*Bergman, Stefan (Brown University, Providence, R.I)*

*naca-tn-972*

*1945*

This report is devoted to the study of two-dimensional steady motion of a compressible fluid. It is shown that the complete flow pattern around a closed obstacle cannot be obtained by the method of Chaplygin. In order to overcome this difficulty, a formula for the stream-function of a two-dimensional subsonic flow is derived. The formula involves an arbitrary function of a complex variable and yields all possible subsonic flow patterns of certain types. Conditions are given so that the flow pattern in the physical plane will represent a flow around a closed curve. The formula obtained can be employed for the approximate determination of a subsonic flow around an obstacle. The method can be extended to partially supersonic flows.

*An Adobe Acrobat (PDF) file of the entire report:*

http://naca.central.cranfield.ac.uk/reports/1945/naca-tn-972.pdf