150A Review Session 2/13/2014 Fluid Statics. Pressure acts in all directions, normal to the surrounding surfaces


 Nathan Murphy
 2 years ago
 Views:
Transcription
1 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 Patm everywhere outside Whenever you are looking for the total pressure, use absolute pressure o Force balances Hydrostatic head = pressure from a static column of fluid From a zdirection force balance on a differential cube: o Differential form: use when a variable is changing continuously Compressible (changing density) fluid, i.e. altitude Force in x or y direction (changing height), i.e. column support o Integrated form: use when all variables are constant Total pressure in z direction, i.e. manometer Buoyancy o Recommended to NOT use a buoyant force Buoyant force is simply a pressure difference o Do a force balance including all the different pressures & weights Downward: gravity (W=mg) and atmospheric pressure (Patm*A) Upward: pressure from fluid below submerged container (ρgδz*a)
2 Manometers o Pressures are equal at the two points that are at the same height and connected by the same fluid o Work up or down from that equality point, including all fluids (& Patm) Compressible fluids o At constant elevation, from ideal gas law, o 3 ways to account for changing elevation using the ideal gas law Isothermal ( ) Linear temperature gradient ( ) Isentropic ( ) Macroscopic Momentum Balances [Accumulation = In Out + Generation] for momentum of fluid o Flow of momentum in (acceleration): o Flow of momentum out (acceleration): o Generation of momentum due to forces acting on fluid o No momentum accumulation at steady state, so This is the same as Newton s second law Sum of the forces on the fluid accelerate fluid o Force due to pressure gradients (careful w/ sign needed for the geometry!) o Friction forces by the wall on the fluid, opposite direction of flow
3 o Body forces due to gravity By Newton s 3 rd law, there is an equal and opposite force of the fluid on the wall Therefore, the force of the fluid on the wall is o Signs: fluid pushes forward as it enters, pushes behind it as it leaves Divide into xdirection and ydirection o Calculate magnitude & direction If in laminar flow, =4/3 (turbulent flow ~1) Derivation of HaganPoiseuille flow below starts from here Macroscopic Mechanical Energy Balances Bernoulli equation: The units of all terms are: Include α when have laminar flow (α=2 for laminar, α~1 for turbulent) Approach for solving Bernoulli problems 1. Make a drawing 2. Label points A ( inlet ) and B ( outlet ) Pick points where you know the properties 3. Write entire Bernoulli equation 4. Eliminate terms that are zero or very small compared to other terms 5. Determine absolute sign of each term Energy you start with needs to balance the energy you convert to 6. Plug in values, check units, solve for unknown
4 Friction Losses Through Conduits Viscous dissipation due to flow through a horizontal, straight, constant D pipe: o By energy balance, equal to the pressure drop along the length: o Plus momentum balance gives in terms of shear stress (τw): o Definition of the Fanning friction factor: o Combining gives in terms of Fanning friction factor: o Expressions for valid for laminar & turbulent flow, Newtonian & non fluids o For noncircular conduits, use same correlations replacing D with Reynold s number defines ratio of inertial forces to viscous forces: Laminar Newtonian flow o Velocity profile can be calculated exactly (HP flow): o Average velocity is: o Volumetric flow rate: o Friction factor is known exactly: Turbulent Newtonian flow o Transition to turbulent flow for Re > 2100 o Friction factor correlated empirically where k is roughness Note that k has dimensions, make sure they match the D o Use the Moody Chart or Churchill Correlations to find o Often have to iterate to solve these problems
5 NonNewtonian Fluid Same momentum and energy balances (Bernoulli), just new Do not obey Newton s law of viscosity where viscosity μ is constant Power law fluids o Nonlinear relation between shear stress and shear rate o Pseudoplastic (shearthinning, most common) i.e. paint, polymer solutions o Dilatant (shearthickening) i.e. cornstarch + water o Effective viscosity must be determined experimentally o New Reynold s number o New critical Reynold s number o Laminar: o Turbulent: use power law chart Bingham plastic o Acts as a solid for, flows as Newtonian fluid for o i.e. ketchup, mayo o Parameters must be determined experimentally o Two important dimensionless parameters: & o Laminar (nonlinear equation): o Turbulent: use Bingham plastic chart
6 Conversions Mass: Distance: Volume: Pressure: Temperature: Viscosity: Force: Power: Other useful information From F=ma,
