Detailed Outline, M E 320 Fluid Flow, Spring Semester 2015

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1 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 vs. inviscid 2. Internal vs. external 3. Compressible vs. Incompressible 4. Laminar vs. turbulent 5. Natural vs. forced 6. Steady vs. unsteady 7. One-, two-, or three-dimensional C. Dimensions, Units, and Significant Digits 1. Dimensions 2. Units 3. Unit conversions, unity conversion ratios 4. Significant digits D. Fluid Properties 1. Kinematic properties 2. Thermodynamic properties 3. Other (miscellaneous) properties a. speed of sound, c b. vapor pressure, P v c. viscosity,, and kinematic viscosity, d. surface tension, s II. Pressure and Fluid Statics (Chapter 3) A. Pressure 1. Some basics 2. Dimensions and units B. Types of Pressure Measurement 1. Absolute pressure 2. Gage pressure 3. Vacuum pressure C. Equation of Fluid Statics 1. Body force (gravity) 2. Surface forces (pressure) 3. Hydrostatic pressure relation 4. Some rules to remember about hydrostatics D. Applications of Fluid Statics 1. Mercury barometer 2. Head as a pressure measurement 3. The U-tube manometer 4. Notes about manometry 5. Isobars E. Hydrostatic Forces on Submerged Surfaces 1. Plane surfaces 2. Curved surfaces 3. Buoyancy and stability a. buoyancy b. stability F. Fluids in Rigid-Body Motion 1. Equations Author: John M. Cimbala, Penn State University Latest revision: 05 January 2015

2 2. Uniform linear acceleration 3. Rigid body rotation III. Fluid Kinematics (Chapter 4) A. Descriptions of Fluid Flow 1. Lagrangian description 2. Eulerian description 3. Acceleration field and material derivative B. Flow Patterns and Flow Visualization 1. Streamlines, pathlines, streaklines, and timelines a. streamline b. pathline c. streakline d. timeline 2. Other flow visualization techniques 3. Fluid flow plots a. profile plots b. vector plots c. contour plots C. Other Kinematic Descriptions 1. Motion and deformation of fluid particles a. translation b. rotation and vorticity c. linear strain d. shear strain 2. Strain rate tensor D. The Reynolds Transport Theorem (RTT) and derivation 2. Applications of the RTT a. conservation of mass b. conservation of energy c. conservation of linear momentum IV. Conservation Laws and the Control Volume (Integral) Technique (Chapters 5 and 6) 1. Overview: Techniques for solving flow problems a. control volume analysis b. dimensional analysis and experiment c. differential analysis B. Conservation of Mass C. Conservation of Energy 3. The kinetic energy correction factor 4. The head form of the energy equation for control volumes 5. Examples 6. Grade lines a. hydraulic grade line (HGL) b. energy grade line (EGL) c. relationship to the energy equation D. The Bernoulli equation 2. Applications a. airplane wing b. Venturi tube c. Pitot-static probe

3 E. Conservation of Linear Momentum 2. The momentum flux correction factor 3. Forces acting on control volume F. Conservation of Angular Momentum V. Dimensional Analysis and Modeling (Chapter 7) A. Primary Dimensions B. Dimensional Homogeneity C. Dimensional Analysis and Similarity 1. Purposes of dimensional analysis 2. Similarity 3. The method of repeating variables D. Experimental Testing and Incomplete Similarity VI. Internal Flow in Pipes (Chapters 8 and 14) 1. Average Velocity in a Pipe 2. Laminar versus turbulent flow a. comparison b. critical Reynolds number for pipe flow c. hydraulic diameter d. the entrance region B. Fully Developed Pipe Flow 1. Comparison of laminar and turbulent flow 2. Wall shear stress 3. Pressure drop in fully developed pipe flow 4. The Darcy friction factor, f 5. The Moody chart 6. Empirical equations a. the Colebrook equation b. the Haaland equation c. the Swamee & Jain equations 7. Examples C. Minor Losses in Pipe Systems 1. Terminology a. loss coefficient b. equivalent length D. Diffusers (Yes, there is a free lunch!) 2. Practical examples 3. Numerical example E. Turbomachinery (Chapter 14) and terminology; types of pumps a. positive displacement pumps (PDP) b. dynamic pumps (1) centrifugal (2) axial (3) mixed 2. Pump performance a. pump performance charts b. matching a pump to a piping system c. dimensionless parameters in pump performance (nondimensional groups and affinity laws)

4 3. Turbines a. types of turbines b. dimensionless parameters in turbine performance F. Piping Networks 1. Pipes in series 2. Pipes in parallel 3. Complex piping networks G. Fluid Meters 1. Local velocity meters a. Pitot-static probe b. hot-wire anemometry c. laser Doppler velocimetry d. PIV 2. Volume flow meters a. end-line devices b. in-line devices (obstruction, positive displacement, turbine, rotameters, and miscellaneous VII. Differential Analysis (Chapters 9 and 15) B. Technique of Differential Analysis C. Conservation of Mass the Continuity Equation 2. Simplifications a. steady but compressible flow b. incompressible but unsteady flow D. The Stream Function, 1. Definition 2. Physical significance of a. streamlines b. volume flow rate 4. Stream function in cylindrical coordinates a. planar flow b. axisymmetric flow c. Examples E. Conservation of Linear Momentum 2. Applications of Navier-Stokes equation, and examples a. Calculation of the pressure field for a known velocity field b. Exact solutions of the continuity and Navier-Stokes equations F. Introduction to computational fluid dynamics (CFD) (Chapter 15) 2. CFD solution procedure 4. Live FlowLab demo VIII. Approximate Solutions of the Navier-Stokes Equations (Chapter 10) B. Nondimensionalization of the Equations 1. Continuity equation 2. Navier-Stokes equation 3. Modified pressure, P C. The Creeping Flow Approximation D. Approximation for Inviscid Regions of Flow 1. Definition and the Euler equation

5 2. The Bernoulli equation in inviscid regions of flow E. The Irrotational Flow Approximation 2. Equations of motion for irrotational flow a. continuity b. Navier-Stokes (reduces to Euler equation) c. Bernoulli d. examples 3. 2-D irrotational flow a. equations b. superposition 4. Elementary planar irrotational flows a. uniform stream b. line source c. line vortex d. doublet 5. Examples of superposition a. The Rankine half-body b. Flow over a circular cylinder c. The method of images F. The Boundary Layer Approximation 2. The boundary layer coordinate system 3. The boundary layer equations 4. The boundary layer procedure 5. Laminar boundary layer on a flat plate a. 99% boundary layer thickness, b. shear stress at the wall, w c. total skin friction drag d. displacement thickness, * 6. Turbulent boundary layer on a flat plate 7. Boundary layers with pressure gradients a. some definitions b. physical explanation for flow separation c. which is better - laminar or turbulent boundary layer? IX. Flow over Bodies - Drag and Lift (Chapter 11) 1. Definitions (drag coefficient, lift coefficient) 2. Power required to overcome aerodynamic drag 3. Drag on automobiles 4. Drag on other objects B. Lift on Bodies 1. 2-D airfoils 2. 3-D wings and the effect of wing tips X. Introduction to Compressible Flow (Chapter 12) 1. Definitions and review (stagnation properties) 2. One-dimensional isentropic adiabatic flow in ducts (converging-diverging nozzles) 3. Choking B. Shock waves 1. Normal shocks 2. Oblique shocks and expansion waves

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