Dimensional Analysis


 Eleanor Robertson
 2 years ago
 Views:
Transcription
1 Dimensional Analysis An Important Example from Fluid Mechanics: Viscous Shear Forces V d t / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / / Ƭ = F/A = μ V/d
2 More generally, the viscous shear stress may be written in terms of the local velocity gradient as, Ƭyx = μ du/dy (shear force in the xdirection, acting on a plane normal to the ydirection) The viscosity μ is often called the absolute or dynamic viscosity to distinguish it from the kinematic viscosity ʋ = μ/ρ, where ρ is the fluid density (g/cm 3 ). The cgs unit of viscosity, called the poise, is 1 g/(cm s); the mks unit is the stoke 1 kg/(m s)
3 The Reynolds number an important dimensionless parameter The Reynolds number is a qualitative expression of the ratio of inertial to viscous forces The mass flow rate per unit area (g cm 2 s 1 ) is the product of the fluid density ρ (g/cm 3 ) and the fluid velocity V (cm/s) The momentum flux is the product of the mass flow rate per unit area, ρv, and the fluid velocity V The momentum flux (inertial force per unit area) = ρv 2 The viscous force per unit area is Ƭyx = μ du/dy = μv/d The Reynolds number is ρv 2 /(μv/d) = ρvd/μ
4 Flow direction Uniform flow past a circular cylinder at Re=ρVd/μ=0.16. In the limit as Re 0 (purely viscous flow) the flow has foreandaft symmetry.
5 Circular cylinder at Re=1.54. At this Reynolds number the flow has lost its foreandaft symmetry.
6 Circular cylinder at Re=9.6. The flow has separated from the cylinder surface to form a pair of recirculating eddies.
7 Circular cylinder at Re=13.1. The standing eddies become elongated along the flow direction as the Reynolds number increases.
8 Circular cylinder at Re=26.
9 Sphere at Re=118. The wake grows more slowly for this axisymmetric flow than for the planar flow around a cylinder.
10 cylinder Von Kármán vortex street in the wake of a cylinder at Re=140
11 cylinder Von Kármán vortex street in the wake of a cylinder at Re=140
12 Circular cylinder at Re=2000. At this Reynolds number a thin boundary layer is welldefined. The boundary layer is laminar over the front, separates and breaks up into a turbulent wake.
13 The Boundary Layer The effects of viscosity are largely confined to a thin layer extending along the cylinder surfaces from the upstream stagnation point to the points of flow separation. This thin surface layer of slowly moving fluid is known as the boundary layer, a concept originating with the studies of Prandtl in the early 1900s. Viscosity also plays a role in a detailed description of the motion of the fluid within the recirculating wake region.
14 Circular cylinder at Re=10,000. The flow pattern remains similar for Re 50,000. Thereafter the boundary layer becomes turbulent and separation is postponed, reducing the size of the wake and causing an abrupt reduction in drag (ca. Re=300,000).
15 Dimensional Analysis Four Physical parameters: a) The viscosity μ, with the dimensions g/(cm s) b) The freestream fluid velocity V (cm/s) c) The flow has a characteristic length scale provided by the diameter d of the cylinder or sphere d) It is also clear that another parameter containing a mass must be involved; this is the density ρ (g/cm 3 ) of the fluid. From these four physical parameters, containing among them the three dimensions M, L, T, we can form the dimensionless Reynolds number. Red = ρvd/μ
16 Now suppose we introduce an additional parameter, namely, the drag force Fd exerted by the fluid on the cylinder or sphere. This will lead to a second dimensionless quantity, the drag coefficient, CD = (Fd/A)/(ρV 2 /2) By convention the area A refers to the forward projected area of the body immersed within the flow.
17 In general, if a problem depends on N parameters containing M dimensions, then there are NM independent dimensionless ratios linked by a unique functional relationship. In the present case, the N parameters are ρ, V, d, μ, and Fd, which contain among them the three dimensions mass, length, and time. We desire the functional relationship that links two dimensionless ratios CD and Red, i.e., CD = CD(Red) Once this relationship is known then we may calculate the drag force Fd by computing CD for any desired Reynolds number, Red.
