Catalog description

" Derivation of governing equations of mass, momentum, and energy for a viscous, compressible fluid; general survey of vortex dynamics, potential flow, viscous flow, and compressible flow. (Every fall) "

Offerings

• next: unknown
• present: Fall 2019
• previous: Fall 1992, Fall 1993, Fall 1994, Fall 2000, Fall 2002

• Elementary fluid mechanics
• Differential equations

Topics

• Philosophy of continuum mechanics
• Some necessary mathematics
  • Vectors and Cartesian tensors
  • Solution of linear algebra equations
  • Eigenvalues and eigenvectors
  • Grad, div, and curl
  • General coordinate transformations
• Kinematics
  • Lagrangian description
  • Eulerian description
  • Material derivatives
  • Stremlines, pathlines, and streaklines
  • Kinematic decomposition of motion: translation, rotation, deformation
  • Expansion rate
  • Invariants of the strain rate and velocity gradient tensors
  • Two-dimensional kinematics
  • Three-dimensional kinetmatics
  • Kinematics as a dynamical system
• Conservation axioms
  • Mass
  • Linear momenta (Newton's second law of motion)
  • Angular momeenta
  • Energy (first law of thermodynamics)
  • Entropy inequality (second law of thermodynamics)
  • Integral forms
  • Summary of axioms
  • Incompleteness of the axioms
• Constitutive relations
  • Frame and material indifference
  • Second law restrictions
  • Fourier's law
  • Stress-strain rate relationship for isotropic, compressible, Newtonian fluids
  • Equations of state
• Full equation system and special cases
  • Boundary and interface conditions
  • Complete set of well-posed dimensionnless model equations
  • Incompressible Navier-Stokes equations
  • Euler equaitons
  • Dimensionles Navier-Stokes equations
  • First integrals of linear momenta
• Vortex dynamics
• Cylindrical coordinates
• Ideal rotational and irrotational vortices
• Helmholtz vorticity transport equation
• Kelvin's circulation theorem
• Potential flow of ideal point vortices
• Streamlines and vortex lines
• One-dimensional compressible flow
• Thermodynamics of general compressible fluids
• Generalized one-dimensional flow equations
• Flow with area change
• Normal shocks: ideal and non-ideal gas
• Flow with area change and normal shocks
• Method of characteristics
• Potential flow
• Stream functions and velocity potentials
• Mathematics of complex variables
• Elementary complex potentials
• Forces induced by potential flow
• Viscous, laminar flow
• Fully developed, one dimensional solutions
• Similarity solutions (Stokes' first problem and Blasius boundary layer)