Lecture 5 Hemodynamics. Description of fluid flow. The equation of continuity
|
|
- Raymond Mosley
- 8 years ago
- Views:
Transcription
1 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 in the circulatory system. ome principles of hydrodynamics are stated below. A line along which a fluid element moves be named a flowline. If every subsequent fluid element, which passes through a given point, takes the same path as the first fluid element, then the flowline is stable. A stable flowline is named a streamline. treamlines may be straight or curved. The tangent drawn at any point off the streamlines represents the direction of velocity at that point. The equation of continuity uppose incompressible fluid which fills completely a channel such as tube and flows along it. Then if some amount of fluid enters one end of the channel, an equal amount must leave the other end. Fig. 1 Flow rate Q is used as the measure of this amount. It means a volume of fluid V, which moves through the cross section of a channel per second. If the fluid enters one end of a tube at the flow rate Q 1, it must leave the other end at the flow rate Q, which is equal to Q 1. This principle is called the equation of continuity. Thus the equation of continuity can be written: where V volume, l =υ t Q 1 = Q linear velocity of fluid flow. V l Q = = = υ = const t t cross sectional area of tube,
2 The flow rate equals the velocity of liquid v multiplied by the cross-sectional area of the channel : υ 1 1υ 1 = υ = (5.) υ1 For a channel which cross section changes from 1 to this yields another form of the equation of continuity υ = const (5.3) This the product of flow velocity and area of cross section is constant at every section of a tube. It may be concluded also that the area of cross section and the flow velocity are at inverse relations. Usually the flow velocity is not equal at the every point of cross section. But the equation of continuity still holds for such cases if it is written in terms of the average flow velocity. Bernoulli s Equation For steady, irrotational flow, the speed, pressure, and elevation of an incompressible, nonviscous fluid are related by an equation discovered by Daniel Bernoulli ( ). where P static pressure, gh ρ hydrostatic pressure, ρυ dynamic pressure. ρυ P + ρ gh + = const, Bernoulli s equations prove that total pressure remains constant along the tube of current during steady-state flow of perfect fluid. Fluid viscosity Viscosity is that property of fluids owing to which they oppose any motion of their neighbouring portions relative to one another. Viscosity is created by internal friction between the molecules. uch friction opposes the development of velocity differences within a fluid. The reciprocal to the viscosity is called fluidity. Various fluids differ greatly by the value of their viscosity. For instance, the viscosity of oil is greater than that of water. Viscosity is a major factor in determining the forces that must be overcome when fluids are transported in the tubes. Viscosity influences also the blood flow in the circulatory system. In an ideal fluid there is no viscosity to hinder the fluid layers as they slide past one another. Within a pipe of uniform cross section, every layer of an ideal fluid
3 moves with the same velocity, even the layer next to the wall, as Fig. (a) shows. When viscosity is present, the fluid layers do not all have the same velocity, as part (b) of the drawing illustrates. The fluid closest to the wall does not move at all, while the fluid at the center of the pipe has the greatest velocity. The fluid layer next to the wall surface does not move, because it is held tightly by intermolecular forces. 3 Fig.. (a) In ideal (nonviscous) fluid flow, all fluid particles across the pipe have the same velocity. (b) In viscous flow, the speed of the fluid is zero at the surface of the pipe and increases to a maximum along the center axis Fig. 3 Fundamental law of viscous liquid was discovered by Newton (1687): F = dυ dy (Newton s formula) where is the coefficient of viscosity and equal to the force of internal friction that acts on the unit area of the layer s surface at the velocity gradient which is equal to one. I Unit of Viscosity: [ ] = Pа s Common Unit of Viscosity: poise (P). [ F ] = H forces of internal friction; dυ 1 = dx c м velocity gradient; [ ] = area of tangent layers. normal = 0,004 0,005 Pа. s. 1 poise (P) = 0.1 Pa s
