The most common methods to identify velocity of flow are pathlines, streaklines and streamlines.


 Carol Fletcher
 2 years ago
 Views:
Transcription
1 4 FLUID FLOW 4.1 Introduction Many civil engineering problems in fluid mechanics are concerned with fluids in motion. The distribution of potable water, the collection of domestic sewage and storm water, and the wave actions on offshore structures are common examples. The viscosity of water is small and therefore in most hydraulic problems associated with civil engineering it is reasonable to ignore the effect of shear forces. 4.2 Velocity of Flow The definition of velocity in a fluid is much more complicated than in the case of a rigid solid. Basically this follows from the fact that the individual particles of a solid are bound together whereas the particles of a fluid can move independently of each other. The most common methods to identify velocity of flow are pathlines, streaklines and streamlines. Pathline  trace the position of a particle at successive intervals of time starting from a given point. Streakline trace of all particles that have previously passed through a common point. Streamline an imaginary curve that is tangential to the velocity vectors of a connected series of fluid particles. In unsteady flow, streamlines, pathlines and streaklines are all different, but in steady flow, streamlines, pathlines and streaklines are identical. The streamline is thus a line representing the direction of flow of the series of particles at a given instant. Because the streamline is always tangential to the flow, it follows that there is no flow across a streamline. P.41
2 4.3 Types of Flow There are several types of flow that occur in practice: uniform and nonuniform flow, steady and unsteady flow, laminar and turbulent flow. Some of them can be explained by means of streamlines Uniform and Nonuniform Flow In uniform flow the velocity (including its magnitude and direction) does not change from one point to another along any of the streamlines in the flow field. Uniform flow Nonuniform flow This means that both the area and velocity of the flow must be the same at every crosssection, and the streamlines must be straight and parallel. If the streamlines are not straight, there will be a change in the direction of the flow. If the streamlines are not parallel, there will be change in the magnitude of the flow. In nonuniform flow the velocity changes from point to point along streamlines. Mathematically, uniform and nonuniform flow can be defined as: dv = 0 ds (uniform flow) dv 0 ds (nonuniform flow) where V = velocity of flow s = position measuring along a streamline P.42
3 4.3.2 Steady and Unsteady Flow Steady flow means the velocity at any point in the flow field does not change with respect to time. If the velocity at a point changes over time, then the flow is unsteady. Mathematically, steady flow and unsteady flow can be presented as follows: dv = 0 dt (steady flow) dv 0 dt (unsteady flow) where V = velocity of flow t = time of study Discharge at a constant rate through a pipe is a common example at steady flow. If the pipe is of a constant diameter, the flow is uniform and steady. In fact, most of the civil engineering hydraulic problems are concerned with steady flow. An example of nonuniform and unsteady flow occurring together is the case of the flow from a nozzle when for some reason there is a change in the discharge rate. There are, therefore, four possible types of flow. Steady uniform flow. Conditions do not change with position or time. The velocity and crosssectional area of the stream of fluid are the same at each crosssection; e.g. flow of a liquid through a pipe of uniform bore running completely full at constant velocity. Steady nonuniform flow. Conditions change from point to point but not with time. The velocity and crosssectional area of the stream may vary from crosssection to crosssection, but, for each crosssection, they will not vary with time; e.g. flow of a liquid at a constant rate through a tapering pipe running completely full. Unsteady uniform flow. At a given instant of time the velocity at every point is the same, but this velocity will change with time; e.g. accelerating flow of a P.43
4 liquid through a pipe of uniform bore running full, such as would occur when a pump is started up. Unsteady nonuniform flow. The crosssectional area and velocity vary from point to point and also change with time; e.g. a wave travelling along a channel Real and Ideal Flow When a real fluid flows past a boundary, the fluid immediately in contact with the boundary will have the same velocity as the boundary. The velocity of successive layers of fluid will increase as moving away from the boundary. Boundary layer V = 0.99Vf Ideal Fluid Free velocity =Vf V = 0.99Vf Boundary layer Real Fluid The part of the flow adjoining the boundary in which this change of velocity occurs is known as the boundary layer. In this region, shear stresses are developed between layers of fluid moving with different velocities as a result of viscosity. The thickness of the boundary layer is defined as the distance from the boundary at which the velocity becomes equal to 99% of the free stream velocity. Outside this boundary layer, the effect of the shear stresses due to the boundary can be ignored and the fluid can be treated as if it were an ideal fluid. If the fluid velocity is high and its viscosity low, the boundary layer is comparatively thin, and the assumption that a real fluid can be treated as an ideal fluid greatly simplifies the analysis of the flow and still leads to useful results One, Two and Three Dimensional Flow P.44
