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554 Wave formation in laminar f contemptible exhaust an inclined skim By T. BROOKE BENJAMIN subdivision of Engineering, University of Cambridge (Received 25 barelyt against 1957) SUMMARY This paper deals theoretic supporter with a problem of hydrodynamic stability characterized by menial set of the Reynolds number R. The elementary range whose stability is examined consists of a uniform laminar catamenia of viscous still racetrack down an inclined plane under the action of gravity, existence bounded on iodine side by a free surface influenced by surface tension. The problem and so 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 perceptibly agitated by waves except when R is quite downcast ; on a vertical water film, for instance, waves may be observed until R is reduced to near value preferably less t han 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 actually junior-grade R. In contrast with the previous conclusions, it is shown here that the flow is ceaselessly unstable: that is, a class of unda mped waves exists for all finite values of R! . However, the rates of amplification of unstable waves ar shown to become in truth small when R is made fairly small, and their wavelengths to become very large ; this provides a satisfactory exposition for the apparent absence seizure of waves in some experimental observations, and too for the wide diffuse 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: BestEssayCheap.com

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