7 HagenPoiseuille Flow in a Pipe Derivation Using the NavierStokes Equations As we saw in class and in the macroscopic momentum balance abvoe, Newton s 2 nd law and a momentum balance give: Note: Think about the signs every time based on how you define what s going in and out of your system! This is analogous to looking at a microscopic scale, where the lefthand side is a density multiplied by acceleration. This is called the Cauchy momentum equation. In class we saw Newton s law of viscosity in 2D, Expanding this to a differential form in all directions and using it in the previous equation, we get the NavierStokes equations for constant and : Now to solve the HagenPoiseuille problem for flow in a pipe, we can make a few simplifications. In an horizontal, constant diameter pipe, there will be no acceleration terms and no gravity terms, so that: Expanding this in Cartesian coordinates for the zcomponent of the velocity: For our pipe problem though, Cylindrical coordinates will be more convenient: Don t get overwhelmed with these expressions, the problems we ll do simplify and drop many of these terms. Also, the complete NavierStokes equations in Cartesian, Cylindrical, and Spherical coordinates are given in Appendix E of your book.
8 Figure: Flow in a straight, horizontal, constant diameter (D) pipe. The velocity profile is as a function of the radius (r) and the overall volumetric flow rate is Q. Pressures are denoted p o and p L at the start z=0 and end z=l of the pipe, respectively. For flow in a pipe, as shown in the diagram, we have only a zcomponent of velocity along the length of the pipe. This is only a function of where the particle is in regards to the radius ( ) of the pipe. It is not a function of the angle ( ) due to symmetry or the location along the length of the pipe (z) as we have said there is no acceleration and the flow is fully developed. Therefore, we have only and we can simplify the above equation: With a constant pressure gradient along the length (L) of the pipe, we can now integrate this equation twice to get the velocity profile,.
9 So now we have an expression for, which as expected from our sketch is parabolic, and we just need to use the boundary conditions to solve for the constants. Boundary conditions: at (1) noslip condition at the surface of the pipe finite at or at r= 0 ( 2) here we know that the velocity is at its maximum in the middle of the pipe Using boundary condition (2) in either form, we can immediately see that and., because Now using boundary condition (1), Putting this all together, we get the velocity profile we saw in class: From this we can easily derive the shear stress of the fluid on the wall ( ) at the pipe surface, as well as the volumetric flow rate (Q) and the average velocity ( ). Let s start with the volumetric flow rate, by integrating over the crosssectional area of the pipe:
10 Where we ve defined pressure drop as in the expression above. Dividing by the crosssectional area over which we determined the volumetric flow rate, we get the average velocity. Now we can also determine the shear stress ( surface (r=r). This is in the direction of the fluid s motion. ) of the fluid on the wall at the pipe Or equivalently, the shear stress exerted by the wall on the fluid ( surface. This is opposing the fluid s motion. ), again at the
Shell 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 informationFE Exam Fluids Review October 23, Important Concepts
FE Exam Fluids Review October 3, 013 mportant Concepts Density, specific volume, specific weight, specific gravity (Water 1000 kg/m^3, Air 1. kg/m^3) Meaning & Symbols? Stress, Pressure, Viscosity; Meaning
More informationFLUID MECHANICS PROF. DR. METİN GÜNER COMPILER
FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES 5.1.3. Pressure and Shear Stress
More informationACCOUNTING FOR FRICTION IN THE BERNOULLI EQUATION FOR FLOW THROUGH PIPES
ACCOUNTING FOR FRICTION IN THE BERNOULLI EQUATION FOR FLOW THROUGH PIPES Some background information first: We have seen that a major limitation of the Bernoulli equation is that it does not account for
More informations and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum equations E. Pipe and other internal flow 7% of FE Morning Session I
Fundamentals of Engineering (FE) Exam General Section Steven Burian Civil & Environmental Engineering October 26, 2010 s and FE X. A. Flow measurement B. properties C. statics D. impulse, and momentum
More informationLesson 6 Review of fundamentals: Fluid flow
Lesson 6 Review of fundamentals: Fluid flow The specific objective of this lesson is to conduct a brief review of the fundamentals of fluid flow and present: A general equation for conservation of mass
More informationDifferential relations for fluid flow
Differential relations for fluid flow In this approach, we apply basic conservation laws to an infinitesimally small control volume. The differential approach provides point by point details of a flow
More informationPage 1. Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.)
