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Some geometrical properties of plane flows

Published online by Cambridge University Press:  24 October 2008

A. G. Hansen  and
M. H. Martin
A. G. Hansen
Affiliation:
Institute for Flud Dynamics and Applied MathematicsUniversity of MarylandCollege Park
M. H. Martin
Affiliation:
Institute for Flud Dynamics and Applied MathematicsUniversity of MarylandCollege Park
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Extract

The geometrical configuration consisting of five straight lines tangent to the stream line (ψ = const.), isobar (p = const.), isocline (θ = const.), isovel (q = const.) and isopycnic (ρ = const.) at a point P of the physical plane in the plane flow of a fluid has a number of interesting properties. The study of this geometric configuration for a wide class of ideal fluids (which includes polytropic gases and incompressible fluids), in particular its properties at sonic points, is the purpose of this paper.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 4 , October 1951 , pp. 763 - 776
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

(1)Martin, M. H.Steady, rotational, plane flow of a gas. American J. Math. 72 (1950), 465–84.CrossRefGoogle Scholar
(2)Martin, M. H.Steady, plane, rotational, Prandtl-Meyer flows. NOLM 10346 Naval Ordnances Laboratory (1949), or J. Math. Phys. 29 (1950), 76–89.CrossRefGoogle Scholar
(3)Meyer, R. The method of characteristics for problems of compressible flow involving two independent variables. Proc. Int. Congr. Mech. (Paris, 1946).Google Scholar
(4)Lighthill, M. J.The hodograph transformation in transonic flow. I. Symmetrical channels. Proc. Roy. Soc. A, 191 (1947), 323–41.Google Scholar
(5)Martin, M. H.A new approach to problems in two-dimensional flow. Quart. Appl. Math. 8 (1950), 137–50.CrossRefGoogle Scholar
(6)Goursat, E.Cours d'analyse, 1 (1927), 100–2.Google Scholar
(7)Martin, M. H.Steady, plane, rotational, Prandtl-Meyer flow of a polytropic gas. J. Math. Phys. 29 (1951), 263–81.CrossRefGoogle Scholar
(8)Prim, R. On a family of rotational gas flows. NOLM 9369, Naval Ordnance Laboratory (1947).Google Scholar