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On the steady motion of viscous liquid in a corner

Published online by Cambridge University Press:  24 October 2008

W. R. Dean  and
P. E. Montagnon
W. R. Dean
Affiliation:
Trinity CollegeCambridge
P. E. Montagnon
Affiliation:
Piepowder, Soldiers Rise, near Wokingham, Berks.
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Extract

1. In a steady two-dimensional motion of viscous liquid in the sharp corner formed by the rigid straight boundaries θ = 0, α, where r, θ are plane polar coordinates, it is found that, near enough to the corner, the most important term in the stream-function is of the form rmf(θ). The index m is evaluated in §§ 2–4 for values of α between 360 and 90°, and is found to be complex if α is less than about 146°; the limiting form of the stream-function when α is small is considered in § 5.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 3 , July 1949 , pp. 389 - 394
Copyright
Copyright © Cambridge Philosophical Society 1949

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References

REFERENCES

(1)Rayleigh, Lord.Scientific Papers, 6. (Cambridge, 1920), 18–21.Google Scholar
(2)Dixon, A. C.Proc. London Math. Soc. (2), 19 (1921), 373–86; J. London Math. Soc. 9 (1934), 61–74.CrossRefGoogle Scholar
(3)Ritz, W.Ann. Phys., Leipzig, 28 (1909), 760.Google Scholar
(4)Dean, W. R.Proc. Cambridge Phil. Soc. 32 (1936), 598 and 36 (1940), 300.CrossRefGoogle Scholar