Fluid Mechanics - Colincaprani

Fluid MechanicsFluid Mechanics2nd YearCivil & Structural EngineeringSemester 22006/7Dr. Colin CapraniChartered Engineer1Dr. C. Caprani

Fluid MechanicsContents1.Introduction . 71.1 Course Outline . 7Goals . 7Syllabus. 81.2 Programme . 9Lectures. 9Assessment. 91.3 Reading Material. 10Lecture Notes . 10Books . 10The Web. 101.4 Fluid Mechanics in Civil/Structural Engineering . 112.Introduction to Fluids . 122.1 Background and Definition. 12Background . 12Definition . 13Definition Applied to Static Fluids. 13Definition Applied to Fluids in Motion . 14Generalized Laws of Viscosity . 172.2 Units . 19Dimensions and Base Units . 19Derived Units . 19SI Prefixes . 21Further Reading . 212.3 Properties . 22Further Reading . 22Mass Density. 222Dr. C. Caprani

Fluid MechanicsSpecific Weight. 22Relative Density (Specific Gravity). 22Bulk Modulus. 23Viscosity. 23Problems - Properties. 253.Hydrostatics . 263.1 Introduction. 26Pressure . 26Pressure Reference Levels . 273.2 Pressure in a Fluid. 28Statics of Definition . 28Pascal’s Law . 29Pressure Variation with Depth. 31Summary . 33Problems - Pressure. 343.3 Pressure Measurement . 36Pressure Head. 36Manometers. 36Problems – Pressure Measurement . 413.4 Fluid Action on Surfaces . 43Plane Surfaces . 43Plane Surface Properties . 46Plane Surfaces – Example. 47Curved Surfaces . 51Curved Surfaces – Example. 55Problems – Fluid Action on Surfaces . 574.Hydrodynamics: Basics. 594.1 General Concepts . 59Introduction. 593Dr. C. Caprani

Fluid MechanicsClassification of Flow Pattern. 59Visualization . 60Dimension of Flow . 62Fundamental Equations. 63Control Volume . 644.2 The Continuity Equation. 65Development . 65Mass Conservation – Example . 684.3 The Energy Equation . 71Development . 71Comments . 74Energy Equation – Example . 754.4 The Momentum Equation . 78Development . 78Application – Fluid Striking a Flat Surface. 79Application – Flow around a bend in a pipe. 81Application – Force exerted by a firehose. 834.5 Modifications to the Basic Equations . 86Flow Measurement – Small Orifices . 86Flow Measurement – Large Orifices . 89Discharge Measurement in Pipelines. 92Velocity and Momentum Factors . 94Accounting for Energy Losses. 96Problems – Energy Losses and Flow Measurement. 995.Hydrodynamics: Flow in Pipes . 1005.1 General Concepts . 100Characteristics of Flow Types . 103Background to Pipe Flow Theory. 1045.2 Laminar Flow. 1054Dr. C. Caprani

Fluid MechanicsSteady Uniform Flow in a Pipe: Momentum Equation . 105Hagen-Poiseuille Equation for Laminar Flow. 108Example: Laminar Flow in Pipe . 1115.3 Turbulent Flow. 113Description . 113Empirical Head Loss in Turbulent Flow . 1145.4 Pipe Friction Factor. 116Laminar Flow. 116Smooth Pipes – Blasius Equation . 116Nikuradse’s Experiments . 117The von Karman and Prandlt Laws . 118The Colebrook-White Transition Formula . 119Moody . 120Barr. 121Hydraulics Research Station Charts . 122Example . 124Problems – Pipe Flows . 1295.5 Pipe Design . 130Local Head Losses . 130Sudden Enlargement . 131Sudden Contraction. 133Example – Pipe flow incorporating local head losses . 134Partially Full Pipes. 136Example . 138Problems – Pipe Design . 1416.Hydrodynamics: Flow in Open Channels . 1426.1 Description . 142Properties . 1436.2 Basics of Channel Flow . 1455Dr. C. Caprani

Fluid MechanicsLaminar and Turbulent Flow . 145Moody Diagrams for Channel Flow . 146Friction Formula for Channels. 147Evaluating Manning’s n. 149Example –Trapezoidal Channel. 1506.3 Varying Flow in Open Channels . 152The Energy Equation . 152Flow Characteristics. 154Example – Open Channel Flow Transition . 157Problems – Open Channel Flow . 1596Dr. C. Caprani

Fluid Mechanics1. Introduction1.1Course OutlineGoalsThe goal is that you will:1. Have fundamental knowledge of fluids:a. compressible and incompressible;b. their properties, basic dimensions and units;2. Know the fundamental laws of mechanics as applied to fluids.3. Understand the limitations of theoretical analysis and the determination ofcorrection factors, friction factors, etc from experiments.4. Be capable of applying the relevant theory to solve problems.7Dr. C. Caprani