Page 1 Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Vlachos Prof. Ardekani
More informationUNIT II Real fluids. FMM / KRG / MECH / NPRCET Page 78. Laminar and turbulent flow
UNIT II Real fluids The flow of real fluids exhibits viscous effect that is they tend to "stick" to solid surfaces and have stresses within their body. You might remember from earlier in the course Newtons
More informationBasic Fluid Mechanics
Basic Fluid Mechanics Chapter 6A: Internal Incompressible Viscous Flow 4/16/2018 C6A: Internal Incompressible Viscous Flow 1 6.1 Introduction For the present chapter we will limit our study to incompressible
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 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 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 informationFluid Mechanics. du dy
FLUID MECHANICS Technical English  I 1 th week Fluid Mechanics FLUID STATICS FLUID DYNAMICS Fluid Statics or Hydrostatics is the study of fluids at rest. The main equation required for this is Newton's
More informationUNIT II CONVECTION HEAT TRANSFER
UNIT II CONVECTION HEAT TRANSFER Convection is the mode of heat transfer between a surface and a fluid moving over it. The energy transfer in convection is predominately due to the bulk motion of the fluid
More informationSignature: (Note that unsigned exams will be given a score of zero.)
Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Dabiri Prof. Wassgren Prof.
More informationFE Fluids Review March 23, 2012 Steve Burian (Civil & Environmental Engineering)
Topic: Fluid Properties 1. If 6 m 3 of oil weighs 47 kn, calculate its specific weight, density, and specific gravity. 2. 10.0 L of an incompressible liquid exert a force of 20 N at the earth s surface.
More informationChemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017
Chemical and Biomolecular Engineering 150A Transport Processes Spring Semester 2017 Objective: Text: To introduce the basic concepts of fluid mechanics and heat transfer necessary for solution of engineering
More informationMicrofluidics 1 Basics, Laminar flow, shear and flow profiles
MT0.6081 Microfluidics and BioMEMS Microfluidics 1 Basics, Laminar flow, shear and flow profiles 11.1.2017 Ville Jokinen Outline of the next 3 weeks: Today: Microfluidics 1: Laminar flow, flow profiles,
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 informationModelling of dispersed, multicomponent, multiphase flows in resource industries. Section 3: Examples of analyses conducted for Newtonian fluids
Modelling of dispersed, multicomponent, multiphase flows in resource industries Section 3: Examples of analyses conducted for Newtonian fluids Globex Julmester 017 Lecture # 04 July 017 Agenda Lecture
More information11.1 Mass Density. Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an
Chapter 11 Fluids 11.1 Mass Density Fluids are materials that can flow, and they include both gases and liquids. The mass density of a liquid or gas is an important factor that determines its behavior
More informationProf. Scalo Prof. Vlachos Prof. Ardekani Prof. Dabiri 08:30 09:20 A.M 10:30 11:20 A.M. 1:30 2:20 P.M. 3:30 4:20 P.M.
