Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-05T02:08:07.545Z Has data issue: false hasContentIssue false
  • English
  • Français

Transonic flow past finite wedges

Published online by Cambridge University Press:  24 October 2008

A. G. Mackie  and
D. C. Pack
A. G. Mackie
Affiliation:
University College (Dundee)University of st Andrews
D. C. Pack
Affiliation:
University College (Dundee)University of st Andrews
Get access Rights & Permissions [Opens in a new window]

Abstract

The solution for the flow of an incompressible fluid past an infinitely long wedge with a finite sloping edge (a finite wedge) is generalized by the hodograph method. In the flow thus obtained the axis of symmetry and a sloping edge of the wedge are again part of one streamline. It becomes possible to describe the flow of an ideal gas past a finite wedge if the hypothesis is made that the first singularity on this streamline, along the sloping edge, corresponds to the shoulder of the wedge. For a given wedge, with gradually increasing velocity at infinity upstream, the singularity appears at first at subsonic velocity. Beyond a certain critical velocity at infinity the singularity is always associated with the speed of sound. The hypothesis thus implies that put forward by Maccoll(9) and supported by Busemann(l). A qualitative examination shows that the solution reproduces experimentally known features of the flow of compressible fluid past a finite wedge.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 48 , Issue 1 , January 1952 , pp. 178 - 187
Copyright
Copyright © Cambridge Philosophical Society 1952

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Busemann, A.Tech. Notes nat. adv. Comm. Aero., Wash., no. 1858 (1949).Google Scholar
(2)Chaplygin, A.Ann. sci. Univ. Moscow, 21 (1904), 1. (Ministry of Supply, R.T.P. translation no. 1267.)Google Scholar
(3)Cherry, T. M.Proc. roy. Soc. A, 192(1947), 45.Google Scholar
(4)Craggs, J. W.Proc. Camb. phil. Soc. 44 (1948), 360.CrossRefGoogle Scholar
(5)Goldstein, S., Lighthill, M. J. and Craggs, J. W.Quart. J. Mech. appl. Math. 1 (1948), 344.CrossRefGoogle Scholar
(6)Hardy, G. H. and Wright, E. M.Theory of numbers (Oxford, 1938).Google Scholar
(7)Lighthill, M. J.Proc. roy. Soc. A, 191 (1947), 341.Google Scholar
(8)Lighthill, M. J.Proc. roy. Soc. A, 191 (1947), 352.Google Scholar
(9)Maccoll, J. W.Sixth Int. Congr. appl. Mech. (Paris, 1946).Google Scholar
(10)Molenbroek, P.Arch. Math. Phys., Lpz. (2), 9 (1890), 157.Google Scholar
(11)Pack, D. C.Rep. Memor. aero. Res. Coun., Lond., no. 2321 (1949).Google Scholar
(12)Tollmien, W.Z. angew. Math. Mech. 21 (1941), 140.CrossRefGoogle Scholar