2.25
Fluid Mechanics
Survey of principal concepts and methods of fluid dynamics. Mass conservation, momentum, and energy equations for continua. Navier-Stokes equation for viscous flows. Similarity and dimensional analysis. Lubrication theory. Boundary layers and separation. Circulation and vorticity theorems. Potential flow. Introduction to turbulence. Lift and drag. Surface tension and surface tension driven flows.
Fall 2013 · Advanced Fluid Mechanics
Topics
- Introduction: Continuum Hypothesis; Thermophysical Properties
- The Material Derivative; Lagrangian and Eulerian Descriptions
- Kinematics of Deformation
- Forces and Stresses at a Point; Hydrostatic Pressure Variations; Rigid Body Motions
- Steady Bernoulli Equation Along / Across Streamlines; Unsteady / Generalized Forms of the Bernoulli Equation
- The Reynolds Transport Theorem
- Conservation of Mass / Energy / Entropy; Conservation of Linear Momentum
- Examples of Conservation of Linear Momentum; Conservation of Angular Momentum
- Conservation of Mass in Differential Form; The Constitutive Equation for Newtonian Fluid; Mechanical Pressure versus Thermodynamic Press
- The Navier Stokes Equation; Boundary Conditions for Navier-Stokes Equations
- Full Developed Flows, Couette and Poiseuille Flows, Stability of Viscous Flows
- The Buckingham Pi Theorem; Physical Significance of Dimensionless Variables
- Asymptotic Limits of the Governing Equations and Scaling with Dimensionless Variables
- Start-Up and Transient Flows; Similarity Solution for a Flat Plate (The Rayleigh Problem)
- Quasi-Fully Developed Flows: Lubrication Analysis
- Free Surfaces and Other Lubrication Flows
- The Velocity Potential and Stream Function; Complex Variable Formulation
- Examples of Potential Flow Solutions
- Definition of Circulation; Connection to Inviscid Flow and Vorticity; Rotational and Irrotational Flows
- Kelvin’s Circulation Theorems; Lift, Induced Drag; Airfoils, Lifting Lines, Propellers, Windmills
- Motivation and Scaling of the Boundary Layer Equations; Measures of Boundary Layer Thickness
- Boundary Layer on a Flat Plate; Effect of a Pressure Gradient: Falkner-Skan Solutions
- Flow Separation; Turbulent Boundary Layers
- Free Surface Force Balance; Scaling and Dimensional Analysis; Capillarity: Simple Static Solutions
- Examples of Flows Driven by Surface Tension
- Course Review
Readings
- Shapiro, Ascher H., and Ain A. Sonin. Advanced Fluid Mechanics Problems . (Self-published manuscript.)
- Kundu, Pijush K., and Ira M. Cohen. Fluid Mechanics . 6th ed. Academic Press, 2015. ISBN: 9780124059351.
- Tritton, D. J. Physical Fluid Dynamics . Springer, 2013. ISBN: 9780442301323.
- We will occasionally use this DVD in class:
- Homsy, G. M., ed. Multimedia Fluid Mechanics . 2nd ed. Cengage Learning, 2011. ISBN: 9780521721691.
Prerequisites & course information
Prereq: 2.006 or 2.06; Coreq: 18.075 or 18.085 G (Fall) 4-0-8 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2013
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.