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Hosoi, Anette, 2.26 Compressible Fluid Dynamics, Spring 2004. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 07 Jul, 2010). License: Creative Commons BY-NC-SA

Compressible Fluid Dynamics

Spring 2004

Photo of F-16 jet model in a wind tunnel test.
F-16 Scamp model being tested in NASA's Basic Aerodynamics Research Tunnel. Photo shows a basic flow visualization test using smoke and a laser light sheet to illuminate the smoke. (Photo courtesy of NASA.)

Course Highlights

This course features lecture notes and problem sets.

Course Description

2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department's sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer.

The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Meyer function; and self-similar compressible flows. The emphasis will be on physical understanding of the phenomena and basic analytical techniques.



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The grade will be based on homework and class participation and a term project as follows:

Homework and Class Participation 60%
Term Project 40%

The homework assignments will apply the material covered in lectures and are essential to learning that material. They will involve theory, modeling, and a few design exercises. The term project, comprised of a short oral presentation and a term paper, will be based on a student-selected topic related to some aspect of compressible fluid flow.

Textbooks and Reference Books

A number of excellent textbooks have been written on compressible fluid dynamics and related subjects. Three primary texts are used for this course (note that only one is required).

Primary Texts

 Thompson, P. A. Compressible Fluid Dynamics. New York, NY: McGraw-Hill, 1972. ISBN: 9780070644052. (Required)
This book is out of print, but reprints may be available from some university bookstores.

Landau, L. D., and E. M. Lifshitz. Fluid Mechanics. 2nd ed. Woburn, MA: Butterworth-Heinemann, 1995.

Liepmann, H. W., and A. Roshko. Elements of Gas Dynamics. Mineola, NY: Dover Publications, 2001. Originally from Wiley, 1957.

Reference Books

Oosthuizen, P. H., and W. E. Carscallen. Compressible Fluid Flow. New York: McGraw-Hill, 1997.

Saad, M. A. Compressible Fluid Flow. 2nd ed. Upper Saddle River, NJ: Prentice-Hall, 1993.

White, F. M. Viscous Fluid Flow. 2nd ed. New York: McGraw-Hill, 1991.
Good material on compressible boundary layer flows.

Zel'dovich, Ya. B., and Yu. P. Raizer. Physics of Shock Waves and High-Temperature Hydrodynamics Phenomena. Mineola NY: Dover Publications, 2002. 
Originally in two volumes from Academic Press, 1967; covers a wide range of advanced topics.

Courant, R., and K. O. Friedrichs. Supersonic Flow and Shock Waves. New York: Springer-Verlag, 1976.

Shapiro, A. H. Compressible Fluid Flow 1 and 2. Hoboken NJ: John Wiley & Sons, 1953.
Good coverage of one-dimensional flow.

Anderson, J. D. Modern Compressible Flow with Historical Perspective. 2nd ed. New York: McGraw-Hill, 1990.
Written from an aerodynamicists's perspective.

Vincenti, W. G., and C. H. Kruger. Introduction to Physical Gas Dynamics. Melbourne, FL: Krieger, 1975.
Good on molecular phenomena and shock wave structure.






Mass Conservation, Euler's Equation
Sound Speed, Mach Number



Ideal Gases
Steady Isentropic Flow, Stagnation State

Problem set 1 out (7 days after session 2)


Variable Area Flow, Choked Flow, Subsonic and Supersonic Nozzles, Restrictors



Energy Equation
Entropy Equation
Flow with Fricton, Fanno Line

Problem set 1 due


Flow with Heat Addition, Rayleigh Line
Shock Waves: Conservation Relations



Hugoniot Relation, Normal Shocks, Moving Shocks, Weak and Strong Shocks

Problem set 2 out


Oblique Shocks

Problem set 2 due


Continuum Shock Wave Structure
Condensation Discontinuities
Unsteady 1D Flows: Finite Amplitude Waves, Characteristics, Riemann Invariants



Piston Problems, Boundary Interactions, Shock Tubes

Problem set 3 out


Steady 2D Supersonic Flows: Mach Waves, Prandtl-Meyer Function, Expansion Fans

Problem set 3 due


Term Paper Presentations

Final project due
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