Page 1 Neatly print your name: Signature: (Note that unsigned exams will be given a score of zero.) Circle your lecture section (1 point if not circled, or circled incorrectly): Prof. Scalo Prof. Vlachos
More informationReference : McCabe, W.L. Smith J.C. & Harriett P., Unit Operations of Chemical
1 Course materials (References) Textbook: Welty J. R., Wicks, C. E., Wilson, R. E., & Rorrer, G., Fundamentals of Momentum Heat, and Mass Transfer, 4th Edition, John Wiley & Sons.2000 Reference : McCabe,
More informationFluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay. Lecture  17 Laminar and Turbulent flows
Fluid Mechanics Prof. T.I. Eldho Department of Civil Engineering Indian Institute of Technology, Bombay Lecture  17 Laminar and Turbulent flows Welcome back to the video course on fluid mechanics. In
More informationInterphase Transport in Isothermal Systems
Transport Phenomena Interphase Transport in Isothermal Systems 1 Interphase Transport in Isothermal Systems 1. Definition of friction factors 2. Friction factors for flow in tubes 3. Friction factors for
More informationFriction Factors and Drag Coefficients
Levicky 1 Friction Factors and Drag Coefficients Several equations that we have seen have included terms to represent dissipation of energy due to the viscous nature of fluid flow. For example, in the
More informationWhat we know about Fluid Mechanics. What we know about Fluid Mechanics
What we know about Fluid Mechanics 1. Survey says. 3. Image from: www.axs.com 4. 5. 6. 1 What we know about Fluid Mechanics 1. MEB (single input, single output, steady, incompressible, no rxn, no phase
More informationFluid Mechanics Testbank By David Admiraal
Fluid Mechanics Testbank By David Admiraal This testbank was created for an introductory fluid mechanics class. The primary intentions of the testbank are to help students improve their performance on
More informationME 309 Fluid Mechanics Fall 2010 Exam 2 1A. 1B.
Fall 010 Exam 1A. 1B. Fall 010 Exam 1C. Water is flowing through a 180º bend. The inner and outer radii of the bend are 0.75 and 1.5 m, respectively. The velocity profile is approximated as C/r where C
More informationChapter 1: Basic Concepts
What is a fluid? A fluid is a substance in the gaseous or liquid form Distinction between solid and fluid? Solid: can resist an applied shear by deforming. Stress is proportional to strain Fluid: deforms
More informationDetailed Outline, M E 320 Fluid Flow, Spring Semester 2015
Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015 I. Introduction (Chapters 1 and 2) A. What is Fluid Mechanics? 1. What is a fluid? 2. What is mechanics? B. Classification of Fluid Flows 1. Viscous
More informationGATE PSU. Chemical Engineering. Fluid Mechanics. For. The Gate Coach 28, Jia Sarai, Near IIT Hauzkhas, New Delhi 16 (+91) ,
For GATE PSU Chemical Engineering Fluid Mechanics GATE Syllabus Fluid statics, Newtonian and nonnewtonian fluids, Bernoulli equation, Macroscopic friction factors, energy balance, dimensional analysis,
More informationObjectives. Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation
Objectives Conservation of mass principle: Mass Equation The Bernoulli equation Conservation of energy principle: Energy equation Conservation of Mass Conservation of Mass Mass, like energy, is a conserved
More informationApproximate physical properties of selected fluids All properties are given at pressure kn/m 2 and temperature 15 C.
Appendix FLUID MECHANICS Approximate physical properties of selected fluids All properties are given at pressure 101. kn/m and temperature 15 C. Liquids Density (kg/m ) Dynamic viscosity (N s/m ) Surface
More informationWilliam В. Brower, Jr. A PRIMER IN FLUID MECHANICS. Dynamics of Flows in One Space Dimension. CRC Press Boca Raton London New York Washington, D.C.