5 When there is no obstruction or channelling, fluid flow can be thought of as threedimensional flow. In situations where the velocity of flow in one coordinate direction has no changes, the flow can be described as twodimensional. The flow between two parallel plates is an example. If the velocity of flow is constant across each section but changes in only one direction, it can be described as onedimensional. The average flow in a duct can be considered as onedimensional. 4.4 Flow Rate and Mean Velocity The quantity of fluid flowing per unit time across any section is called the flow rate or the discharge. It may be expressed in terms of volume flow rate, m 3 /s; weight flow rate, kn/s or mass flow rate, kg/s. In dealing with incompressible fluids, volume flow rate is commonly used, whereas weight flow rate or mass flow rate is more convenient with compressible fluids. In a real fluid, the velocity adjacent to a solid boundary will be zero. For a pipe, the velocity profile would be as shown in fig (a) below for laminar flow and fig (b) for turbulent flow. u r r dr R u (a) Laminar flow (b) Turbulent flow Flow rate is the volume rate of flow passing a given section of the flow stream. It is also called discharged. Mathematically, flow rate can be defined as follows: Q = A V. da where Q = flow rate, m 3 /s P.45
6 If v is constant, Q = V.A V = velocity of flow, m/s da = area normal to the direction of velocity, m 2 In many practical problems, such as the flow of water through a pipe, the diameter of the pipe, and the discharge are given, and the velocity of the flow is the determined from, Q V = A The velocity so obtained is called the average velocity or mean velocity. By definition, it is simply the discharge divided by the crosssectional area. P.46
FLUID MECHANICS. Gaza. Chapter CHAPTER 44. Motion of Fluid Particles and Streams. Dr. Khalil Mahmoud ALASTAL
FLUID MECHANICS Gaza Chapter CHAPTER 44 Motion of Fluid Particles and Streams Dr. Khalil Mahmoud ALASTAL Objectives of this Chapter: Introduce concepts necessary to analyze fluids in motion. Identify differences
More informationLecture 2 Flow classifications and continuity
Lecture 2 Flow classifications and continuity Dr Tim Gough: t.gough@bradford.ac.uk General information 1 No tutorial week 3 3 rd October 2013 this Thursday. Attempt tutorial based on examples from today
More informationAnNajah National University Civil Engineering Department. Fluid Mechanics. Chapter 1. General Introduction
1 AnNajah National University Civil Engineering Department Fluid Mechanics Chapter 1 General Introduction 2 What is Fluid Mechanics? Mechanics deals with the behavior of both stationary and moving bodies
More information6. Basic basic equations I ( )
6. Basic basic equations I (4.24.4) Steady and uniform flows, streamline, streamtube One, two, and threedimensional flow Laminar and turbulent flow Reynolds number System and control volume Continuity
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 informationPHYSICAL MECHANISM OF CONVECTION
Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter
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 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 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 informationLECTURE NOTES  III. Prof. Dr. Atıl BULU
LECTURE NOTES  III «FLUID MECHANICS» Istanbul Technical University College of Civil Engineering Civil Engineering Department Hydraulics Division CHAPTER KINEMATICS OF FLUIDS.. FLUID IN MOTION Fluid motion
More information!! +! 2!! +!"!! =!! +! 2!! +!"!! +!!"!"!"
Homework 4 Solutions 1. (15 points) Bernoulli s equation can be adapted for use in evaluating unsteady flow conditions, such as those encountered during start up processes. For example, consider the large
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 informationBERNOULLI EQUATION. The motion of a fluid is usually extremely complex.
BERNOULLI EQUATION The motion of a fluid is usually extremely complex. The study of a fluid at rest, or in relative equilibrium, was simplified by the absence of shear stress, but when a fluid flows over
More informationChapter 5 Control Volume Approach and Continuity Equation
Chapter 5 Control Volume Approach and Continuity Equation Lagrangian and Eulerian Approach To evaluate the pressure and velocities at arbitrary locations in a flow field. The flow into a sudden contraction,
More informationChapter 3 Bernoulli Equation
1 Bernoulli Equation 3.1 Flow Patterns: Streamlines, Pathlines, Streaklines 1) A streamline, is a line that is everywhere tangent to the velocity vector at a given instant. Examples of streamlines around
More informationCHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS NOOR ALIZA AHMAD
CHAPTER 3 BASIC EQUATIONS IN FLUID MECHANICS 1 INTRODUCTION Flow often referred as an ideal fluid. We presume that such a fluid has no viscosity. However, this is an idealized situation that does not exist.
