BME 419/519 Hernandez 2002


 Hilary Newman
 1 years ago
 Views:
Transcription
1 Vascular Biology 2  Hemodynamics A. Flow relationships : some basic definitions Q v = A v = velocity, Q = flow rate A = cross sectional area Ohm s Law for fluids: Flow is driven by a pressure gradient P Q = R P = pressure gradient, R = resistance thus, cardiac output: Q = MAPMVP / total peripheral Resistance. (note about pressure units: 1 mm Hg = 1.36 cm H 2 O = 1330 dynes/cm 2, 1 Newton = 10 5 dynes = 0.22 lb) B. Elastic Properties of Vessels. 1. Elasticity. the vessel walls are elastic and deform if there is a pressure gradient across them. a. Hook s Law. As you apply force, the vessel deforms, storing energy like a spring. F = kx F = force, x = displacement b. Young s elastic modulus: consider a rod with a specific cross sectional area. The Y.M. is the specific stress (Force/Area) needed to double the initial length of the rod. In the case of the vessels, we look at the increase in radius.
2 Material Young s Elastic Mod. dynes/cm 2 Rubber 4x10 7 Steel 2x10 12 VSM 10 6 Elastin 6x10 6 Collagen Compliance : How much the vessel s volume changes as the intraluminal pressure changes (at equilibrium). V C = P C = compliance, V = change in blood volume due to P = change in blood pressure. 3. Distensibility: compliance relative to some initial state (at equilibrium). V D = PV i D = distensibility, Vi = initial blood volume 4. Windkessel Effect. The previous relationships are true for equilibrium conditions. However, the vessels take some time to distend. Relationship between the rate of pressure build/up and the concomitant rate of volume change. dv dp = C dt dt simple example: aortic pressure following diastole: dv = Qin ( t) Qout ( t) dt P dp = Qin ( t) = C R dt dp 1 = P( t) dt CR behaves like a discharging capacitor (see below)
3 Note the analogy between fluid mechanics and circuits: Q= flow I = current P= Pressure Drop V = voltage drop C=compliance C = capacitance V= volume Q = charge R = resistance R = resistance You can use the same techniques on both! C. Blood s viscosity and flow : Poiseuille s equation 1. Viscosity: mechanical property of fluids that slows down their flow due to internal forces. Newton s definition: shear stress τ F / A η = = = shear rate du / dy U / Y nonnewtonian fluid is one that doesn t behave like this (nonconstant relationship between shear stress and shear rate) 2. Poiseuille s Equation: determines the resistance to flow of a vessel given the viscoelastic properties of the fluid under the following assumptions: Laminar flow Newtonian fluid Straight, rigid pipe Constant flow and therefore, 8ηL R = π 4 r P Q = = R R = resistance, η = viscosity (function of hematocrit primarily) L = length (won t usually change) r = radius : this is the most critical. Arterioles can essentially shunt flow because of this property. 4 Pπr 8ηL P = pressure drop through a segment of length L
4 3. Considerations: a. Combined resistance : this works just like circuits do i. Series ii. Parallel b. The real world: NonNewtonian Behavior (??) i. Plug flow happens near the inlet of a tube, before laminar floe is fully developed. Capillaries can also show plug flow. ii. Distortion of erythrocytes. Greater hematocrit greater viscosity
5 c. Different types of flow exist: i. Plug flow: all molecules move at the same speed. Happens only at very small diameters, and slow flows. ii. Laminar Flow. Due to friction against vessel walls, the blood near the center of the tube flows faster than that on the periphery. Infinitesimally thin concentric cylinders sliding past each other. The velocity profile is shaped like a parabola. iii. Turbulent flow. Chaotic, random. Occurs when the Reynolds number for a fluid is exceeded. 2rvρ Re = η d. shear stress (force/area) : the viscous drag of the blood creates a shear force on the intraluminal side of the vessel walls. Using Poiseuille s eq.