18 In principle this relationship is given by theoretical solution of the equations that govern the motion of a viscous fluid (the NavierStokes equations). In reality the flow field around a cylinder or sphere, for an arbitrarily chosen Reynolds number, is, in general, quite complicated and even numerical solutions are beyond the capabilities of present computer technology. However, the use of dimensional analysis enables the experimenter to readily determine the relationship C D (Re d ). Because C D depends only on Re d, dimensional analysis tells us that it is unnecessary to carry out drag measurements for four independent variables (ρ, V, d, and μ); the experimenter need only vary Re d with any convenient choices of the parameters ρ, V, d, and μ. This provides a tremendous economy of effort. Moreover, once C D (Re d ) has been determined, this is a universal relationship that will apply to a sphere of arbitary diameter, immersed in any fluid (air, water, glycerine, motor oil, molasses, etc.) moving with any velocity consistent with the range of Re d over which C D (Re d ) is known
19
20 For Stokes flow Fd = 3πμVd
21 Dimensionless Quantities (set = to unity to define length and energy scales)
22 (length scale) we set this quantity equal to unity. Then the energy scale
23 Radiation from an Accelerating Charge
24
25 Vortex Shedding; the Tacoma Narrows Bridge Disaster of 1940
26 Consider the shedding of vortices in the wake of a cylinder of diameter d. Assume the physical quantities responsible for the shedding are: d, V, μ, ρ, and ω. V is the wind velocity, μ and ρ are the viscosity and density of air and ω is the vortex shedding frequency. The five physical quantities contain among them the 3 dimensions, M, L, T. The number of independent dimensionless groups is therefore 53=2. Two independent groups are ρvd/μ and ωd/v, the Reynolds and Strouhal numbers, respectively. The dependence of the Strouhal number on the Reynolds number would be established by choosing parameters in any convenient manner such that each number is varied over a wide range. An approach, suited for measurements in a given fluid with fixed values for ρ and μ, would be to vary both the Reynolds and Strouhal numbers by varying V and d while observing changes in ω.
27 Capillary Waves
28 Spherical Blast Wave
29 Poiseuille s Law
30 Hull Speed
31
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 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 (20022006) Fluent Inc. (2002) 1 Overview Drag. The boundarylayer
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 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 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 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 informationFluids in Motion Supplement I
Fluids in Motion Supplement I Cutnell & Johnson describe a number of different types of flow: Compressible vs incompressible (most liquids are very close to incompressible) Steady vs Unsteady Viscous or
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 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 informationChapter 7. External Forced Convection. Multi Energy Transport (MET) Lab. 1 School of Mechanical Engineering
Chapter 7 Eternal Forced Convection 1 School of Mechanical Engineering Contents Chapter 7 71 rag and Heat Transfer in Eternal Flow 3 page 72 Parallel Flow Over Flat Plates 5 page 73 Flow Across Cylinders
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 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 informationFLUID 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 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 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 informationME19b. SOLUTIONS. Feb. 11, 2010. Due Feb. 18
ME19b. SOLTIONS. Feb. 11, 21. Due Feb. 18 PROBLEM B14 Consider the long thin racing boats used in competitive rowing events. Assume that the major component of resistance to motion is the skin friction
More informationVISCOSITY OF A LIQUID. To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied.