William В. Brower, Jr. A PRIMER IN FLUID MECHANICS Dynamics of Flows in One Space Dimension CRC Press Boca Raton London New York Washington, D.C. Table of Contents Chapter 1 Fluid Properties Kinetic Theory
More informationOE4625 Dredge Pumps and Slurry Transport. Vaclav Matousek October 13, 2004
OE465 Vaclav Matousek October 13, 004 1 Dredge Vermelding Pumps onderdeel and Slurry organisatie Transport OE465 Vaclav Matousek October 13, 004 Dredge Vermelding Pumps onderdeel and Slurry organisatie
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 informationINSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad AERONAUTICAL ENGINEERING QUESTION BANK : AERONAUTICAL ENGINEERING.
Course Name Course Code Class Branch INSTITUTE OF AERONAUTICAL ENGINEERING Dundigal, Hyderabad  00 0 AERONAUTICAL ENGINEERING : Mechanics of Fluids : A00 : III B. Tech Year : 0 0 Course Coordinator
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 information1 FLUIDS AND THEIR PROPERTIES
FLUID MECHANICS CONTENTS CHAPTER DESCRIPTION PAGE NO 1 FLUIDS AND THEIR PROPERTIES PART A NOTES 1.1 Introduction 1.2 Fluids 1.3 Newton s Law of Viscosity 1.4 The Continuum Concept of a Fluid 1.5 Types
More informationEngineering Fluid Mechanics
Engineering Fluid Mechanics Eighth Edition Clayton T. Crowe WASHINGTON STATE UNIVERSITY, PULLMAN Donald F. Elger UNIVERSITY OF IDAHO, MOSCOW John A. Roberson WASHINGTON STATE UNIVERSITY, PULLMAN WILEY
More informationForces and Motion in One Dimension
Nicholas J. Giordano www.cengage.com/physics/giordano Forces and Motion in One Dimension Applications of Newton s Laws We will learn how Newton s Laws apply in various situations We will begin with motion
More informationME 305 Fluid Mechanics I. Part 8 Viscous Flow in Pipes and Ducts. Flow in Pipes and Ducts. Flow in Pipes and Ducts (cont d)
ME 305 Fluid Mechanics I Flow in Pipes and Ducts Flow in closed conduits (circular pipes and noncircular ducts) are very common. Part 8 Viscous Flow in Pipes and Ducts These presentations are prepared
More informationPrinciples of Convection
Principles of Convection Point Conduction & convection are similar both require the presence of a material medium. But convection requires the presence of fluid motion. Heat transfer through the: Solid
More informationChapter 6. Losses due to Fluid Friction
Chapter 6 Losses due to Fluid Friction 1 Objectives To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate. To correlate this in terms of the
More informationBernoulli and Pipe Flow
Civil Engineering Hydraulics Mechanics of Fluids Head Loss Calculations Bernoulli and The Bernoulli equation that we worked with was a bit simplistic in the way it looked at a fluid system All real systems
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 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 informationB.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I
Department of Chemical Engineering B.E/B.Tech/M.E/M.Tech : Chemical Engineering Regulation: 2016 PG Specialisation : NA Sub. Code / Sub. Name : CH16304 FLUID MECHANICS Unit : I LP: CH 16304 Rev. No: 00
More informationV/ t = 0 p/ t = 0 ρ/ t = 0. V/ s = 0 p/ s = 0 ρ/ s = 0
UNIT III FLOW THROUGH PIPES 1. List the types of fluid flow. Steady and unsteady flow Uniform and nonuniform flow Laminar and Turbulent flow Compressible and incompressible flow Rotational and irrotational
More informationPiping Systems and Flow Analysis (Chapter 3)
Piping Systems and Flow Analysis (Chapter 3) 2 Learning Outcomes (Chapter 3) Losses in Piping Systems Major losses Minor losses Pipe Networks Pipes in series Pipes in parallel Manifolds and Distribution
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 informationLinear Transport Relations (LTR)
Linear Transport Relations (LTR) Much of Transport Phenomena deals with the exchange of momentum, mass, or heat between two (or many) objects. Often, the most mathematically simple way to consider how
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 informationShell/Integral Balances (SIB)
Shell/Integral Balances (SIB) Shell/Integral Balances Shell or integral (macroscopic) balances are often relatively simple to solve, both conceptually and mechanically, as only limited data is necessary.