More informationME3560 Tentative Schedule Spring 2019
ME3560 Tentative Schedule Spring 2019 Week Number Date Lecture Topics Covered Prior to Lecture Read Section Assignment Prep Problems for Prep Probs. Must be Solved by 1 Monday 1/7/2019 1 Introduction to
More informationME3560 Tentative Schedule Fall 2018
ME3560 Tentative Schedule Fall 2018 Week Number 1 Wednesday 8/29/2018 1 Date Lecture Topics Covered Introduction to course, syllabus and class policies. Math Review. Differentiation. Prior to Lecture Read
More informationNPTEL Quiz Hydraulics
Introduction NPTEL Quiz Hydraulics 1. An ideal fluid is a. One which obeys Newton s law of viscosity b. Frictionless and incompressible c. Very viscous d. Frictionless and compressible 2. The unit of kinematic
More informationvector H. If O is the point about which moments are desired, the angular moment about O is given:
The angular momentum A control volume analysis can be applied to the angular momentum, by letting B equal to angularmomentum vector H. If O is the point about which moments are desired, the angular moment
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 informationPart A: 1 pts each, 10 pts total, no partial credit.
Part A: 1 pts each, 10 pts total, no partial credit. 1) (Correct: 1 pt/ Wrong: 3 pts). The sum of static, dynamic, and hydrostatic pressures is constant when flow is steady, irrotational, incompressible,
More informationIn which of the following scenarios is applying the following form of Bernoulli s equation: steady, inviscid, uniform stream of water. Ma = 0.
bernoulli_11 In which of the following scenarios is applying the following form of Bernoulli s equation: p V z constant! g + g + = from point 1 to point valid? a. 1 stagnant column of water steady, inviscid,
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 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 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 information2 Internal Fluid Flow
Internal Fluid Flow.1 Definitions Fluid Dynamics The study of fluids in motion. Static Pressure The pressure at a given point exerted by the static head of the fluid present directly above that point.
More informationLecture 3 The energy equation
Lecture 3 The energy equation Dr Tim Gough: t.gough@bradford.ac.uk General information Lab groups now assigned Timetable up to week 6 published Is there anyone not yet on the list? Week 3 Week 4 Week 5
More informationBenha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 201 May 24/ 2016
Benha University College of Engineering at Benha Questions For Corrective Final Examination Subject: Fluid Mechanics M 01 May 4/ 016 Second year Mech. Time :180 min. Examiner:Dr.Mohamed Elsharnoby Attempt
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 informationUniversity of Engineering and Technology, Taxila. Department of Civil Engineering
University of Engineering and Technology, Taxila Department of Civil Engineering Course Title: CE201 Fluid Mechanics  I Prerequisite(s): None Credit Hours: 2 + 1 Contact Hours: 2 + 3 Text Book(s): Reference
More informationMass of fluid leaving per unit time
5 ENERGY EQUATION OF FLUID MOTION 5.1 Eulerian Approach & Control Volume In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics.
More informationEXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER
EXPERIMENT No.1 FLOW MEASUREMENT BY ORIFICEMETER 1.1 AIM: To determine the coefficient of discharge of the orifice meter 1.2 EQUIPMENTS REQUIRED: Orifice meter test rig, Stopwatch 1.3 PREPARATION 1.3.1
More informationStudy fluid dynamics. Understanding Bernoulli s Equation.