VISCOSITY OF A LIQUID August 19, 004 OBJECTIVE: EQUIPMENT: To determine the viscosity of a lubricating oil. Time permitting, the temperature variation of viscosity can also be studied. Viscosity apparatus
More informationFluid 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 informationA fundamental study of the flow past a circular cylinder using Abaqus/CFD
A fundamental study of the flow past a circular cylinder using Abaqus/CFD Masami Sato, and Takaya Kobayashi Mechanical Design & Analysis Corporation Abstract: The latest release of Abaqus version 6.10
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 informationIntroduction to Fluid Mechanics. Chapter 9 External Incompressible Viscous Flow. Pritchard
Introduction to Fluid Mechanics Chapter 9 External Incompressible Viscous Flow Main Topics The BoundaryLayer Concept BoundaryLayer Thicknesses Laminar FlatPlate Boundary Layer: Exact Solution Momentum
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 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 informationLecture 8  Turbulence. Applied Computational Fluid Dynamics
Lecture 8  Turbulence Applied Computational Fluid Dynamics Instructor: André Bakker http://www.bakker.org André Bakker (20022006) Fluent Inc. (2002) 1 Turbulence What is turbulence? Effect of turbulence
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 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 information11 NavierStokes equations and turbulence
11 NavierStokes equations and turbulence So far, we have considered ideal gas dynamics governed by the Euler equations, where internal friction in the gas is assumed to be absent. Real fluids have internal
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 informationDimensional Analysis, hydraulic similitude and model investigation. Dr. Sanghamitra Kundu
Dimensional Analysis, hydraulic similitude and model investigation Dr. Sanghamitra Kundu Introduction Although many practical engineering problems involving fluid mechanics can be solved by using the equations
More informationHEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi
HEAT TRANSFER ANALYSIS IN A 3D SQUARE CHANNEL LAMINAR FLOW WITH USING BAFFLES 1 Vikram Bishnoi 2 Rajesh Dudi 1 Scholar and 2 Assistant Professor,Department of Mechanical Engineering, OITM, Hisar (Haryana)
More informationViscous Flow in Pipes
Viscous Flow in Pipes Excerpted from supplemental materials of Prof. KuangAn Chang, Dept. of Civil Engin., Texas A&M Univ., for his spring 2008 course CVEN 311, Fluid Dynamics. (See a related handout
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 informationAnalysis of Vortex Shedding Mechanism through PIV Measurement of Flow past a Rotating Circular Cylinder
Analysis of Vortex Shedding Mechanism through PIV Measurement of Flow past a Rotating Circular Cylinder Linh Duong *, Siao Chung Luo, Yong Tian Chew Department of Mechanical Engineering, National University
More informationChapter 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 informationThe ratio of inertial to viscous forces is commonly used to scale fluid flow, and is called the Reynolds number, given as:
12.001 LAB 3C: STOKES FLOW DUE: WEDNESDAY, MARCH 9 Lab Overview and Background The viscosity of a fluid describes its resistance to deformation. Water has a very low viscosity; the force of gravity causes
More 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 informationTYPES OF FLUID FLOW. Laminar or streamline flow. Turbulent flow
FLUID DYNAMICS We will deal with Intrinsic properties of fluids Fluids behavior under various conditions Methods by which we can manipulate and utilize the fluids to produce desired results TYPES OF FLUID
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 informationENSC 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 informationAerodynamics of Rotating Discs
Proceedings of ICFD 10: Tenth International Congress of FluidofDynamics Proceedings ICFD 10: December 1619, 2010, Stella Di MareTenth Sea Club Hotel, Ain Soukhna, Egypt International Congress of Red FluidSea,
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 (20022006) Fluent Inc. (2002) 1 Outline Overview. Inlet and outlet boundaries.
More informationCE 3500 Fluid Mechanics / Fall 2014 / City College of New York
1 Drag Coefficient The force ( F ) of the wind blowing against a building is given by F=C D ρu 2 A/2, where U is the wind speed, ρ is density of the air, A the crosssectional area of the building, and
More information6.055J/2.038J (Spring 2009)
6.055J/2.038J (Spring 2009) Solution set 05 Do the following warmups and problems. Due in class on Wednesday, 13 May 2009. Open universe: Collaboration, notes, and other sources of information are encouraged.
More informationFluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture  22 Laminar and Turbulent flows
Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture  22 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. So
More informationModule 2: Review of Fluid Mechanics Basic Principles for Water Resources Engineering. Basic Definitions. Basic Definitions.
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 informationCFD and EXPERIMENTAL ANALYSIS of VORTEX SHEDDING BEHIND DSHAPED CYLINDER
CFD and EXPERIMENTAL ANALYSIS of VORTEX SHEDDING BEHIND DSHAPED CYLINDER Chandrakant D. Mhalungekar Department of Mechanical Engineering, MIT College of Engineering, Pune 411038, Pune University, India.