More informationMULTIPLECHOICE PROBLEMS:(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)
MULTIPLECHOICE PROLEMS:(Two marks per answer) (Circle the Letter eside the Most Correct Answer in the Questions elow.) 1. The absolute viscosity µ of a fluid is primarily a function of: a. Density. b.
More informationUNIT I FLUID PROPERTIES AND STATICS
SIDDHARTH GROUP OF INSTITUTIONS :: PUTTUR Siddharth Nagar, Narayanavanam Road 517583 QUESTION BANK (DESCRIPTIVE) Subject with Code : Fluid Mechanics (16CE106) Year & Sem: IIB.Tech & ISem Course & Branch:
More informationME 305 Fluid Mechanics I. Chapter 8 Viscous Flow in Pipes and Ducts
ME 305 Fluid Mechanics I Chapter 8 Viscous Flow in Pipes and Ducts These presentations are prepared by Dr. Cüneyt Sert Department of Mechanical Engineering Middle East Technical University Ankara, Turkey
More information2 NavierStokes Equations
1 Integral analysis 1. Water enters a pipe bend horizontally with a uniform velocity, u 1 = 5 m/s. The pipe is bended at 90 so that the water leaves it vertically downwards. The input diameter d 1 = 0.1
More informationch01.qxd 8/4/04 2:33 PM Page 1 Part 1 Basic Principles of Open Channel Flows
ch01.qxd 8/4/04 2:33 PM Page 1 Part 1 Basic Principles of Open Channel Flows ch01.qxd 8/4/04 2:33 PM Page 3 Introduction 1 Summary The introduction chapter reviews briefly the basic fluid properties
More informationHOW TO GET A GOOD GRADE ON THE MME 2273B FLUID MECHANICS 1 EXAM. Common mistakes made on the final exam and how to avoid them
HOW TO GET A GOOD GRADE ON THE MME 2273B FLUID MECHANICS 1 EXAM Common mistakes made on the final exam and how to avoid them HOW TO GET A GOOD GRADE ON THE MME 2273B EXAM Introduction You now have a lot
More information3.8 The First Law of Thermodynamics and the Energy Equation
CEE 3310 Control Volume Analysis, Sep 30, 2011 65 Review Conservation of angular momentum 1D form ( r F )ext = [ˆ ] ( r v)d + ( r v) out ṁ out ( r v) in ṁ in t CV 3.8 The First Law of Thermodynamics and
More informationIntroduction to Aerodynamics. Dr. Guven Aerospace Engineer (P.hD)
Introduction to Aerodynamics Dr. Guven Aerospace Engineer (P.hD) Aerodynamic Forces All aerodynamic forces are generated wither through pressure distribution or a shear stress distribution on a body. The
More informationFluid Dynamics Exercises and questions for the course
Fluid Dynamics Exercises and questions for the course January 15, 2014 A two dimensional flow field characterised by the following velocity components in polar coordinates is called a free vortex: u r
More informationChapter 10 Flow in Conduits
Chapter 10 Flow in Conduits 10.1 Classifying Flow Laminar Flow and Turbulent Flow Laminar flow Unpredictable Turbulent flow Near entrance: undeveloped developing flow In developing flow, the wall shear
More informationChapter 9: Differential Analysis
91 Introduction 92 Conservation of Mass 93 The Stream Function 94 Conservation of Linear Momentum 95 Navier Stokes Equation 96 Differential Analysis Problems Recall 91 Introduction (1) Chap 5: Control
More informationChapter 4 Dynamics: Newton s Laws of Motion
Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal
More informationFluid Mechanics Abdusselam Altunkaynak
Fluid Mechanics Abdusselam Altunkaynak 1. Unit systems 1.1 Introduction Natural events are independent on units. The unit to be used in a certain variable is related to the advantage that we get from it.
