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A New Exact Solution of One Dimensional Steady Gradually Varied Flow in Open Channels

机译：明渠一维稳定渐变流动的新精确解

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摘要

One dimensional steady gradually varied flow in open channels is of academic and practical importance. Ita been studied for various applications and in various contexts since the 19th Century. There several classes of gradually varied flow; i.e., one or more dimensions, steady and transient flows. Gradually varied flow may occur in several channel geometries comprising rectangular, trapezoidal, parabolic bottom surfaces and diverse configurations: simple channels, compound channels, and channel networks. The wide rectangular channel case is of particular interest in its own right, as well as serving as a validation benchmark for transient, and multiple dimensional gradually varied flow, the latter normally solved by numerical techniques and therefore requiring calibration. In this paper, a new exact analytical and easy to compute solution is developed. It is shown that this solution possesses the ease of computation as an advantage in comparison with existent exact solutions reported in the literature. As this solution involves a multiple valued function, it is consistent with the nonuniqueness propert of the intial value problem of one dimensional steady gradually varied flow.
机译：在开放渠道中一维稳定，逐渐变化的流动具有学术和实践意义。自19世纪以来，已经针对各种应用和各种环境对它进行了研究。有几类逐渐变化的流量。即一个或多个维度，稳定和短暂的流量。逐渐变化的流量可能会在几种通道几何形状中发生，包括矩形，梯形，抛物线形的底面和各种配置：简单通道，复合通道和通道网络。宽矩形通道的情况本身特别令人关注，并且可以用作瞬态和多维逐渐变化的流量的验证基准，后者通常由数值技术解决，因此需要校准。在本文中，开发了一种新的精确分析且易于计算的解决方案。结果表明，与文献报道的精确解相比，该解决方案具有易于计算的优点。由于该解决方案涉及一个多值函数，因此它与一维稳定逐渐变化的流量的初值问题的非唯一性一致。

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