6 F Pr 4ηQ τ w = = = 3 A 2L πr τ w = wall shear stress this can cause tears inside the lumen (dissecting aneurysm). High velocity in the aorta more likely place to happen : bad news! D. Pressure inside capillaries: Law of LaPlace Sources of pressure: a. Hydrostatic pressure: pressure due to gravity function of body part, height, position,.etc. P hs = ρ h g ρ = fluid density, h =vertical distance to a reference ( phlebostatic )level g = gravitational force constant b. Static (intraluminal or transluminal) pressure : Pressure in the vessels without the hydrostatic pressure. I.e. measured at the reference level: patient is supine and all organs are at the same level as the heart.  Law of Laplace: T = rp T = tension in vessel wall, P = intraluminal pressure r = radius of vessel Implication thin walled capillaries can stand high internal pressures, because of their small lumen
7 . Stress : force per unit area on the vessel wall. Strain is the resultant deformation. Stress in vessel wall σ = rp w σ = vessel wall stress w = wall thickness BUT: As the vessel gets stretched out, the wall gets thinner, more fragile (ie greater stress with the same pressure), less compliant. (notice table above: the capillaries and the aorta withstand similar (ratio ~ 10) pressure, but there is a lot less tension in capillaries (ratio~10 9 ). This radius dependence keeps the capillaries from rupturing. E. Bernoulli s Relationships Under the following conditions: i.constant flow ii.nonviscous fluid iii.incompressible fluid. the total pressure in a section of a vessel is constant and can be divided into a static and a dynamic component. Bernoulli s Law: 2 P + ρ v = constant 2 2 v P d = ρ 2 P d = dynamic component to pressure ρ = density of the fluid v = velocity of flow (analogous to conservation of energy: P.E. + K.E. = constant)
8 as a fluid moves faster, it exerts a smaller radial pressure on the vessel. (note: the L shaped tube measures the total pressure. The straight tube measures the static radial pressure) Physiological Examples: Stenosis, Aneurysm: Consider a long continuous tube. Flow must be the same throughout the whole length (conservation of mass). If we reduce the crosssectional area of a segment (stenosis), then the flow velocity must increase proportionally to maintain flow constant. The static pressure is reduced. An aneurysm is exactly the opposite effect.
9 In light of the fluid mechanics principles we have seen, and what we know about the geometry the above picture should make more sense.
Week 8. Topics: Next deadline: Viscous fluid flow (Study guide 14. Sections 12.4 and 12.5.) Bolus flow (Study guide 15. Section 12.6.
8/1 Topics: Week 8 Viscous fluid flow (Study guide 14. Sections 12.4 and 12.5.) Bolus flow (Study guide 15. Section 12.6.) Pulsatile flow (Study guide 15. Section 12.7.) Next deadline: Friday October 31
More informationFurther Applications of Newton s Laws  Friction Static and Kinetic Friction
urther pplications of Newton s Laws  riction Static and Kinetic riction The normal force is related to friction. When two surfaces slid over one another, they experience a force do to microscopic contact
More informationFluid Mechanics II Viscosity and shear stresses
Fluid Mechanics II Viscosity and shear stresses Shear stresses in a Newtonian fluid A fluid at rest can not resist shearing forces. Under the action of such forces it deforms continuously, however small
More information1. Introduction, fluid properties (1.1, 2.8, 4.1, and handouts)
1. Introduction, fluid properties (1.1, 2.8, 4.1, and handouts) Introduction, general information Course overview Fluids as a continuum Density Compressibility Viscosity Exercises: A1 Fluid mechanics Fluid
More informationShell Balances in Fluid Mechanics
Shell Balances in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University When fluid flow occurs in a single direction everywhere in a system, shell
More informationRutgers University Department of Physics & Astronomy. 01:750:271 Honors Physics I Fall Lecture 19. Home Page. Title Page. Page 1 of 36.
Rutgers University Department of Physics & Astronomy 01:750:271 Honors Physics I Fall 2015 Lecture 19 Page 1 of 36 12. Equilibrium and Elasticity How do objects behave under applied external forces? Under
More informationFORMULA SHEET. General formulas:
FORMULA SHEET You may use this formula sheet during the Advanced Transport Phenomena course and it should contain all formulas you need during this course. Note that the weeks are numbered from 1.1 to
More informationSteven Burian Civil & Environmental Engineering September 25, 2013
Fundamentals of Engineering (FE) Exam Mechanics Steven Burian Civil & Environmental Engineering September 25, 2013 s and FE Morning ( Mechanics) A. Flow measurement 7% of FE Morning B. properties Session
More informationPhysics 201 Chapter 13 Lecture 1
Physics 201 Chapter 13 Lecture 1 Fluid Statics Pascal s Principle Archimedes Principle (Buoyancy) Fluid Dynamics Continuity Equation Bernoulli Equation 11/30/2009 Physics 201, UWMadison 1 Fluids Density
More informationFor more info
Characteristic of Ideal fluid: (a) It is incompressible (b) It is nonviscous (c) Flow of ideal fluid is irrational (d) It is capable of exhibiting steady flow Stream line flow: Flow of a liquid fluid
More informationObjectives: After completion of this module, you should be able to:
Chapter 12 Objectives: After completion of this module, you should be able to: Demonstrate your understanding of elasticity, elastic limit, stress, strain, and ultimate strength. Write and apply formulas
More informationcos(θ)sin(θ) Alternative Exercise Correct Correct θ = 0 skiladæmi 10 Part A Part B Part C Due: 11:59pm on Wednesday, November 11, 2015
skiladæmi 10 Due: 11:59pm on Wednesday, November 11, 015 You will receive no credit for items you complete after the assignment is due Grading Policy Alternative Exercise 1115 A bar with cross sectional
More informationViscoelasticity. Basic Notions & Examples. Formalism for Linear Viscoelasticity. Simple Models & Mechanical Analogies. Nonlinear behavior
Viscoelasticity Basic Notions & Examples Formalism for Linear Viscoelasticity Simple Models & Mechanical Analogies Nonlinear behavior Viscoelastic Behavior Generic Viscoelasticity: exhibition of both
More informationPhysics. Assignment1(UNITS AND MEASUREMENT)
Assignment1(UNITS AND MEASUREMENT) 1. Define physical quantity and write steps for measurement. 2. What are fundamental units and derived units? 3. List the seven basic and two supplementary physical
More informationTECHNISCHE UNIVERSITEIT EINDHOVEN Department of Biomedical Engineering, section Cardiovascular Biomechanics
TECHNISCHE UNIVERSITEIT EINDHOVEN Department of Biomedical Engineering, section Cardiovascular Biomechanics Exam Cardiovascular Fluid Mechanics (8W9) page 1/4 Monday March 1, 8, 1417 hour Maximum score
More information150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces
Fluid Statics Pressure acts in all directions, normal to the surrounding surfaces or Whenever a pressure difference is the driving force, use gauge pressure o Bernoulli equation o Momentum balance with
More informationChapter 12. Static Equilibrium and Elasticity
Chapter 12 Static Equilibrium and Elasticity Static Equilibrium Equilibrium implies that the object moves with both constant velocity and constant angular velocity relative to an observer in an inertial
More informationPhysics 3 Summer 1990 Lab 7  Hydrodynamics
Physics 3 Summer 1990 Lab 7  Hydrodynamics Theory Consider an ideal liquid, one which is incompressible and which has no internal friction, flowing through pipe of varying cross section as shown in figure
More informationPHYSICS. Course Structure. Unit Topics Marks. Physical World and Measurement. 1 Physical World. 2 Units and Measurements.
PHYSICS Course Structure Unit Topics Marks I Physical World and Measurement 1 Physical World 2 Units and Measurements II Kinematics 3 Motion in a Straight Line 23 4 Motion in a Plane III Laws of Motion
More informationPhysics 207 Lecture 22. Lecture 22
Goals: Lecture Chapter 15 Use an idealfluid model to study fluid flow. Investigate the elastic deformation of solids and liquids Chapter 16 Recognize and use the state variables that characterize macroscopic
More informationPIPE FLOWS: LECTURE /04/2017. Yesterday, for the example problem Δp = f(v, ρ, μ, L, D) We came up with the non dimensional relation
/04/07 ECTURE 4 PIPE FOWS: Yesterday, for the example problem Δp = f(v, ρ, μ,, ) We came up with the non dimensional relation f (, ) 3 V or, p f(, ) You can plot π versus π with π 3 as a parameter. Or,
More informationViscosity and Polymer Melt Flow. RheologyProcessing / Chapter 2 1
Viscosity and Polymer Melt Flow RheologyProcessing / Chapter 2 1 Viscosity: a fluid property resistance to flow (a more technical definition resistance to shearing) Remember that: τ μ du dy shear stress
More informationChapter 13 ELASTIC PROPERTIES OF MATERIALS
Physics Including Human Applications 280 Chapter 13 ELASTIC PROPERTIES OF MATERIALS GOALS When you have mastered the contents of this chapter, you will be able to achieve the following goals: Definitions
More informationThermal physics revision questions
Thermal physics revision questions ONE SECTION OF QUESTIONS TO BE COMPLETED AND MARKED EVERY WEEK AFTER HALF TERM. Section 1: Energy 1. Define the law of conservation of energy. Energy is neither created
More informationLecture 2: Hydrodynamics at milli micrometer scale
1 at milli micrometer scale Introduction Flows at milli and micro meter scales are found in various fields, used for several processes and open up possibilities for new applications: Injection Engineering
More informationCHAPTER 3 THE EFFECTS OF FORCES ON MATERIALS
CHAPTER THE EFFECTS OF FORCES ON MATERIALS EXERCISE 1, Page 50 1. A rectangular bar having a crosssectional area of 80 mm has a tensile force of 0 kn applied to it. Determine the stress in the bar. Stress
More informationChapter 26 Elastic Properties of Materials
Chapter 26 Elastic Properties of Materials 26.1 Introduction... 1 26.2 Stress and Strain in Tension and Compression... 2 26.3 Shear Stress and Strain... 4 Example 26.1: Stretched wire... 5 26.4 Elastic
More informationFigure 3: Problem 7. (a) 0.9 m (b) 1.8 m (c) 2.7 m (d) 3.6 m
1. For the manometer shown in figure 1, if the absolute pressure at point A is 1.013 10 5 Pa, the absolute pressure at point B is (ρ water =10 3 kg/m 3, ρ Hg =13.56 10 3 kg/m 3, ρ oil = 800kg/m 3 ): (a)
More informationMECHANICAL PROPERTIES
MECHANICAL PROPERTIES Rheology S.C. BAYNE, 1 J.Y. Thompson 2 1 University of Michigan School of Dentistry, Ann Arbor, MI 481091078 sbayne@umich.edu 2 Nova Southeastern College of Dental Medicine, Ft.