Chapter Objectives Study fluid dynamics. Understanding Bernoulli s Equation. Chapter Outline 1. Fluid Flow. Bernoulli s Equation 3. Viscosity and Turbulence 1. Fluid Flow An ideal fluid is a fluid that
More informationWeek 8. Steady Flow Engineering Devices. GENESYS Laboratory
Week 8. Steady Flow Engineering Devices Objectives 1. Solve energy balance problems for common steadyflow devices such as nozzles, compressors, turbines, throttling valves, mixers, heaters, and heat exchangers
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 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 informationAA210A Fundamentals of Compressible Flow. Chapter 1  Introduction to fluid flow
AA210A Fundamentals of Compressible Flow Chapter 1  Introduction to fluid flow 1 1.2 Conservation of mass Mass flux in the xdirection [ ρu ] = M L 3 L T = M L 2 T Momentum per unit volume Mass per unit
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 information5 ENERGY EQUATION OF FLUID MOTION
5 ENERGY EQUATION OF FLUID MOTION 5.1 Introduction In order to develop the equations that describe a flow, it is assumed that fluids are subject to certain fundamental laws of physics. The pertinent laws
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 informationHYDRAULICS STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL HYDRAULICS
1 STAFF SELECTION COMMISSION CIVIL ENGINEERING STUDY MATERIAL Syllabus Hydraulics ( Fluid Mechanics ) Fluid properties, hydrostatics, measurements of flow, Bernoulli's theorem and its application, flow
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 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 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 informationCHAPTER 4 KINEMATICS OF FLOW
CHAPTER 4 KINEMATICS OF FLOW 4.1 Introduction: In hydrostatics one deals with liquids at rest in which there is no relative motion between fluid particles and therefore no shear stresses exist. Since no
More informationFor example an empty bucket weighs 2.0kg. After 7 seconds of collecting water the bucket weighs 8.0kg, then:
Hydraulic Coefficient & Flow Measurements ELEMENTARY HYDRAULICS National Certificate in Technology (Civil Engineering) Chapter 3 1. Mass flow rate If we want to measure the rate at which water is flowing
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 informationFluids. Fluids in Motion or Fluid Dynamics
Fluids Fluids in Motion or Fluid Dynamics Resources: Serway  Chapter 9: 9.79.8 Physics B Lesson 3: Fluid Flow Continuity Physics B Lesson 4: Bernoulli's Equation MIT  8: Hydrostatics, Archimedes' Principle,
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 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 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 informationROAD MAP... D0: Reynolds Transport Theorem D1: Conservation of Mass D2: Conservation of Momentum D3: Conservation of Energy
ES06 Fluid Mechani UNIT D: Flow Field Analysis ROAD MAP... D0: Reynolds Transport Theorem D1: Conservation of Mass D: Conservation of Momentum D3: Conservation of Energy ES06 Fluid Mechani Unit D0:
More informationExperiment To determine the coefficient of impact for vanes. Experiment To determine the coefficient of discharge of an orifice meter.
SUBJECT: FLUID MECHANICS VIVA QUESTIONS (M.E 4 th SEM) Experiment To determine the coefficient of impact for vanes. Q1. Explain impulse momentum principal. Ans1. Momentum equation is based on Newton s
More informationHYDRAULICS 1 (HYDRODYNAMICS) SPRING 2005
HYDRAULICS (HYDRODYNAMICS) SPRING 005 Part. FluidFlow Principles. Introduction. Definitions. Notation and fluid properties.3 Hydrostatics.4 Fluid dynamics.5 Control volumes.6 Visualising fluid flow.7
More informationREE Internal Fluid Flow Sheet 2  Solution Fundamentals of Fluid Mechanics
REE 307  Internal Fluid Flow Sheet 2  Solution Fundamentals of Fluid Mechanics 1. Is the following flows physically possible, that is, satisfy the continuity equation? Substitute the expressions for
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 informationFluid Dynamics Midterm Exam #2 November 10, 2008, 7:008:40 pm in CE 110
CVEN 311501 Fluid Dynamics Midterm Exam #2 November 10, 2008, 7:008:40 pm in CE 110 Name: UIN: Instructions: Fill in your name and UIN in the space above. There should be 11 pages including this one.
More informationFundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics
Fundamentals of Fluid Dynamics: Ideal Flow Theory & Basic Aerodynamics Introductory Course on Multiphysics Modelling TOMASZ G. ZIELIŃSKI (after: D.J. ACHESON s Elementary Fluid Dynamics ) bluebox.ippt.pan.pl/
More informationExam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118
CVEN 311501 (Socolofsky) Fluid Dynamics Exam #2: Fluid Kinematics and Conservation Laws April 13, 2016, 7:00 p.m. 8:40 p.m. in CE 118 Name: : UIN: : Instructions: Fill in your name and UIN in the space
More informationTherefore, the control volume in this case can be treated as a solid body, with a net force or thrust of. bm # V
When the mass m of the control volume remains nearly constant, the first term of the Eq. 6 8 simply becomes mass times acceleration since 39 CHAPTER 6 d(mv ) CV m dv CV CV (ma ) CV Therefore, the control
More informationChapter 4 DYNAMICS OF FLUID FLOW
Faculty Of Engineering at Shobra nd Year Civil  016 Chapter 4 DYNAMICS OF FLUID FLOW 41 Types of Energy 4 Euler s Equation 43 Bernoulli s Equation 44 Total Energy Line (TEL) and Hydraulic Grade Line
More informationConvection. forced convection when the flow is caused by external means, such as by a fan, a pump, or atmospheric winds.
