecture - 4 Turbines, Cavitation Very good afternoon to everyone,

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

CEE 370 Fall 2015. Laboratory #3 Open Channel Flow

CEE 370 Fall 2015. Laboratory #3 Open Channel Flow CEE 70 Fall 015 Laboratory # Open Channel Flow Objective: The objective of this experiment is to measure the flow of fluid through open channels using a V-notch weir and a hydraulic jump. Introduction:

More information

Entrance Conditions. Chapter 8. Islamic Azad University

Entrance Conditions. Chapter 8. Islamic Azad University Chapter 8 Convection: Internal Flow Islamic Azad University Karaj Branch Entrance Conditions Must distinguish between entrance and fully developed regions. Hydrodynamic Effects: Assume laminar flow with

More information

Chapter 13 Fluids. Copyright 2009 Pearson Education, Inc.

Chapter 13 Fluids. Copyright 2009 Pearson Education, Inc. Chapter 13 Fluids 13-1 Phases of Matter The three common phases of matter are solid, liquid, and gas. A solid has a definite shape and size. A liquid has a fixed volume but can be any shape. A gas can

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

14-1. Fluids in Motion There are two types of fluid motion called laminar flow and turbulent flow.

14-1. Fluids in Motion There are two types of fluid motion called laminar flow and turbulent flow. Fluid Dynamics Sections Covered in the Text: Chapter 15, except 15.6 To complete our study of fluids we now examine fluids in motion. For the most part the study of fluids in motion was put into an organized

More information

Chapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any

Chapter 10. Flow Rate. Flow Rate. Flow Measurements. The velocity of the flow is described at any Chapter 10 Flow Measurements Material from Theory and Design for Mechanical Measurements; Figliola, Third Edition Flow Rate Flow rate can be expressed in terms of volume flow rate (volume/time) or mass

More information

Fluid Mechanics for Masters Students

Fluid Mechanics for Masters Students Fluid Mechanics for Masters Students Olivier Cleynen last edited July 2, 2016 http://fluidmech.ariadacapo.net 2 Contents Start 1 0 Fundamentals 7 0.1 Concept of a fluid.................................

More information

Performance 4. Fluid Statics, Dynamics, and Airspeed Indicators

Performance 4. Fluid Statics, Dynamics, and Airspeed Indicators Performance 4. Fluid Statics, Dynamics, and Airspeed Indicators From our previous brief encounter with fluid mechanics we developed two equations: the one-dimensional continuity equation, and the differential

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 7. General Energy Equation

More information

FLUID FLOW Introduction General Description

FLUID FLOW Introduction General Description FLUID FLOW Introduction Fluid flow is an important part of many processes, including transporting materials from one point to another, mixing of materials, and chemical reactions. In this experiment, you

More information

Open Channel Flow 2F-2. A. Introduction. B. Definitions. Design Manual Chapter 2 - Stormwater 2F - Open Channel Flow

Open Channel Flow 2F-2. A. Introduction. B. Definitions. Design Manual Chapter 2 - Stormwater 2F - Open Channel Flow Design Manual Chapter 2 - Stormwater 2F - Open Channel Flow 2F-2 Open Channel Flow A. Introduction The beginning of any channel design or modification is to understand the hydraulics of the stream. The

More information

1 The basic equations of fluid dynamics

1 The basic equations of fluid dynamics 1 The basic equations of fluid dynamics The main task in fluid dynamics is to find the velocity field describing the flow in a given domain. To do this, one uses the basic equations of fluid flow, which

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

CHAPTER 9 CHANNELS APPENDIX A. Hydraulic Design Equations for Open Channel Flow

CHAPTER 9 CHANNELS APPENDIX A. Hydraulic Design Equations for Open Channel Flow CHAPTER 9 CHANNELS APPENDIX A Hydraulic Design Equations for Open Channel Flow SEPTEMBER 2009 CHAPTER 9 APPENDIX A Hydraulic Design Equations for Open Channel Flow Introduction The Equations presented

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

Viscous flow in pipe

Viscous flow in pipe Viscous flow in pipe Henryk Kudela Contents 1 Laminar or turbulent flow 1 2 Balance of Momentum - Navier-Stokes Equation 2 3 Laminar flow in pipe 2 3.1 Friction factor for laminar flow...........................

More information

FLUID MECHANICS FOR CIVIL ENGINEERS

FLUID MECHANICS FOR CIVIL ENGINEERS FLUID MECHANICS FOR CIVIL ENGINEERS Bruce Hunt Department of Civil Engineering University Of Canterbury Christchurch, New Zealand? Bruce Hunt, 1995 Table of Contents Chapter 1 Introduction... 1.1 Fluid

More information

FIGURE P8 50E FIGURE P8 62. Minor Losses

FIGURE P8 50E FIGURE P8 62. Minor Losses 8 48 Glycerin at 40 C with r 1252 kg/m 3 and m 0.27 kg/m s is flowing through a 4-cm-diameter horizontal smooth pipe with an average velocity of 3.5 m/s. Determine the pressure drop per 10 m of the pipe.

More information

XI / PHYSICS FLUIDS IN MOTION 11/PA

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

More information