Fluid Dynamics

In the summer of 1941 Brown University undertook a Program of Advanced Instruction and Research in Mechanics. This in fact was the precursor to the present day Division of Applied Mathematics. Certainly an outstanding feature of this program must have been the lectures in Fluid Dynamics by Professor Friedrichs and the late Professor von Mises. Their notes were prepared in mimeograph form and given a wide distribution at that time. Since their appearance these lectures have had a strong influence on teaching and research in the subject. As the reader soon learns the notes have lost none of their vitality over the years. Indeed in certain instances only in the last few years has the -field caught up with the ideas developed in the course of these lectures. Many ideas of value are still to be found in these notes and the Editors are most happy to be able to include this volume in the series. The corrections which have accumulated over the years have been incorporated, and in addition an index has been added. With these exceptions all desire to revise has been resisted. Also in this connection we are very grateful to Dr. T. H. Chong for carefully overseeing the preparation of the present manuscript.

I — General Theory of Perfect Fluids.- 1. Equations of motion.- 2. Bernoulli equation.- 3. Circulation.- 4. Helmholtz’ vortex theory.- 5. Relation between vorticity and Bernoulli function.- 6. Equation for vortex-free motion.- 7. Momentum theorems for perfect fluid motion.- II — Motion in Two Dimensions-Airwing of Infinite Span.- 1. Steady motion of an incompressible fluid.- 2. Steady, irrotational motion of an incompressible fluid.- 3. Effect of uniform flow upon immersed bodies.- 4. Circular cross-section and theorem of Joukowski.- 5. Solution of the problem for a single wing profile.- 6. Examples of Airwing sections.- 7. The direct problem-theory of thin wings.- 8. Final remarks.- III — Motion in Three Dimensions-Airwing of Finite Span.- 1. Vortex lines and vortex sheets.- 2. Horseshoe vortex lines and sheets.- 3. Lanchester-Prandtl wing theory.- 4. Airwing of minimum drag.- 5. General problem.- 6. Formal solution of the integral equation.- 7. Application of the theory to the biplane.- IV — Theory of Viscous Fluids.- 1. Couette and Poiseuille flow.- 2. Navier-Stokes equation.- 3. Problems.- 4. Similarity.- 5. Small Reynolds number.- 6. Unsteady flow.- 7. Flow in convergent and divergent channels.- 8. Flow towards a plane plate.- 9. The mathematical structure of the boundary layer problem.- 10. Boundary layer equations.- 11. Flow along a flat plate.- 12. Displacement thickness — momentum equation.- 13. Jets and wakes.- 14. von Mises equations.- 15. Curves walls and separation.- 16. Instability of vortex motion.- V — Compressible Fluids.- 1. Equations of motion for compressible fluids.- 2. Introductory concepts of thermodynamics.- 3. Steady flow in one-dimensional treatment.- 4. Compression shocks.- 5. Non-steady one-dimensional flow.- 6. Two-dimensional,steady, adiabatic flow.- 7. Nearly constant, parallel flow.- 8. Flow in and around corners. Oblique shocks.- 9. Non-adiabatic flow and boundary layer.- Problems.- Problem 1.- Problem 2.- Problem 3,4,5,6.- Problem 7.- Problem 8,9,10.- Problem 11.- Problem 12.- Problem 13.- Problem 14,15.- Problem 16.- Problem 17,18.- Problem 19,20.- Problem 21.- Problem 22.- Problem 23,24.- Problem 25.- Problem 26.- Problem 27.- Problem 28.- Problem 29.- Problem 30.- Problem 31.