4 dυ The fluids whose viscosity may be defined by Newton s equation ( F ~ dx ) are called Newtonian fluids. They are homogeneous fluids, such as water, spirits, solution of electrolytes etc. There do exist, however, more complicated heterogeneous fluids for which the Newtonian description is inadequate. The viscosity of these fluids depends at high rate on the velocity of flow. They are called non-newtonian fluids. This category of fluids includes suspensions, emulsions, foams and even the solutions of macromolecules such as proteins. Relative viscosity is equal to the ratio of the coefficient of viscosity of the given fluid to the coefficient of viscosity of distilled water at one and the same temperature: rel =. w Kinematic viscosity is ratio of the coefficient of viscosity to density: ρ ν = ( ρ density of the liquid). [ ] m ν =. s Laminar and turbulent flow If each fluid layer slips over the other, different layers do not get mixed then the flow called laminar. In the laminar flow every particle of fluid follows the path of its preceding particle. The velocity of flow at any point of fluid remains stable. The streamlines do not intersect each other. The other kind of flow is named turbulent. The turbulent flow is unstable. The flow of fluid is curled and all layers merge in one stream. The flowlines become zigzag. The velocity of a particle crossing particular point of fluid is not constant and varies with time. The turbulent flow needs more energy than the laminar one because additionally energy is used in producing currents through the fluid. English physicist Reynolds investigated the conditions under which a flow becomes laminar or turbulent. The transition from laminar flow into turbulent one depends on the value of dimensionless quantity called the Reynolds number (Re). Reynolds number for a liquid flowing in a cylindrical tube is defined by the equation: ρυ D Rе = here υ is an average velocity of flow; D diameter of a tube; ρ density of fluid; viscosity. The critical value of Reynolds number for cylindrical tubes at which laminar flow turns into turbulent is Blood flow in the circulatory system is laminar with the exception of aorta. In aorta it may become turbulent during a physical work which greatly increases velocity of blood. Blood flow may be turbulent also in arteries the cross-section area of which is diminished by some pathological process. If Re < Re cr, then flow is laminar. If Re > Re cr, then flow is turbulent. The change of blood viscosity value (for example, in patients with anemia) may be diagnosed owing to turbulent noises. It may be explained by the fact that at anemia viscosity coefficient decreases by a factor of -3 and even more. Correspondingly, Reynolds number increases since Re ~1// As a result Reynolds 4
5 number becomes greater than its critical value and the transition from laminar blood flow to turbulent one tarts place. Medical application of transition between laminar and turbulent flow of blood is connected with measuring of blood pressure by Korotkov method. In accordance with this method systolic (upper) pressure is measured at the moment when blood begins to squeeze through the hole in artery compressed by the cuff. Exactly at this moment noises appear resulting from turbulent flow of blood. Diastolic (lower) pressure is fixed at the moment when these noises disappear as a result of release of cuff and transition of flow from laminar to turbulent. 5 Pressure (P) - is the force exerted by blood on blood vessels per unit area: F P =, [P] = Pа.. Volume velocity ( Q ) is called a value numerically equal to the volume of fluid passing per unit time through this section: time: 3 V m Q =, [ Q] =. t s Linear velocity (υ ) is the path traversed by the particles of blood per unit l = t υ ; [ ] m υ =. s Formula of dependence the linear and volume velocity: Q = υ, where cross-sectional area of fluid flow. Formula of Poiseuille Let us find linear and volume velocity of flow for steady-state stream of viscous fluid through a vessel with radius R, length l, pressure differential at its ends P 1 P : 4 πr ( P1 P ) Q = (formula of Hagen-Poiseuille) 8 l is dynamic coefficient of viscosity. 8 l X π r Quantity = 4 is called hydraulic resistance: Q Ρ X =, (formula of Poiseuille) Ρ =Q X. Distribution of mean pressure Mean arterial pressure determined by the formula: P mean Рs Рd = Pd +, 3
6 6 wherе Р s systolic pressure, Р d diastolic pressure.