More informationIntroduction to Microfluidics. Date: 2013/04/26. Dr. YiChung Tung. Outline
Introduction to Microfluidics Date: 2013/04/26 Dr. YiChung Tung Outline Introduction to Microfluidics Basic Fluid Mechanics Concepts Equivalent Fluidic Circuit Model Conclusion What is Microfluidics Microfluidics
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 informationProblem 1. 12ft. Find: Velocity of truck for both drag situations. Equations: Drag F Weight. For force balance analysis: Lift and Drag: Solution:
Problem 1 Given: Truck traveling down 7% grade Width 10ft m 5 tons 50,000 lb Rolling resistance on concrete 1.% weight C 0.96 without air deflector C 0.70 with air deflector V 100 7 1ft Find: Velocity
More informationE 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 informationChapter 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 informationCE 204 FLUID MECHANICS
CE 204 FLUID MECHANICS Onur AKAY Assistant Professor Okan University Department of Civil Engineering Akfırat Campus 34959 TuzlaIstanbul/TURKEY Phone: +902166771630 ext.1974 Fax: +902166771486 Email:
More informationDepartment of Mechanical Engineering
Department of Mechanical Engineering AMEE 401/ AUTO 400 Aerodynamics Instructor: Marios M. Fyrillas Email: m.fyrillas@frederick.ac.cy QUESTION 1 HOMEWORK ASSIGNMENT #1 SOLUTION a. Explain the meaning of
More informationChapter 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 informationViscous flow in pipe
Viscous flow in pipe Henryk Kudela Contents 1 Laminar or turbulent flow 1 2 Balance of Momentum  NavierStokes Equation 2 3 Laminar flow in pipe 2 3.1 Friction factor for laminar flow...........................
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. InkJet Technology 9. Liquid Handling 10.Microarrays 11.Microreactors
More informationSteven Burian Civil & Environmental Engineering March 27, 2015
Fundamentals of Engineering (FE) Exam Mechanics Steven Burian Civil & Environmental Engineering March 27, 2015 s and FE Morning ( Mechanics) A. Flow measurement 7% of FE Morning B. properties Session C.
More informationAA200 Chapter 9  Viscous flow along a wall
AA200 Chapter 9  Viscous flow along a wall 9.1 The noslip 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 informationBackwater Rise and Drag Characteristics of Bridge Piers under Subcritical
European Water 36: 735, 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 informationAids needed for demonstrations: viscous fluid (water), tubes (pipes), injections, paper, stopwatches, vessels,, weights
1 Viscous and turbulent flow Level: high school (1617 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 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 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 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 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 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 informationI. INTRODUCTION: Phenomenology. N / m. N / m (2) kg G. Let s consider a shear force experiment on a solid cube. (Fig. 1)
I. INTRODUCTION: Phenomenology Let s consider a shear force experiment on a solid cube. (Fig. 1) We can easily verify that for the solid not to move or rotate, all forces acting on the cube must be of
More 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 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 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 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 informationLecture 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 informationLecture 24  Surface tension, viscous flow, thermodynamics
Lecture 24  Surface tension, viscous flow, thermodynamics Surface tension, surface energy The atoms at the surface of a solid or liquid are not happy. Their bonding is less ideal than the bonding of atoms
More informationChapter 5. Microfluidic Dynamics
Chapter 5 Thermofluid Engineering and Microsystems Microfluidic Dynamics NavierStokes equation 1. The momentum equation 2. Interpretation of the NSequation 3. Characteristics of flows in microfluidics
More informationBoundary Conditions in Fluid Mechanics
Boundary Conditions in Fluid Mechanics R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkson University The governing equations for the velocity and pressure fields are partial
More informationExperiment: Viscosity Measurement B
Experiment: Viscosity Measurement B The Falling Ball Viscometer Purpose The purpose of this experiment is to measure the viscosity of an unknown polydimethylsiloxiane (PDMS) solution with a falling ball