More informationChapter 3 NonNewtonian fluid
Chapter 3 NonNewtonian fluid 31. Introduction: The study of the deformation of flowing fluids is called rheology; the rheological behavior of various fluids is sketchen Figure 31. Newtonian fluids,
More informationDIMENSIONS AND UNITS
DIMENSIONS AND UNITS A dimension is the measure by which a physical variable is expressed quantitatively. A unit is a particular way of attaching a number to the quantitative dimension. Primary Dimension
More information10  FLUID MECHANICS Page 1
0  FLUID MECHANICS Page Introduction Fluid is a matter in a state which can flow. Liquids, gases, molten metal and tar are examples of fluids. Fluid mechanics is studied in two parts: ( i ) Fluid statics
More informationLecture 8 Equilibrium and Elasticity
Lecture 8 Equilibrium and Elasticity July 19 EQUILIBRIUM AND ELASTICITY CHAPTER 12 Give a sharp blow one end of a stick on the table. Find center of percussion. Baseball bat center of percussion Equilibrium
More informationNicholas J. Giordano. Chapter 10 Fluids
Nicholas J. Giordano www.cengage.com/physics/giordano Chapter 10 Fluids Fluids A fluid may be either a liquid or a gas Some characteristics of a fluid Flows from one place to another Shape varies according
More informationCLASS SCHEDULE 2013 FALL
CLASS SCHEDULE 2013 FALL Class # or Lab # 1 Date Aug 26 2 28 Important Concepts (Section # in Text Reading, Lecture note) Examples/Lab Activities Definition fluid; continuum hypothesis; fluid properties
More informationLECTURE 4 FLUID FLOW & SURFACE TENSION. Lecture Instructor: Kazumi Tolich
LECTURE 4 FLUID FLOW & SURFACE TENSION Lecture Instructor: Kazumi Tolich Lecture 4 2 Reading chapter 15.6 to 15.9 Continuity equation Bernoulli s equation n Torricelli s law Viscosity Surface tension Equation
More informationMechanical Engineering Programme of Study
Mechanical Engineering Programme of Study Fluid Mechanics Instructor: Marios M. Fyrillas Email: eng.fm@fit.ac.cy SOLVED EXAMPLES ON VISCOUS FLOW 1. Consider steady, laminar flow between two fixed parallel
More informationStatics. Phys101 Lectures 19,20. Key points: The Conditions for static equilibrium Solving statics problems Stress and strain. Ref: 91,2,3,4,5.
Phys101 Lectures 19,20 Statics Key points: The Conditions for static equilibrium Solving statics problems Stress and strain Ref: 91,2,3,4,5. Page 1 The Conditions for Static Equilibrium An object in static
More informationof Friction in Fluids Dept. of Earth & Clim. Sci., SFSU
Summary. Shear is the gradient of velocity in a direction normal to the velocity. In the presence of shear, collisions among molecules in random motion tend to transfer momentum downshear (from faster
More informationVisualization of flow pattern over or around immersed objects in open channel flow.
