MECH 221 FLUID MECHANICS (Fall 06/07) Tutorial 1
MECH 221 Fluid Mechanics (Fall Semester 2006/2007) Instructor: Prof. C. T. Hsu, Mechanical Engineering Email:mecthsu@ust.hk Tel: 2358-7188 ; Office: Rm 2561 Office hour – to be arranged Prerequisites: MATH 100/101 & MATH 150/151 Lecture Time: Tue & Thu; 12:00 – 13:20 Classroom: Rm 1403 Tutorial Time: Wed; 09:00 – 09:50 Classroom: Rm 2503 Leading TA: SIN Ka Fai, Kelvin (meskf@ust.hk) Second TA: CHAU Man Hei (mehei@ust.hk) Tel: 2358-8808 ; Office: Rm 1213; Office hour: Wed; 15:00 – 16:30
Assessments #Homework = 10 points Mid term Exam = 30 points Final Exam = 45 points *Others = 15 points # Home works distributed through website every week on Wednesday. Due one week after distribution (collected after tutorial) https://teaching.ust.hk/~mech221/ * Including short quiz, attendance, classroom behavior, etc
Course Focus Fundamental Concepts Fluid Statics Fluid Kinematics, Integral and Differential Equations of Fluid Flows Conservation of Mass, Momentum and Energy Dimensional Analysis Inviscid Flows, Boundary Layer Flows, Pipe Flows, Open Channel Flows
Course Notes Text Book: Fundamentals of Fluid Mechanics, 5th or 4th edition B.R. Munson, D.F. Young and T.H. Okiishi, Wiley and Sons, 2005 or 2002 Most materials are available from course web https://teaching.ust.hk/~mech221/ Reading the handout may not be sufficient. It is useful to take notes as the instructor explains concepts and elaborates on the handout
Syllabus 1. Introduction (Chapter 1) Week 1 2. Fluid Statics (Chapter 2) Weeks 2-3 3. Fluids in Motions (Chapter 3) Weeks 3 -4 4. Kinematics of Fluid Motion (Chapter 4) Weeks 4-5 Integral and Differential Forms of Equations of Motion (Chapters 5 & 6) Weeks 6-8 Mid-term Week 8 6. Dimensional Analysis (Chapter 7) Week 9 7. Inviscid Flows (Chapter 6) Week 10 8. Boundary Layer Flows (Chapter 9) Weeks 11-12 9. Flows in Pipes (Chapter 8) Weeks 12-13 10. Open Channel Flows (Chapter 10) Weeks 13-14 Summary Review Week 14 Final According to the University Schedule
Historic Background Prandtl (1875-1953) Fluid Mechanics is the modern science developed mainly by Prandtl and von Karman to study fluid motion by matching experimental data with theoretical models. Thus, combining Aero/Hydrodynamics with Hydraulics. Indeed, modern research facilities employ mathematicians, physicists, engineers and technicians, who working in teams to bring together both view points: experiment and theory. Von Karman (1881-1963)
Do you know….? Tsien Hsue-shen (錢學森) Father of Chinese Rocketry Student of von Karman in 1936 From left to right: Ludwig Prandtl, H.S. Tsien, Theodore von Kármán
Fluid Mechanics Definition “Fluid”: a substance that deforms continuously when acted on by a shearing stress of any magnitude. “Mechanics”: the branch of applied mathematics that deals with the motion and equilibrium of bodies and the action of forces, and includes kinematics, dynamics, and statics. “Fluid mechanics”: a branch of science that studies the mechanics of those free moving particles.
Mechanics of Particle Liquid Gas
Fluid Modeling Microscopic: Mesoscopic: Macroscopic: Study the behavior of molecules VERY complicated!!! Mesoscopic: Statistical physics Macroscopic: Continuum assumption Navier-Stokes Equation
Continuum Assumption What does “large enough” mean?? …… A fluid particle is a volume large enough to contain a sufficient number of molecules of the fluid to give an average value for any property that is continuous in space, independent of the number of molecules. What does “large enough” mean?? How can we determine??
Continuum Assumption Knudsen number: Kn = / L - mean free path L - characteristic length
Continuum Assumption For continuum assumption: Kn << 1 • Kn < 0.001 - Non-slip fluid flow - B.C.s: no velocity slip - No temp. jump - Classical fluid mechanics • 0.001< Kn < 0.1 - Slip fluid flow - Continuum with slip B.C.s • 0.1< Kn< 10 - Transition flow - No continuum, kinetic gas • 10<Kn - Free molecular flow - Molecular dynamics
Example 1 For air duct: Kn = 10-7/(0.0254) = 3.937x10-6 < 0.001 Characteristic scales for standard air: -> mean free path, (sea level) ~ 10-7 m Characteristic length (L): -> Diameter of the duct (D) = 1 inch (25.4mm) Kn = 10-7/(0.0254) = 3.937x10-6 < 0.001 (Continuum and non-slip fluid flow) D Air flow
Example 2 For airplane: Kn = 10-7/(10) = 10-8 < 0.001 Characteristic scales for standard air: -> mean free path, (h=sea level) ~ 10-7 m Characteristic length (L): -> Length of the airplane = 10m Kn = 10-7/(10) = 10-8 < 0.001 (Continuum and non-slip fluid flow) L h
Example 3 For micro-channel: Kn = 10-7/(10-6) = 0.1 Characteristic scales for standard air: -> mean free path, (sea level) ~ 10-7 m Characteristic length (L): -> Width of the micro-channel = 1μm = 10-6m Kn = 10-7/(10-6) = 0.1 (Slip fluid flow? Transaction flow? Or others?) L
Properties Thermodynamical Physical Mean free time - n Convection time scale - s Mach number – M Physical REV – Representative Elementary Volume Density - Viscosity - µ
Viscosity Power law: = k ( u/ y)m Newtonian fluid: k = µ, m=1 Non-Newtonian fluid: m1 Bingham plastic fluid: = 0 +µu/y : Shearing stress [N/m2] µ: dynamic viscosity [kg/(m.s)] : kinematic viscosity: = µ/ [m2/s]
Dimensional Analysis (MLT) Primary quantities: Mass: M Length: L Time: T Example: Velocity: Length/Time = LT-1 Momentum: Mass x Velocity = MLT-1 Density: Mass/Volume = ML-3
Unit conversion Length Volume Energy Power Mass Force Pressure 1 inch = 25.4mm Volume 1 L = (10cm)3=0.001m3 Energy 1 Btu = 1055.056J 1 kcal = 4186.8J 1 kWh = 3,600,000J Power 1 hp(UK) = 745.7W Mass 1 lbm = 0.4536kg Force 1 lbf = 4.448N Pressure 1 bar = 100,000Pa 1 psi = 6894.757Pa 1 mmHg = 133Pa (γHg = 133kN/m3)