明渠层流的总流微分模型与最小能耗原理

Differential model of total flow and principle of minimum energy dissipation for laminar flow in open channel

明渠流是自然界与工程技术中广泛存在的一类流动.通过理论分析和推导,得到如下成果:1)以粘性流体力学理论为基础得到了明渠层流总流微分模型的控制方程,与以往的控制方程不同,该控制方程是由明渠中均质不可压缩粘性液体层流运动的流场控制方程与边界条件通过直接积分得到,其能实现明渠层流流场描述与总流描述的对接,且运动方程中的能坡有显示表达式;2)提出并证明了明渠恒定均匀层流的最小能耗原理.

Open channel flow is a type of flow that exists widely in nature and is used in engineering technologies. Through a theoretical analysis, this paper obtains the following results: 1) Based on the theory of viscous fluid dynamics, the governing equations of the laminar total flow differential model in an open channel are obtained and differ from the previous governing equations. The governing equation in this paper is derived from the control equation of homogeneous incompressible viscous fluid laminar flow in an open channel and the boundary conditions through direct integration, and it can realize the connection between the description of laminar flow field and the total flow in an open channel. Further, the total flow energy loss has a display expression. 2) The principle of minimum energy dissipation for a constant uniform laminar flow in open channels is proposed and proved.