EXPERIMENT SEVEN: FLOW VISUALIZATION AND ANALYSIS I OBJECTIVE OF THE EXPERIMENT: Visualization of flow pattern over or around immersed objects in open channel flow. II THEORY AND EQUATION: Open channel:
More informationFluid Mechanics. Chapter 12. PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman
Chapter 12 Fluid Mechanics PowerPoint Lectures for University Physics, Thirteenth Edition Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Goals for Chapter 12 To study the concept of density
More information1. Introduction, tensors, kinematics
1. Introduction, tensors, kinematics Content: Introduction to fluids, Cartesian tensors, vector algebra using tensor notation, operators in tensor form, Eulerian and Lagrangian description of scalar and
More informationMechanics of Solids. Mechanics Of Solids. Suraj kr. Ray Department of Civil Engineering
Mechanics Of Solids Suraj kr. Ray (surajjj2445@gmail.com) Department of Civil Engineering 1 Mechanics of Solids is a branch of applied mechanics that deals with the behaviour of solid bodies subjected
More informationToday s menu. Last lecture. A/D conversion. A/D conversion (cont d...) Sampling
Last lecture Capacitive sensing elements. Inductive sensing elements. Reactive Deflection bridges. Electromagnetic sensing elements. Thermoelectric sensing elements. Elastic sensing elements. Piezoelectric
More informationCENG 501 Examination Problem: Estimation of Viscosity with a Falling  Cylinder Viscometer
CENG 501 Examination Problem: Estimation of Viscosity with a Falling  Cylinder Viscometer You are assigned to design a fallingcylinder viscometer to measure the viscosity of Newtonian liquids. A schematic
More informationPHY121 Physics for the Life Sciences I
PHY Physics for the Life Sciences I Lecture 0. Fluid flow: kinematics describing the motion. Fluid flow: dynamics causes and effects, Bernoulli s Equation 3. Viscosity and Poiseuille s Law for narrow tubes
More informationAnalyze a Load Bearing Structure using MATLAB
Analyze a Load Bearing Structure using MATLAB Instructor: Prof. Shahrokh Ahmadi (ECE Dept.) Teaching Assistant: Kartik Bulusu (MAE Dept.) Email: bulusu@gwu.edu September 16, 2005 1 Brief Discussion of
More informationStatic Equilibrium; Elasticity & Fracture
Static Equilibrium; Elasticity & Fracture The Conditions for Equilibrium Statics is concerned with the calculation of the forces acting on and within structures that are in equilibrium. An object with
More informationNEW HORIZON PRE UNIVERSITY COLLEGE LESSON PLAN FOR THE ACADEMIC YEAR Department of PHYSICS ( I PUC)
NEW HORIZON PRE UNIVERSITY COLLEGE LESSON PLAN FOR THE ACADEMIC YEAR 017 018 Department of PHYSICS ( I PUC) Week  Month: June Chapter (Physical world) Scope and excitement of Physics
More informationCHARACTERISTIC OF FLUIDS. A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude.
CHARACTERISTIC OF FLUIDS A fluid is defined as a substance that deforms continuously when acted on by a shearing stress at any magnitude. In a fluid at rest, normal stress is called pressure. 1 Dimensions,
More informationSummary PHY101 ( 2 ) T / Hanadi Al Harbi
الكمية Physical Quantity القانون Low التعريف Definition الوحدة SI Unit Linear Momentum P = mθ be equal to the mass of an object times its velocity. Kg. m/s vector quantity Stress F \ A the external force
More informationModeling Mechanical Systems
Modeling Mechanical Systems Mechanical systems can be either translational or rotational. Although the fundamental relationships for both types are derived from Newton s law, they are different enough
More informationANSWERS 403 INDEX. Bulk modulus 238 Buoyant force 251
ANSWERS 403 INDEX A Absolute scale temperature 276 Absolute zero 276 Acceleration (linear) 45 Acceleration due to gravity 49,189 Accuracy 22 Actionreaction 97 Addition of vectors 67 Adiabatic process
More informationHoney Coiling  A Study on the Gravitational Regime of Liquid Rope Coiling
Honey Coiling  A Study on the Gravitational Regime of Liquid Rope Coiling Patrick Meister, MNG Rämibühl, patrickmeister@ymail.com 1 Introduction We report on the coiling motion a falling stream of viscous
More informationStress, Strain, and Viscosity. San Andreas Fault Palmdale
Stress, Strain, and Viscosity San Andreas Fault Palmdale Solids and Liquids Solid Behavior: Liquid Behavior:  elastic  fluid  rebound  no rebound  retain original shape  shape changes  small deformations
More informationChapter 5 Elastic Strain, Deflection, and Stability 1. Elastic StressStrain Relationship
Chapter 5 Elastic Strain, Deflection, and Stability Elastic StressStrain Relationship A stress in the xdirection causes a strain in the xdirection by σ x also causes a strain in the ydirection & zdirection