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 informationXI / 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 informationFLUID 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 informationFluids 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 informationDifferential 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 informationINTRODUCTION 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 information1. 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 informationBasic 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 informationAids 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 informationVISUAL 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 informationFor 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 informationA LAMINAR FLOW ELEMENT WITH A LINEAR PRESSURE DROP VERSUS VOLUMETRIC FLOW. 1998 ASME Fluids Engineering Division Summer Meeting
TELEDYNE HASTINGS TECHNICAL PAPERS INSTRUMENTS A LAMINAR FLOW ELEMENT WITH A LINEAR PRESSURE DROP VERSUS VOLUMETRIC FLOW Proceedings of FEDSM 98: June -5, 998, Washington, DC FEDSM98 49 ABSTRACT The pressure
More information2.2.1 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 informationViscous 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 informationViscosity (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 informationChapter 28 Fluid Dynamics
Chapter 28 Fluid Dynamics 28.1 Ideal Fluids... 1 28.2 Velocity Vector Field... 1 28.3 Mass Continuity Equation... 3 28.4 Bernoulli s Principle... 4 28.5 Worked Examples: Bernoulli s Equation... 7 Example
More informationFluid 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 informationDistinguished 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 informationFluid 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 informationTeil 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 informationChapter 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 informationThe 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 informationNotes 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 informationHeat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati
Heat Transfer Prof. Dr. Ale Kumar Ghosal Department of Chemical Engineering Indian Institute of Technology, Guwahati Module No. # 04 Convective Heat Transfer Lecture No. # 03 Heat Transfer Correlation
More informationOpen 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 informationFluid 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
More informationChapter 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 informationExperiment 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 informationDiffusion 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 informationNUMERICAL 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 informationContents. 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 informationIntroduction to Microfluidics. Date: 2013/04/26. Dr. Yi-Chung Tung. Outline
Introduction to Microfluidics Date: 2013/04/26 Dr. Yi-Chung Tung Outline Introduction to Microfluidics Basic Fluid Mechanics Concepts Equivalent Fluidic Circuit Model Conclusion What is Microfluidics Microfluidics
More informationME 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 informationCh 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)
More informationBasic 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 information4.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 informationFundamentals of Fluid Mechanics
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
More informationUrban 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 informationdu 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 informationHEAVY 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
More informationCE 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 informationPUMPS 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
More informationSIZE 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 informationChapter 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 informationNavier-Stokes Equation Solved in Comsol 4.1. Copyright Bruce A. Finlayson, 2010 See also Introduction to Chemical Engineering Computing, Wiley (2006).
Introduction to Chemical Engineering Computing Copyright, Bruce A. Finlayson, 2004 1 Navier-Stokes Equation Solved in Comsol 4.1. Copyright Bruce A. Finlayson, 2010 See also Introduction to Chemical Engineering
More informationRheological 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
More informationFLUID 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 informationOUTCOME 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 informationLaminar Flow and Heat Transfer of Herschel-Bulkley Fluids in a Rectangular Duct; Finite-Element Analysis
Tamkang Journal of Science and Engineering, Vol. 12, No. 1, pp. 99 107 (2009) 99 Laminar Flow and Heat Transfer of Herschel-Bulkley Fluids in a Rectangular Duct; Finite-Element Analysis M. E. Sayed-Ahmed
More informationCBE 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 informationAgoraLink Agora for Life Science Technologies Linköpings Universitet Kurs i Fysiologisk mätteknik Biofluidflöden
AgoraLink Agora for Life Science Technologies Linköpings Universitet Kurs i Fysiologisk mätteknik Biofluidflöden Fysiologisk mätteknik Anatomy of the heart The complex myocardium structure right ventricle
More informationSwissmetro 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 informationPaul Clements, SpR in Anaesthetics, Hope Hospital, Salford, UK. Carl Gwinnutt, Consultant Anaesthetist, Hope Hospital, Salford, UK.
