Note: this is just a general information page, not an official site for students enrolled in ME509.

Course Description

Continuum description and fluid properties. Basic laws for a continuum in integral and differential form. Kinematics of fluid flow and tensor calculus using index notation. Navier–Stokes equations and elementary solutions. Ideal fluid flow and basic inviscid hydrodynamics. Vorticity and streamfunction. Dimensional analysis of fluid mechanics problems. Boundary layer theory. Equations of motion for viscous flows. Viscous flow applications and lubrication theory. Instability and transition to turbulence.

Sample course profile.

Learning Objectives

Gain understanding of fundamentals of fluid mechanics through the derivation, application, and simplification of the Navier–Stokes equations. Apply this understanding to solve canonical and engineering fluid mechanics problems.

Typically offered in the Fall semester, and via EPE in odd years. 3 credit hours.


Undergraduate fluid mechanics/aerodynamics (e.g., ME 30900 or AAE 33400 at Purdue or equivalent), advanced calculus, linear algebra and differential equations.

Topics Covered

  1. Concept of a continuum and index notation.
  2. Eulerian and Lagrangian descriptions of a flow field.
  3. The Reynolds Transport Theorem and basic laws (mass, momentum, energy) for a continuum.
  4. Derivation of the Navier–Stokes equations of a Newtonian fluid and elementary solutions.
  5. Vorticity transport and vorticity-streamfunction equations.
  6. Dimensional analysis.
  7. Ideal fluids: potential flow theory and solutions in terms of complex variables.
  8. Derivation of Prandtl's boundary layer equations and solution of Blasius' problem.
  9. Low Reynolds number hydrodynamics, Stokes' equations and solutions.
  10. Lubrication theory and viscous flows with a small length scale.
  11. Introduction to hydrodynamic stability.
  12. Introduction to turbulence and Reynolds averaging.


Weekly assignments.




In-class midterm and a final.


R. L. Panton, Incompressible Flow, 4th ed., Wiley (2013).

Computer Requirements

Basic MATLAB, Python or equivalent knowledge to generate plots and solve differential equations numerically.