More information2007 Problem Topic Comment 1 Kinematics Positiontime equation Kinematics 7 2 Kinematics Velocitytime graph Dynamics 6 3 Kinematics Average velocity
2007 Problem Topic Comment 1 Kinematics Positiontime equation Kinematics 7 2 Kinematics Velocitytime graph Dynamics 6 3 Kinematics Average velocity Energy 7 4 Kinematics Free fall Collisions 3 5 Dynamics
More informationGame Physics. Game and Media Technology Master Program  Utrecht University. Dr. Nicolas Pronost
Game and Media Technology Master Program  Utrecht University Dr. Nicolas Pronost Soft body physics Soft bodies In reality, objects are not purely rigid for some it is a good approximation but if you hit
More informationTranslational Motion Rotational Motion Equations Sheet
PHYSICS 01 Translational Motion Rotational Motion Equations Sheet LINEAR ANGULAR Time t t Displacement x; (x = rθ) θ Velocity v = Δx/Δt; (v = rω) ω = Δθ/Δt Acceleration a = Δv/Δt; (a = rα) α = Δω/Δt (
More informationChapter 3. Load and Stress Analysis
Chapter 3 Load and Stress Analysis 2 Shear Force and Bending Moments in Beams Internal shear force V & bending moment M must ensure equilibrium Fig. 3 2 Sign Conventions for Bending and Shear Fig. 3 3
More informationPharmaceutical compounding I Colloidal and SurfaceChemical Aspects of Dosage Forms Dr. rer. nat. Rebaz H. Ali
University of Sulaimani School of Pharmacy Dept. of Pharmaceutics Pharmaceutical Compounding Pharmaceutical compounding I Colloidal and SurfaceChemical Aspects of Dosage Forms Dr. rer. nat. Rebaz H. Ali
More informationTECHNISCHE UNIVERSITEIT EINDHOVEN Faculteit Biomedische Technologie, groep Cardiovasculaire Biomechanica
TECHNISCHE UNIVERSITEIT EINDHOVEN Faculteit Biomedische Technologie, groep Cardiovasculaire Biomechanica Tentamen Cardiovasculaire Stromingsleer (8W090) blad /4 dinsdag 8 mei 2007, 92 uur Maximum score
More informationChapter 13 Elastic Properties of Materials
Chapter 13 Elastic Properties of Materials 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
More informationMathematical Model of Blood Flow in Carotid Bifurcation
Excerpt from the Proceedings of the COMSOL Conference 2009 Milan Mathematical Model of Blood Flow in Carotid Bifurcation E. Muraca *,1, V. Gramigna 1, and G. Fragomeni 1 1 Department of Experimental Medicine
More informationPressure drop due to viscosity in a round pipe of radius R is given by the Poiseuille equation: P L. = 8η v R 2
PHY 302 K. Solutions for Problem set # 12. Textbook problem 10.55: Pressure drop due to viscosity in a round pipe of radius R is given by the Poiseuille equation: P L 8η v R 2 8ηF πr 4 (1) where η is viscosity
More informationNon Newtonian Fluid Dynamics
PDHonline Course M417 (3 PDH) Non Newtonian Fluid Dynamics Instructor: Paul G. Conley, PE 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 220306658 Phone & Fax: 7039880088 www.pdhonline.org
More information1 2 Models, Theories, and Laws 1.5 Distinguish between models, theories, and laws 2.1 State the origin of significant figures in measurement
Textbook Correlation Textbook Correlation Physics 1115/2015 Chapter 1 Introduction, Measurement, Estimating 1.1 Describe thoughts of Aristotle vs. Galileo in describing motion 1 1 Nature of Science 1.2
More information1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor.
Elasticity Homework Problems 2014 Section 1. The Strain Tensor. 1. A pure shear deformation is shown. The volume is unchanged. What is the strain tensor. 2. Given a steel bar compressed with a deformation
More informationMEASUREMENT; SIMPLE HARMONIC MOTION; MOMENT OF INERTIA, SURFACE TENSION; KINETIC THEORY OF GASES AND ACOUSTICS
CHAPTER MEASUREMENT; SIMPLE HARMONIC MOTION; MOMENT OF INERTIA, SURFACE TENSION; KINETIC THEORY OF GASES AND ACOUSTICS. MEASUREMENT. If the wavelength of the green line of the visible spectrum is 546 nm,
More informationEQUILIBRIUM and ELASTICITY
PH 2211D Spring 2013 EQUILIBRIUM and ELASTICITY Lectures 3032 Chapter 12 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition) 1 Chapter 12 Equilibrium and Elasticity In this chapter we will
More informationEXAMPLE SHEET FOR TOPIC 3 AUTUMN 2013
EXAMPLE SHEET FOR TOPIC ATMN 01 Q1. se dimensional analysis to investigate how the capillary rise h of a liquid in a tube varies with tube diameter d, gravity g, fluid density ρ, surface tension σ and
More informationAerodynamics. Basic Aerodynamics. Continuity equation (mass conserved) Some thermodynamics. Energy equation (energy conserved)
Flow with no friction (inviscid) Aerodynamics Basic Aerodynamics Continuity equation (mass conserved) Flow with friction (viscous) Momentum equation (F = ma) 1. Euler s equation 2. Bernoulli s equation
More informationToo many answers to list.