The Physics of Flow Paul Clements, SpR in Anaesthetics, Hope Hospital, Salford, UK. Carl Gwinnutt, Consultant Anaesthetist, Hope Hospital, Salford, UK. Introduction Flow is defined as the quantity of fluid
More informationA Comparison of Analytical and Finite Element Solutions for Laminar Flow Conditions Near Gaussian Constrictions
A Comparison of Analytical and Finite Element Solutions for Laminar Flow Conditions Near Gaussian Constrictions by Laura Noelle Race An Engineering Project Submitted to the Graduate Faculty of Rensselaer
More informationChapter 8: Flow in Pipes
Objectives 1. Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow 2. Calculate the major and minor losses associated with pipe flow in piping networks
More informationContents. 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 informationMicrofluidic Principles Part 1
Introduction to BioMEMS & Medical Microdevices Microfluidic Principles Part 1 Companion lecture to the textbook: Fundamentals of BioMEMS and Medical Microdevices, by Dr. Steven S. Saliterman www.tc.umn.edu/~drsteve
More informationEXAMPLE: Water Flow in a Pipe
EXAMPLE: Water Flow in a Pipe P 1 > P 2 Velocity profile is parabolic (we will learn why it is parabolic later, but since friction comes from walls the shape is intuitive) The pressure drops linearly along
More informationDimensional 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 informationThe 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 informationMeasurement 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 informationOpen 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 informationHydraulic losses in pipes
Hydraulic losses in pipes Henryk Kudela Contents 1 Viscous flows in pipes 1 1.1 Moody Chart.................................... 2 1.2 Types of Fluid Flow Problems........................... 5 1.3 Minor
More informationCE 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 informationoil 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 informationChapter 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 informationCEE 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 informationFLUID 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 informationDimensional 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 informationChapter 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 informationA 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 informationHead Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids
Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness
More informationLecture 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 informationWhat is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation)
OPEN CHANNEL FLOW 1 3 Question What is the most obvious difference between pipe flow and open channel flow????????????? (in terms of flow conditions and energy situation) Typical open channel shapes Figure
More informationWhen 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 information4 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
More informationL r = L m /L p. L r = L p /L m
NOTE: In the set of lectures 19/20 I defined the length ratio as L r = L m /L p The textbook by Finnermore & Franzini defines it as L r = L p /L m To avoid confusion let's keep the textbook definition,
More informationLecture 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 informationSteady Heat Conduction
Steady Heat Conduction In thermodynamics, we considered the amount of heat transfer as a system undergoes a process from one equilibrium state to another. hermodynamics gives no indication of how long
More informationp 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 informationLaminar and Turbulent flow. Flow Sensors. Reynolds Number. Thermal flow Sensor. Flow and Flow rate. R = Mass Flow controllers
Flow and Flow rate. Laminar and Turbulent flow Laminar flow: smooth, orderly and regular Mechanical sensors have inertia, which can integrate out small variations due to turbulence Turbulent flow: chaotic
More informationHow To Understand Fluid Mechanics
Module : Review of Fluid Mechanics Basic Principles for Water Resources Engineering Robert Pitt University of Alabama and Shirley Clark Penn State - Harrisburg Mass quantity of matter that a substance
More informationNatural 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 informationExperiment (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 informationFREESTUDY 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 information2.0 BASIC CONCEPTS OF OPEN CHANNEL FLOW MEASUREMENT
2.0 BASIC CONCEPTS OF OPEN CHANNEL FLOW MEASUREMENT Open channel flow is defined as flow in any channel where the liquid flows with a free surface. Open channel flow is not under pressure; gravity is the
More informationAbaqus/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 informationPipe 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 informationBattery Thermal Management System Design Modeling
Battery Thermal Management System Design Modeling Gi-Heon Kim, Ph.D Ahmad Pesaran, Ph.D (ahmad_pesaran@nrel.gov) National Renewable Energy Laboratory, Golden, Colorado, U.S.A. EVS October -8, 8, 006 Yokohama,
More informationBackwater Rise and Drag Characteristics of Bridge Piers under Subcritical
European Water 36: 7-35, 11. 11 E.W. Publications Backwater Rise and Drag Characteristics of Bridge Piers under Subcritical Flow Conditions C.R. Suribabu *, R.M. Sabarish, R. Narasimhan and A.R. Chandhru
More information1 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 informationHigh 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 informationsensors ISSN 1424-8220 www.mdpi.com/journal/sensors
Sensors 2010, 10, 10560-10570; doi:10.3390/s101210560 OPEN ACCESS sensors ISSN 1424-8220 www.mdpi.com/journal/sensors Article A New Approach to Laminar Flowmeters Fernando Lopez Pena *, Alvaro Deibe Diaz,
More informationHeat Exchangers - Introduction
Heat Exchangers - Introduction Concentric Pipe Heat Exchange T h1 T c1 T c2 T h1 Energy Balance on Cold Stream (differential) dq C = wc p C dt C = C C dt C Energy Balance on Hot Stream (differential) dq
More informationPractice 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 informationFluid Dynamics Basics
Fluid Dynamics Basics Bernoulli s Equation A very important equation in fluid dynamics is the Bernoulli equation. This equation has four variables: velocity ( ), elevation ( ), pressure ( ), and density
More informationPressure. Pressure. Atmospheric pressure. Conceptual example 1: Blood pressure. Pressure is force per unit area:
Pressure Pressure is force per unit area: F P = A Pressure Te direction of te force exerted on an object by a fluid is toward te object and perpendicular to its surface. At a microscopic level, te force
More information1.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