1. Approved for publication by Director, U.S. Geological Survey, January 23, 1986.
2. For example, see H.W. Liepmann and A. Roshko, Elements of Gasdynamics (Wiley, New York, 1957). For the sake of brevity, references in this paper are limited. The author has published detailed analyses of the three geologic problems discussed here in the references cited below, and the reader will find references to other relevant work in those papers.
3. This analogy was apparently first described by D. Riabouchinsky, C. R. Acad. Sci. 195, 998–999 (1932). For a more accessible reference, see Modern Developments in Gas Dynamics, edited by W.H.T. Loh (Plenum, New York, 1969), pp. 1–60.
4. For example, see P.A. Thompson, Compressible-fluid Dynamics (McGraw-Hill, New York, 1972), pp. 517–531.
5. In the spirit of emphasizing the similarity of the various flow fields discussed in this paper, the word “nozzle” will be used interchangeably with the words “flume”, “channel”, and “conduit”, and the word “contouring” will be used interchangeably with the word “eroding”.