ECE/ME 9 Spring 08, Prof. Feinerman, Test # solutions 5/6/08, Closed Book and Closed Notes Undergraduates x 8.5, σ 1.0, Graduates x 78.5, σ 1. Element Molecular weight, grams Atomic number Density, gm/cc
More informationChapter II: Reversible process and work
Chapter II: Reversible process and work 1 Process Defined by change in a system, a thermodynamic process is a passage of a thermodynamic system from an initial to a final state of thermodynamic equilibrium.
More informationElastic Properties of Solid Materials. Notes based on those by James Irvine at
Elastic Properties of Solid Materials Notes based on those by James Irvine at www.antonineeducation.co.uk Key Words Density, Elastic, Plastic, Stress, Strain, Young modulus We study how materials behave
More informationContents. Microfluidics  Jens Ducrée Physics: Laminar and Turbulent Flow 1
Contents 1. Introduction 2. Fluids 3. Physics of Microfluidic Systems 4. Microfabrication Technologies 5. Flow Control 6. Micropumps 7. Sensors 8. InkJet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More informationTALLINN UNIVERSITY OF TECHNOLOGY, DIVISION OF PHYSICS 13. STOKES METHOD
13. STOKES METHOD 1. Objective To determine the coefficient of viscosity of a known fluid using Stokes method.. Equipment needed A glass vessel with glycerine, micrometer calliper, stopwatch, ruler. 3.
More informationA concrete cylinder having a a diameter of of in. mm and elasticity. Stress and Strain: Stress and Strain: 0.
2011 earson Education, Inc., Upper Saddle River, NJ. ll rights reserved. This material is protected under all copyright laws as they currently 8 1. 3 1. concrete cylinder having a a diameter of of 6.00
More informationR09. d water surface. Prove that the depth of pressure is equal to p +.
Code No:A109210105 R09 SET1 B.Tech II Year  I Semester Examinations, December 2011 FLUID MECHANICS (CIVIL ENGINEERING) Time: 3 hours Max. Marks: 75 Answer any five questions All questions carry equal
More informationME3250 Fluid Dynamics I
ME3250 Fluid Dynamics I Section I, Fall 2012 Instructor: Prof. Zhuyin Ren Department of Mechanical Engineering University of Connecticut Course Information Website: http://www.engr.uconn.edu/~rzr11001/me3250_f12/
More informationChapter 14. Lecture 1 Fluid Mechanics. Dr. Armen Kocharian
Chapter 14 Lecture 1 Fluid Mechanics Dr. Armen Kocharian States of Matter Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas unconfined Has neither a definite
More informationMECE 3321 MECHANICS OF SOLIDS CHAPTER 3
MECE 3321 MECHANICS OF SOLIDS CHAPTER 3 Samantha Ramirez TENSION AND COMPRESSION TESTS Tension and compression tests are used primarily to determine the relationship between σ avg and ε avg in any material.
More informationTheoretical Seismology. Astrophysics and Cosmology and Earth and Environmental Physics. Anelasticity. Fabio ROMANELLI
Theoretical Seismology Astrophysics and Cosmology and Earth and Environmental Physics Anelasticity Fabio ROMANELLI Department of Mathematics & Geosciences University of Trieste romanel@units.it Intrinsic
More informationINTRODUCTION TO FLUID MECHANICS June 27, 2013
INTRODUCTION TO FLUID MECHANICS June 27, 2013 PROBLEM 3 (1 hour) A perfect liquid of constant density ρ and constant viscosity µ fills the space between two infinite parallel walls separated by a distance
More informationQuiz 1. Introduction to Polymers
100406 Quiz 1. Introduction to Polymers 1) Polymers are different than lowmolecular weight oligomers. For example an oligomeric polyethylene is wax, oligomeric polystyrene is similar to naphthalene (moth
More informationFlow and Transport. c(s, t)s ds,
Flow and Transport 1. The Transport Equation We shall describe the transport of a dissolved chemical by water that is traveling with uniform velocity ν through a long thin tube G with uniform cross section
More informationChapter 5 Torsion STRUCTURAL MECHANICS: CE203. Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson
STRUCTURAL MECHANICS: CE203 Chapter 5 Torsion Notes are based on Mechanics of Materials: by R. C. Hibbeler, 7th Edition, Pearson Dr B. Achour & Dr Eng. K. Elkashif Civil Engineering Department, University
More informationChapter 10: Boiling and Condensation 1. Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI.
