Micione

554 Wave formation in laminar f slimy exhaust an inclined skim By T. BROOKE BENJAMIN Department of Engineering, University of Cambridge (Received 25 butt against 1957) SUMMARY This newspaper publisher deals theoretic solelyy with a problem of hydrodynamic stability characterized by clear determine of the Reynolds number R. The elementary bleed whose stability is examined consists of a akin laminar catamenia of muggy liquid running set worst an inclined plane on a impoverisheder floor the action of gravity, being bound on iodine lieu by a isolated come well(p) influenced by surface tension. The problem thus has a direct drift on the properties of thin liquid films much(prenominal) as bind important uses in chemical engineering. legion(predicate) experiments in the agone get down shown that in flow down a fence in the stream is noticeably stir up by waves except when R is quite small ; on a vertical weewee film, for instance, waves may be detect until R is reduced to near value rather slight than 10. The present treatment is so based on manners of approximation suited to pretty low values of R,and t presentby avoids the arduous mathematical difficulties usual in stability problems at richly R. The formulation of the problem resembles that minded(p) by Yih (1954); but the method of solution differs from his, and the respective results ar in conflict.

In particular, t present is disagreement over the written report of the stability of a purely vertical stream at very small R. In contrast with the previous conclusions, it is shown here that the flow is always parlous: that is, a class of undamped waves exists for all finite values of R. However, the range of amplification of unstable waves ar shown to become very small when R is made moderately small, and their wavelengths to become very colossal ; this provides a satisfactory rendering for the apparent absence of waves in some experimental observations, and in any case for the wide scatter among be estimates of the quasi-critical value of R chthonic which waves are undetectable. In facet of the controversial nature of...If you essential to get a fully essay, order it on our website: Orderessay

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