Fluid MechanicsSyllabusBasics: Definition of a fluid: concept of ideal and real fluids, both compressible andincompressible. Properties of fluids and their variation with temperature and pressure and thedimensions of these properties.Hydrostatics: The variation of pressure with depth of liquid. The measurement of pressure and forces on immersed surfaces.Hydrodynamics: Description of various types of fluid flow; laminar and turbulent flow;Reynolds’s number, critical Reynolds’s number for pipe flow. Conservation of energy and Bernoulli’s theorem. Simple applications of thecontinuity and momentum equations. Flow measurement e.g. Venturi meter, orifice plate, Pitot tube, notches andweirs. Hagen-Poiseuille equation: its use and application. Concept of major and minor losses in pipe flow, shear stress, friction factor,and friction head loss in pipe flow. Darcy-Weisbach equation, hydraulic gradient and total energy lines. Series andparallel pipe flow. Flow under varying head. Chezy equation (theoretical and empirical) for flow in an open channel. Practical application of fluid mechanics in civil engineering.8Dr. C. Caprani

Fluid Mechanics1.2ProgrammeLecturesThere are 4 hours of lectures per week. One of these will be considered as a tutorialclass – to be confirmed.The lectures are: Monday, 11:00-12:00, Rm. 209 and 17:00-18:00, Rm 134; Wednesday, to be confirmed.AssessmentThe marks awarded for this subject are assigned as follows: 80% for end-of-semester examination; 20% for laboratory work and reports.9Dr. C. Caprani

Fluid Mechanics1.3Reading MaterialLecture NotesThe notes that you will take in class will cover the basic outline of the necessaryideas. It will be essential to do some extra reading for this subject.Obviously only topics covered in the notes will be examined. However, it often aidsunderstanding to hear/read different ways of explaining the same topic.BooksBooks on Fluid Mechanics are kept in Section 532 of the library. However, any ofthese books should help you understand fluid mechanics: Douglas, J.F., Swaffield, J.A., Gasiorek, J.M. and Jack, L.B. (2005), FluidMechanics, 5th Edn., Prentice Hall. Massey, B. and Ward-Smith, J. (2005), Mechanics of Fluids, 8th Edn.,Routledge. Chadwick, A., Morfett, J. and Borthwick, M. (2004), Hydraulics in Civil andEnvironmental Engineering, 4th Edn., E & FN Spon. Douglas, J.F. and Mathews, R.D. (1996), Solving Problems in FluidMechanics, Vols. I and II, 3rd Edn., Longman.The WebThere are many sites that can help you with this subject. In particular there arepictures and movies that will aid your understanding of the physical processes behindthe theories.If you find a good site, please let me know and we will develop a list for the class.10Dr. C. Caprani

Fluid Mechanics1.4Fluid Mechanics in Civil/Structural EngineeringEvery civil/structural engineering graduate needs to have a thorough understanding offluids. This is more obvious for civil engineers but is equally valid for structuralengineers: Drainage for developments; Attenuation of surface water for city centre sites; Sea and river (flood) defences; Water distribution/sewerage (sanitation) networks; Hydraulic design of water/sewage treatment works; Dams; Irrigation; Pumps and Turbines; Water retaining structures. Flow of air in / around buildings; Bridge piers in rivers; Ground-water flow.As these mostly involve water, we will mostly examine fluid mechanics with this inmind.Remember: it is estimated that drainage and sewage systems – as designed by civilengineers – have saved more lives than all of medical science. Fluid mechanics isintegral to our work.11Dr. C. Caprani

Fluid Mechanics2. Introduction to Fluids2.1Background and DefinitionBackground There are three states of matter: solids, liquids and gases. Both liquids and gases are classified as fluids. Fluids do not resist a change in shape. Therefore fluids assume the shape of thecontainer they occupy. Liquids may be considered to have a fixed volume and therefore can have afree surface. Liquids are almost incompressible. Conversely, gases are easily compressed and will expand to fill a containerthey occupy. We will usually be interested in liquids, either at rest or in motion.Liquid showing free surfaceGas filling volumeBehaviour of fluids in containers12Dr. C. Caprani

Fluid MechanicsDefinitionThe strict definition of a fluid is:A fluid is a substance which conforms continuously under the action ofshearing forces.To understand this, remind ourselves of what a shear force is:Application and effect of shear force on a bookDefinition Applied to Static FluidsAccording to this definition, if we apply a shear force to a fluid it will deform andtake up a state in which no shear force exists. Therefore, we can say:If a fluid is at rest there can be no shearing forces acting and therefore allforces in the fluid must be perpendicular to the planes in which they act.Note here that we specify that the fluid must be at rest. This is because, it is foundexperimentally that fluids in motion can have slight resistance to shear force. This isthe source of viscosity.13Dr. C. Caprani

Fluid MechanicsDefinition Applied to Fluids in MotionFor example, consider the fluid shown flowing along a fixed surface. At the surfacethere will be little movement of the fluid (it will ‘stick’ to the surface), whilst furtheraway from the surface the fluid flows faster (has greater velocity):If one layer of is moving faster than another layer of fluid, there must be shear forcesacting between them. For example, if we have fluid in contact with a conveyor beltthat is moving we will get the behaviour shown:Ideal fluidReal (Viscous) FluidWhen fluid is in motion, any difference in velocity between adjacent layers has thesame effect as the conveyor belt does.Therefore, to represent real fluids in motion we must consider the action of shearforces.14Dr. C. Caprani

Fluid MechanicsConsider the small element of fluid shown

Fluid Mechanics 1 Dr. C. Caprani Fluid Mechanics 2nd Year Civil & Structural Engineering Semester 2 2006/7 Dr. Colin Caprani Chartered Engineer