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 informationChapter 9: Differential Analysis of Fluid Flow
of Fluid Flow Objectives 1. Understand how the differential equations of mass and momentum conservation are derived. 2. Calculate the stream function and pressure field, and plot streamlines for a known
More informationThe Reynolds experiment
Chapter 13 The Reynolds experiment 13.1 Laminar and turbulent flows Let us consider a horizontal pipe of circular section of infinite extension subject to a constant pressure gradient (see section [10.4]).
More informationLECTURE 1 THE CONTENTS OF THIS LECTURE ARE AS FOLLOWS:
LECTURE 1 THE CONTENTS OF THIS LECTURE ARE AS FOLLOWS: 1.0 INTRODUCTION TO FLUID AND BASIC EQUATIONS 2.0 REYNOLDS NUMBER AND CRITICAL VELOCITY 3.0 APPROACH TOWARDS REYNOLDS NUMBER REFERENCES Page 1 of
More informationCOURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour. Basic Equations in fluid Dynamics
COURSE NUMBER: ME 321 Fluid Mechanics I 3 credit hour Basic Equations in fluid Dynamics Course teacher Dr. M. Mahbubur Razzaque Professor Department of Mechanical Engineering BUET 1 Description of Fluid
More informationMECHANICAL PROPERTIES OF FLUIDS:
Important Definitions: MECHANICAL PROPERTIES OF FLUIDS: Fluid: A substance that can flow is called Fluid Both liquids and gases are fluids Pressure: The normal force acting per unit area of a surface is
More informationMicroscopic Momentum Balance Equation (NavierStokes)
CM3110 Transport I Part I: Fluid Mechanics Microscopic Momentum Balance Equation (NavierStokes) Professor Faith Morrison Department of Chemical Engineering Michigan Technological University 1 Microscopic
More informationFLOW IN CONDUITS. Shear stress distribution across a pipe section. Chapter 10
Chapter 10 Shear stress distribution across a pipe section FLOW IN CONDUITS For steady, uniform flow, the momentum balance in s for the fluid cylinder yields Fluid Mechanics, Spring Term 2010 Velocity
More information2. FLUIDFLOW EQUATIONS SPRING 2019
2. FLUIDFLOW EQUATIONS SPRING 2019 2.1 Introduction 2.2 Conservative differential equations 2.3 Nonconservative differential equations 2.4 Nondimensionalisation Summary Examples 2.1 Introduction Fluid
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 informationFLOW MEASUREMENT IN PIPES EXPERIMENT
University of Leicester Engineering Department FLOW MEASUREMENT IN PIPES EXPERIMENT Page 1 FORMAL LABORATORY REPORT Name of the experiment: FLOW MEASUREMENT IN PIPES Author: Apollin nana chaazou Partner
More informationFluid Mechanics Qualifying Examination Sample Exam 2
Fluid Mechanics Qualifying Examination Sample Exam 2 Allotted Time: 3 Hours The exam is closed book and closed notes. Students are allowed one (doublesided) formula sheet. There are five questions on
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 informationBoundaryLayer Theory
Hermann Schlichting Klaus Gersten BoundaryLayer Theory With contributions from Egon Krause and Herbert Oertel Jr. Translated by Katherine Mayes 8th Revised and Enlarged Edition With 287 Figures and 22
More informationτ du In his lecture we shall look at how the forces due to momentum changes on the fluid and viscous forces compare and what changes take place.
4. Real fluids The flow of real fluids exhibits viscous effect, that is they tend to stick to solid surfaces and have stresses within their body. You might remember from earlier in the course Newtons law
More informationMULTIPLECHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct Answer in the Questions Below.)