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 informationPhysics for the Life Sciences: Fall 2008 Lecture #25
Physics for the Life Sciences: Fall 2008 Lecture #25 Real fluids: As we have mentioned several times, real fluids are more complex than the ideal fluids described by the continuity equation and Bernoulli
More informationLecture 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 (00006) Fluent Inc. (00) 1 Classification: fluid flow vs. granular flow
More informationFluent 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 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 informationPressure Measurements
Pressure Measurements Measurable pressures Absolute pressure Gage pressure Differential pressure Atmospheric/barometric pressure Static pressure Total Pressure Pressure Measurement Mechanical Pressure
More informationComparison of CFD models for multiphase flow evolution in bridge scour processes
Comparison of CFD models for multiphase flow evolution in bridge scour processes A. BayónBarrachina, D. Valero, F.J. Vallès Morán, P. A. LópezJiménez Dept. of Hydraulic and Environmental Engineering
More informationCHAPTER 4 FLOW IN CHANNELS
CHAPTER 4 FLOW IN CHANNELS INTRODUCTION 1 Flows in conduits or channels are of interest in science, engineering, and everyday life. Flows in closed conduits or channels, like pipes or air ducts, are entirely
More informationFundamentals of Transport Processes Prof. Kumaran Department of Chemical Engineering Indian Institute of Science, Bangalore
Fundamentals of Transport Processes Prof. Kumaran Department of Chemical Engineering Indian Institute of Science, Bangalore Module No. # 02 Lecture No. # 06 Mechanisms of diffusion1 Welcome to the sixth
More informationFLUID MECHANICS IM0235 DIFFERENTIAL EQUATIONS  CB0235 2014_1
COURSE CODE INTENSITY PREREQUISITE COREQUISITE 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 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 informationApplied 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 informationAir Resistance: Distinguishing Between Laminar and Turbulent Flow 0.1 Introduction
Air Resistance: Distinguishing Between Laminar and Turbulent Flow 0.1 Introduction You have probably heard that objects fall (really, accelerate) at the same rate, independent of their mass. Galileo demonstrated
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 informationJournal bearings/sliding bearings
Journal bearings/sliding bearings Operating conditions: Advantages:  Vibration damping, impact damping, noise damping  not sensitive for vibrations, low operating noise level  dust tight (if lubricated
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 crosssectional
More informationViscosity. Desmond Schipper Andrew R. Barron. 1 Introduction
OpenStaxCNX module: m50215 1 Viscosity Desmond Schipper Andrew R. Barron This work is produced by OpenStaxCNX and licensed under the Creative Commons Attribution License 4.0 Abstract This module discusses
More informationNUMERICAL STUDY OF FLOW AND TURBULENCE THROUGH SUBMERGED VEGETATION
NUMERICAL STUDY OF FLOW AND TURBULENCE THROUGH SUBMERGED VEGETATION HYUNG SUK KIM (1), MOONHYEONG PARK (2), MOHAMED NABI (3) & ICHIRO KIMURA (4) (1) Korea Institute of Civil Engineering and Building Technology,
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 informationCFD SUPPORTED EXAMINATION OF BUOY DESIGN FOR WAVE ENERGY CONVERSION
CFD SUPPORTED EXAMINATION OF BUOY DESIGN FOR WAVE ENERGY CONVERSION Nadir Yilmaz, Geoffrey E. Trapp, Scott M. Gagan, Timothy R. Emmerich Department of Mechanical Engineering, New Mexico Institute of Mining
More informationModule 2 : Convection. Lecture 20a : Illustrative examples
Module 2 : Convection Lecture 20a : Illustrative examples Objectives In this class: Examples will be taken where the concepts discussed for heat transfer for tubular geometries in earlier classes will
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 Onedimensional Gas Dynamics (Contd.) We
More informationPhysics of the Atmosphere I
Physics of the Atmosphere I WS 2008/09 Ulrich Platt Institut f. Umweltphysik R. 424 Ulrich.Platt@iup.uniheidelberg.de heidelberg.de Last week The conservation of mass implies the continuity equation:
More informationTurbulence: The manifestation of eddies and their role in conservation laws
Turbulence: The manifestation of eddies and their role in conservation laws George E. Hrabovsky MAST Presentation Given to the Chaos and Complex Systems Seminar University of Wisconsin  Madison 26 February,
More informationHeat 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