Micione

554

Wave formation in laminar f miserable exhaust an inclined skim
By T. BROOKE BENJAMIN Department of Engineering, University of Cambridge
(Received 25 butt against 1957)

SUMMARY This paper deals theoretic ally with a problem of hydrodynamic stability characterized by small values of the Reynolds number R. The elementary flow whose stability is examined consists of a uniform laminar catamenia of viscous liquid running down an inclined plane under the action of gravity, being bounded on iodine side by a free surface influenced by surface tension. The problem thus has a direct drift on the properties of thin liquid films such as bind important uses in chemical engineering. Numerous experiments in the agone have shown that in flow down a fence in the stream is noticeably agitated by waves except when R is quite small ; on a vertical water film, for instance, waves may be observed until R is reduced to near value rather less than 10. The present treatment is thence based on methods of approximation suited to pretty low values of R,and t presentby avoids the severe mathematical difficulties usual in stability problems at high R. The formulation of the problem resembles that granted by Yih (1954); but the method of solution differs from his, and the respective results ar in conflict.



In particular, there is disagreement over the bailiwick of the stability of a strictly vertical stream at very small R. In contrast with the previous conclusions, it is shown here that the flow is always unstable: that is, a class of undamped waves exists for all finite values of R. However, the rates of amplification of unstable waves ar shown to become very small when R is made fairly small, and their wavelengths to become very large ; this provides a satisfactory exposition for the apparent absence of waves in some experimental observations, and too for the wide scatter among existing estimates of the quasi-critical value of R under which waves are undetectable. In view of the controversial nature of...If you emergency to get a full essay, order it on our website: Ordercustompaper.com



If you want to get a full essay, wisit our page: write my paper