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Note on the slow motion of fluid

Published online by Cambridge University Press:  24 October 2008

W. R. Dean
W. R. Dean
Affiliation:
Trinity CollegeCambridge
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Extract

In this paper we consider the slow two-dimensional motion of viscous liquid past a sharp edge projecting into the stream, the motion being one of uniform shear apart from the disturbance caused by the projection. A special form is assumed for the boundary so that a method lately developed by N. Muschelišvili can be used in solving the biharmonic equation; a simple expression in finite terms is found for the stream function ψ1. Fig. 1 shows the section ABC of the fixed boundary of the liquid, the equation of the curve ABC is given in § 2, and ψ1 in § 3.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 36 , Issue 3 , July 1940 , pp. 300 - 313
Copyright
Copyright © Cambridge Philosophical Society 1940

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References

* Dean, W. R., Proc. Cambridge Phil. Soc. 35 (1939), 27–43.CrossRefGoogle Scholar

* Z. angew. Math. Mech. 13 (1933), 264–82.Google Scholar

* N. Muschelišvili, loc. cit. p. 265, equation (8).

† Loc. cit. p. 270, equations (33) and (34).

* It is simplest to postpone consideration of any singularities that the functions may have on the boundary.

* Proc. Cambridge Phil. Soc. 32 (1936), 598–613.Google Scholar

* From (36), sin θ cos 3θ; it can be verified that this is a first approximation to the term in ψ1 on the right-hand side of equation (18).

* Loc. cit. § 14.