Test Midterm 1 F2013 MULTIPLECHOICE PROBLEMS :(Two marks per answer) (Circle the Letter Beside the Most Correct nswer in the Questions Below.) 1. The absolute viscosity µ of a fluid is primarily a function
More informationESS314. Basics of Geophysical Fluid Dynamics by John Booker and Gerard Roe. Conservation Laws
ESS314 Basics of Geophysical Fluid Dynamics by John Booker and Gerard Roe Conservation Laws The big differences between fluids and other forms of matter are that they are continuous and they deform internally
More informationS.E. (Mech.) (First Sem.) EXAMINATION, (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum Marks : 100
Total No. of Questions 12] [Total No. of Printed Pages 8 Seat No. [4262]113 S.E. (Mech.) (First Sem.) EXAMINATION, 2012 (Common to Mech/Sandwich) FLUID MECHANICS (2008 PATTERN) Time : Three Hours Maximum
More informationFACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4)
FACULTY OF CHEMICAL & ENERGY ENGINEERING FLUID MECHANICS LABORATORY TITLE OF EXPERIMENT: MINOR LOSSES IN PIPE (E4) 1 1.0 Objectives The objective of this experiment is to calculate loss coefficient (K
More informationMECHANICAL PROPERTIES OF FLUIDS
CHAPTER10 MECHANICAL PROPERTIES OF FLUIDS QUESTIONS 1 marks questions 1. What are fluids? 2. How are fluids different from solids? 3. Define thrust of a liquid. 4. Define liquid pressure. 5. Is pressure
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 informationFundamentals of Fluid Dynamics: Elementary Viscous Flow
Fundamentals of Fluid Dynamics: Elementary Viscous Flow Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI bluebox.ippt.pan.pl/ tzielins/ Institute of Fundamental Technological Research
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 informationExercise sheet 5 (Pipe flow)
Exercise sheet 5 (Pipe flow) last edited June 4, 2018 These lecture notes are based on textbooks by White [13], Çengel & al.[16], and Munson & al.[18]. Except otherwise indicated, we assume that fluids
More informationSourabh V. Apte. 308 Rogers Hall
Sourabh V. Apte 308 Rogers Hall sva@engr.orst.edu 1 Topics Quick overview of Fluid properties, units Hydrostatic forces Conservation laws (mass, momentum, energy) Flow through pipes (friction loss, Moody
More informationcentrifugal acceleration, whose magnitude is r cos, is zero at the poles and maximum at the equator. This distribution of the centrifugal acceleration
Lecture 10. Equations of Motion Centripetal Acceleration, Gravitation and Gravity The centripetal acceleration of a body located on the Earth's surface at a distance from the center is the force (per unit
More informationChapter 5(Section1) Friction in Solids and Liquids
Chapter 5(Section1) Friction in Solids and Liquids Que 1: Define friction. What are its causes? Ans : Friction: When two bodies are in contact with each other and if one body is made to move then the
More informationTable of Contents. Preface... xiii
Preface... xiii PART I. ELEMENTS IN FLUID MECHANICS... 1 Chapter 1. Local Equations of Fluid Mechanics... 3 1.1. Forces, stress tensor, and pressure... 4 1.2. Navier Stokes equations in Cartesian coordinates...
More informationChapter 6. Losses due to Fluid Friction
Chapter 6 Losses due to Fluid Friction 1 Objectives ä To measure the pressure drop in the straight section of smooth, rough, and packed pipes as a function of flow rate. ä To correlate this in terms of
More informationFLUID MECHANICS PROF. DR. METİN GÜNER COMPILER
FLUID MECHANICS PROF. DR. METİN GÜNER COMPILER ANKARA UNIVERSITY FACULTY OF AGRICULTURE DEPARTMENT OF AGRICULTURAL MACHINERY AND TECHNOLOGIES ENGINEERING 1 5. FLOW IN PIPES Liquid or gas flow through pipes
More informationFluid Flow Analysis Penn State Chemical Engineering
Fluid Flow Analysis Penn State Chemical Engineering Revised Spring 2015 Table of Contents LEARNING OBJECTIVES... 1 EXPERIMENTAL OBJECTIVES AND OVERVIEW... 1 PRELAB STUDY... 2 EXPERIMENTS IN THE LAB...
More information