Simple Approximate Treatments of Certain Incompressible Duct Flow Problems Involving Separation

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Abstract
Many examples of abrupt conduit change, for example, sudden or gradual contractions, mitre bends etc., have been treated by free-streamline, potential flow theory in conjunction with the classical Borda result for sudden expansion loss. These analyses have provided results which show moderate but rarely close agreement with experimental evidence. Here a fresh and simpler look is taken at such problems, on the basis of radical simplifying assumptions about the flow geometry and pressure distribution. It is demonstrated that direct application of the linear momentum equation, in association, where appropriate, with the Bernoulli equation, can yield results for head loss and contraction coefficients which are in consistently good agreement with experimental data (especially as far as head loss is concerned). It is shown in passing that these simplified arguments can even be used to provide a satisfactory approximation to the profile of a contracting jet, suggesting wider applications of the method in more complex geometrical situations. The analysis is advanced in a teaching context to illustrate the power of momentum and energy methods in providing immediately useful solutions to certain problems involving abrupt change.

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