Chapter 10: Boiling and Condensation 1 1 Based on lecture by Yoav Peles, Mech. Aero. Nuc. Eng., RPI. Objectives When you finish studying this chapter, you should be able to: Differentiate between evaporation
More informationLECTURE 6 ENERGY LOSSES IN HYDRAULIC SYSTEMS SELF EVALUATION QUESTIONS AND ANSWERS
LECTURE 6 ENERGY LOSSES IN HYDRAULIC SYSTEMS SELF EVALUATION QUESTIONS AND ANSWERS 1. What is the head loss ( in units of bars) across a 30mm wide open gate valve when oil ( SG=0.9) flow through at a
More informationElements of Rock Mechanics
Elements of Rock Mechanics Stress and strain Creep Constitutive equation Hooke's law Empirical relations Effects of porosity and fluids Anelasticity and viscoelasticity Reading: Shearer, 3 Stress Consider
More informationFluids. Fluid = Gas or Liquid. Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion
Chapter 14 Fluids Fluids Density Pressure in a Fluid Buoyancy and Archimedes Principle Fluids in Motion Fluid = Gas or Liquid MFMcGrawPHY45 Chap_14HaFluidsRevised 10/13/01 Densities MFMcGrawPHY45 Chap_14HaFluidsRevised
More informationPART 1B EXPERIMENTAL ENGINEERING. SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) BOUNDARY LAYERS AND DRAG
1 PART 1B EXPERIMENTAL ENGINEERING SUBJECT: FLUID MECHANICS & HEAT TRANSFER LOCATION: HYDRAULICS LAB (Gnd Floor Inglis Bldg) EXPERIMENT T3 (LONG) BOUNDARY LAYERS AND DRAG OBJECTIVES a) To measure the velocity
More informationPhysics A  PHY 2048C
Kinetic Mechanical Physics A  PHY 2048C and 11/01/2017 My Office Hours: Thursday 2:003:00 PM 212 Keen Building Warmup Questions Kinetic Mechanical 1 How do you determine the direction of kinetic energy
More informationQuiz 1 Introduction to Polymers (Please answer each question even if you guess)
080407 Quiz 1 Introduction to Polymers (Please answer each question even if you guess) This week we explored the definition of a polymer in terms of properties. 1) The flow of polymer melts and concentrated
More informationFLUID FLOW IDEAL FLUID EQUATION OF CONTINUITY
VISUAL PHYSICS School of Physics University of Sydney Australia FLUID FLOW IDEAL FLUID EQUATION OF CONTINUITY? How can the blood deliver oxygen to body so successfully? How do we model fluids flowing in
More informationWater Circuit Lab. The pressure drop along a straight pipe segment can be calculated using the following set of equations:
Water Circuit Lab When a fluid flows in a conduit, there is friction between the flowing fluid and the pipe walls. The result of this friction is a net loss of energy in the flowing fluid. The fluid pressure
More informationReynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment:
7 STEADY FLOW IN PIPES 7.1 Reynolds Number Reynolds, an engineering professor in early 1880 demonstrated two different types of flow through an experiment: Laminar flow Turbulent flow Reynolds apparatus
More informationChapter 16 Electrical Energy Capacitance. HW: 1, 2, 3, 5, 7, 12, 13, 17, 21, 25, 27 33, 35, 37a, 43, 45, 49, 51
Chapter 16 Electrical Energy Capacitance HW: 1, 2, 3, 5, 7, 12, 13, 17, 21, 25, 27 33, 35, 37a, 43, 45, 49, 51 Electrical Potential Reminder from physics 1: Work done by a conservative force, depends only
More informationContinuum Mechanics. Continuum Mechanics and Constitutive Equations
Continuum Mechanics Continuum Mechanics and Constitutive Equations Continuum mechanics pertains to the description of mechanical behavior of materials under the assumption that the material is a uniform
More informationViscous Fluids. Amanda Meier. December 14th, 2011
Viscous Fluids Amanda Meier December 14th, 2011 Abstract Fluids are represented by continuous media described by mass density, velocity and pressure. An Eulerian description of uids focuses on the transport
More information