Convection The convection heat transfer mode is comprised of two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic,
More informationChapter Four fluid flow mass, energy, Bernoulli and momentum
41Conservation of Mass Principle Consider a control volume of arbitrary shape, as shown in Fig (41). Figure (41): the differential control volume and differential control volume (Total mass entering
More informationRate of Flow Quantity of fluid passing through any section (area) per unit time
Kinematics of Fluid Flow Kinematics is the science which deals with study of motion of liquids without considering the forces causing the motion. Rate of Flow Quantity of fluid passing through any section
More informationChapter 2: Basic Governing Equations
1 Reynolds Transport Theorem (RTT)  Continuity Equation 3 The Linear Momentum Equation 4 The First Law of Thermodynamics 5 General Equation in Conservative Form 6 General Equation in NonConservative
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 informationRecap: Static Fluids
Recap: Static Fluids Archimedes principal states that the buoyant force acting on an object is equal to the weight of fluid displaced. If the average density of object is greater than density of fluid
More informationFLUID MECHANICS. Chapter 3 Elementary Fluid Dynamics  The Bernoulli Equation
FLUID MECHANICS Chapter 3 Elementary Fluid Dynamics  The Bernoulli Equation CHAP 3. ELEMENTARY FLUID DYNAMICS  THE BERNOULLI EQUATION CONTENTS 3. Newton s Second Law 3. F = ma along a Streamline 3.3
More informationENGINEERING FLUID MECHANICS. CHAPTER 1 Properties of Fluids
CHAPTER 1 Properties of Fluids ENGINEERING FLUID MECHANICS 1.1 Introduction 1.2 Development of Fluid Mechanics 1.3 Units of Measurement (SI units) 1.4 Mass, Density, Specific Weight, Specific Volume, Specific
More informationAPPLIED FLUID DYNAMICS HANDBOOK
APPLIED FLUID DYNAMICS HANDBOOK ROBERT D. BLEVINS H imhnisdia ttodisdiule Darmstadt Fachbereich Mechanik 'rw.nr.. [VNR1 VAN NOSTRAND REINHOLD COMPANY ' ' New York Contents Preface / v 1. Definitions /
More informationFluid Mechanics. Spring 2009
Instructor: Dr. YangCheng Shih Department of Energy and Refrigerating AirConditioning Engineering National Taipei University of Technology Spring 2009 Chapter 1 Introduction 11 General Remarks 12 Scope
More informationAE/ME 339. K. M. Isaac Professor of Aerospace Engineering. 12/21/01 topic7_ns_equations 1
AE/ME 339 Professor of Aerospace Engineering 12/21/01 topic7_ns_equations 1 Continuity equation Governing equation summary Nonconservation form D Dt. V 0.(2.29) Conservation form ( V ) 0...(2.33) t 12/21/01
More informationV (r,t) = i ˆ u( x, y,z,t) + ˆ j v( x, y,z,t) + k ˆ w( x, y, z,t)
IV. DIFFERENTIAL RELATIONS FOR A FLUID PARTICLE This chapter presents the development and application of the basic differential equations of fluid motion. Simplifications in the general equations and common
More informationIntroduction to Chemical Engineering Thermodynamics. Chapter 7. KFUPM Housam Binous CHE 303
Introduction to Chemical Engineering Thermodynamics Chapter 7 1 Thermodynamics of flow is based on mass, energy and entropy balances Fluid mechanics encompasses the above balances and conservation of momentum
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 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 information10.52 Mechanics of Fluids Spring 2006 Problem Set 3
10.52 Mechanics of Fluids Spring 2006 Problem Set 3 Problem 1 Mass transfer studies involving the transport of a solute from a gas to a liquid often involve the use of a laminar jet of liquid. The situation
More informationChapter 6: Momentum Analysis
61 Introduction 62Newton s Law and Conservation of Momentum 63 Choosing a Control Volume 64 Forces Acting on a Control Volume 65Linear Momentum Equation 66 Angular Momentum 67 The Second Law of
More informationIntroduction to Marine Hydrodynamics
1896 1920 1987 2006 Introduction to Marine Hydrodynamics (NA235) Department of Naval Architecture and Ocean Engineering School of Naval Architecture, Ocean & Civil Engineering First Assignment The first
More informationExternal Flow and Boundary Layer Concepts
1 2 Lecture (8) on Fayoum University External Flow and Boundary Layer Concepts By Dr. Emad M. Saad Mechanical Engineering Dept. Faculty of Engineering Fayoum University Faculty of Engineering Mechanical
More informationIn this section, mathematical description of the motion of fluid elements moving in a flow field is
