Mechanical Engineering 425, Fundamentals of Fluid Dynamics

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Catalog description

Basis for advanced courses in fluid dynamics. Stress, flow kinematics, rate of strain, material derivatives, and general balance equation. Navier-Stokes relationship. Reynolds number classification, Stokes flow, and Oseen's improvement.

Prerequisite: None.

Who takes it

This course is usually taken by graduate students majoring in Fluid Mechanics. Also, graduate students not majoring in Fluid Mechanics often take 425 as a part of their breadth requirement. Undergraduates interested in fluids, may take 425 as an elective. Graduate students usually start this series in the fall quarter of their first year.

What it's about

The first course is primarily focused on deriving the conservation equations and solving incompressible flow problems. One of the primary objectives is make the students well versed with indicial and vector notation - a critical tool in graduate studies.

Lectures:

These courses meet three days per week for 50 minute lectures. A sample course outline is given below:

  • Introduction:
    • Historical remarks
    • Properties of fluids and the continuum hypothesis
    • Classical thermodynamics
  • Vector calculus:
    • Symbolic or Gibbs notation and index notation
    • Tensors and tensor operations
    • Integral formulas
  • Kinematics:
    • Lagrangian and Eulerian descriptions
    • Stream, path and streak lines
    • Deformation and deformations-rate tensors
    • Vorticity and circulation
  • Conservation laws:
    • Conservation of mass
    • Momentum and energy
    • Introduction to Newtonian and non-Newtonian theologies derivation of Navier-Stokes equation
  • Laminar flows:
    • Pressure driven (Poiseuille) flows
    • Plane and circular Couette flows
    • Double falling film
    • Impulsively started plate (Stokes' first problem, the Rayleigh problem)
    • Oscillating plate (Stokes' second problem)
    • Diffusion of vortex sheet
    • Decay of line vortex (Oseen vortex).
  • Approximations of Navier-Stokes equation:
    • Non-dimensionalization of the governing equations
    • Introduction to various approximations of Navier-Stokes equation
  • Conclusion:
    • Remarks on computational fluid dynamics and experimental techniques in fluid dynamics

Assignment/Evaluation:

Homeworks, journal paper reading assignments, projects, mid-term and final exams.

Textbook:

Pijush K. Kundu & Ira M. Cohen, Fluid Mechanics, 2nd Ed, Academic Press, 2001.

Contact:

Professor: Neelesh Patankar
e-mail: n-patankar@northwestern.edu