An Analytical Method for the Design of Two-Dimensional Contractions

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Abstract
Summary An analytical method is presented for the design of two-dimensional contractions. In this method, the complex potential of the flow of an infinite row of equally spaced line sources normal to a uniform stream is obtained. By adjusting the strength of the sources, the streamlines of the main stream are used as boundaries of two-dimensional contractions of various contraction ratios. It is found that, in all cases, there is a region in the main stream between two neighbouring sources in which the speed of flow increases monotonically along streamlines. Contractions formed by any of the streamlines in this region would therefore have favourable pressure distribution along their boundaries except for very small adverse pressure gradient at the inlet and outlet which are due to the introduction of parallel sections.

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