Jun. 05, 015 Chapter 6. Differential Analysis of Fluid Flow 6.1 Fluid Element Kinematics In this section, mathematical description of the motion of fluid elements moving in a flow field is given. A small
More informationpiston control surface
Lecture Thermodynamics 4 Enthalpy Consider a quasistatic hydrostatic constant pressure (isobaric) process weights piston, p gas Q control surface fi, p gas U U 1 = Q +W = Q  Ú pdv = Q  p + p fi (U +
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 informationChapter 4 Continuity Equation and Reynolds Transport Theorem
Chapter 4 Continuity Equation and Reynolds Transport Theorem 4.1 Control Volume 4. The Continuity Equation for OneDimensional Steady Flow 4.3 The Continuity Equation for TwoDimensional Steady Flow 4.4
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 informationIntroduction to Fluid Dynamics
Introduction to Fluid Dynamics Roger K. Smith Skript  auf englisch! Umsonst im Internet http://www.meteo.physik.unimuenchen.de Wählen: Lehre Manuskripte Download User Name: meteo Password: download Aim
More informationBasic Fluid Mechanics
Basic Fluid Mechanics Chapter 5: Application of Bernoulli Equation 4/16/2018 C5: Application of Bernoulli Equation 1 5.1 Introduction In this chapter we will show that the equation of motion of a particle
More informationFluid Mechanics c) Orificemeter a) Viscous force, Turbulence force, Compressible force a) Turbulence force c) Integration d) The flow is rotational
Fluid Mechanics 1. Which is the cheapest device for measuring flow / discharge rate. a) Venturimeter b) Pitot tube c) Orificemeter d) None of the mentioned 2. Which forces are neglected to obtain Euler
More informationBACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING)
No. of Printed Pages : 6 BME028 BACHELOR OF TECHNOLOGY IN MECHANICAL ENGINEERING (COMPUTER INTEGRATED MANUFACTURING) TermEnd Examination December, 2011 00792 BME028 : FLUID MECHANICS Time : 3 hours
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 informationconservation of linear momentum 1+8Fr = 1+ Sufficiently short that energy loss due to channel friction is negligible h L = 0 Bernoulli s equation.
174 Review Flow through a contraction Critical and choked flows The hydraulic jump conservation of linear momentum y y 1 = 1+ 1+8Fr 1 8.1 Rapidly Varied Flows Weirs 8.1.1 BroadCrested Weir Consider the
More information1 Onedimensional analysis
Onedimensional analysis. Introduction The simplest models for gas liquid flow systems are ones for which the velocity is uniform over a crosssection and unidirectional. This includes flows in a long
More informationMicrofluidic Devices. Microfluidic Device Market. Microfluidic Principles Part 1. Introduction to BioMEMS & Medical Microdevices.
Introduction to BioMEMS & Medical Microdevices Microfluidic Principles Part 1 Companion lecture to the textbook: Fundamentals of BioMEMS and Medical Microdevices, by Prof., http://saliterman.umn.edu/,
More informationReview of Fluid Mechanics
Chapter 3 Review of Fluid Mechanics 3.1 Units and Basic Definitions Newton s Second law forms the basis of all units of measurement. For a particle of mass m subjected to a resultant force F the law may
More information6.1 Momentum Equation for Frictionless Flow: Euler s Equation The equations of motion for frictionless flow, called Euler s
Chapter 6 INCOMPRESSIBLE INVISCID FLOW All real fluids possess viscosity. However in many flow cases it is reasonable to neglect the effects of viscosity. It is useful to investigate the dynamics of an
More informationCHAPTER 4. Basics of Fluid Dynamics
CHAPTER 4 Basics of Fluid Dynamics What is a fluid? A fluid is a substance that can flow, has no fixed shape, and offers little resistance to an external stress In a fluid the constituent particles (atoms,
More informationCHAPTER 2 INVISCID FLOW
CHAPTER 2 INVISCID FLOW Changes due to motion through a field; Newton s second law (f = ma) applied to a fluid: Euler s equation; Euler s equation integrated along a streamline: Bernoulli s equation; Bernoulli
More informationCHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE
CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE In this chapter, the governing equations for the proposed numerical model with discretisation methods are presented. Spiral
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 information