中文摘要：

本文讨论了Y型二级管路分别在占地面积、体积以及占地面积、表面积约束下的最优管径比、最优管长比、最优分岔角度。优化方法采用拉格朗日乘子法和虚功原理方法。通过分析发现：最优树状管路的结构参数随约束条件和流动状态的变化而变化．这意味着对层流流动和湍流流动的情况，树状结构最优参数会表现出差异。本文的忧化结果为不同情况下的树状结构设计提供了基本参考。

英文摘要：

In this paper, the flow resistance of the two-level tree network is discussed in detail. The Lagrange- multiplier method and virtual work principle are applied. The optimal angles ,length ratio and diameter ratio are calculated systematically under different constraints （volume, surface）. It is found that the optimal structure parameters change with the flowing state and the given constraint. The optimization results world provide fundamental reference for the designers of fluid tree-shaped networks.