Subsonic Adiabatic Flow in a Duct of Constant Cross-Sectional Area

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Abstract
Summary Starting from the momentum integral equation an analysis is made of fully-developed flow in a straight pipe. This analysis shows the assumptions implicit in the one-dimensional theory of adiabatic constant-area flow with friction. For conditions of practical interest the approximations associated with the use of the one-dimensional flow theory are shown to be small. Flow with a developing velocity profile and flow in a bend are then analysed. Introducing approximations revealed in the analysis of fully-developed flow, a simple relation is obtained between the variation of mean flow properties along the duct under incompressible and compressible flow conditions. This relation may be written in the same form as the corresponding relation derived using the one-dimensional flow theory. In a similar manner to one-dimensional flow theory, the relation is readily extended to apply over a series of components of constant cross-sectional area. The results of the analysis are also presented in terms of static and total pressure loss coefficients. This form of presentation demonstrates that there are appreciable effects of Mach number, on the pressure loss coefficients, where they are often assumed to be small. The analysis does not enable the variation of the mean flow properties to be calculated ab initio. Its application is to be found in problems where a knowledge of the performance of a component, or series of components, is required under compressible flow conditions, the performance under incompressible flow conditions already being available from theoretical or experimental data. A comparison of predicted and experimental data for flow in bends and flow in combinations of duct components shows good agreement over much of the subsonic speed regime.

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