管流与明渠层流的总流机械能方程及机械能损失计算

The mechanical energy equation and the calculation of mechanical energy loss for total laminar flow in pipes and open channels

管流与明渠流同属流体力学中的内流,其总流机械能方程在水力学中称为总流能量方程。现有水力学中的总流能量方程是以理想不可压缩液体的伯努利方程为基础得到的,无法得到总流机械能损失的表达式。该文作者曾直接从黏性不可压缩流体运动的控制方程出发分别得到了管流及明渠流的总流机械能方程,解决了以上问题。考虑到层流条件下明渠流自由表面的变形特点,该文在前述工作基础上,将管流及明渠流在层流条件下的总流机械能方程进行了统一,同时还分别计算了管流(圆管、不同长短半轴比的椭圆管、不同宽高比的矩形管和不同内外径比圆环管)及明渠流(不同宽深比的矩形明渠)在层流条件下的总流机械能损失系数。结果表明:在同一雷诺数条件下,圆管层流的总流机械能损失系数比椭圆管层流、矩形管层流、圆环管层流及较大宽深比的矩形明渠层流的机械能损失系数要小。

Pipe flow and channel flow are internal flows in fluid mechanics. The mechanical energy equation for total flow is called energy equation for total flow in hydraulics. The energy equation for total flow in hydraulics was deduced based on the Bernoulli＇s equation for the incompressible ideal liquid. The formula of mechanical energy loss can not be obtained by this way. The energy equations for pipe flow and channel flow have been deduced from the governing equation of incompressible viscous flow respectively and the above problems have been solved. The unified energy equation for total laminar flow in pipes and open channels is obtained based on the existing results considering the free surface characteristics of laminar channel flow. The mechanical energy losses of laminar pipe flow（ flow in circular pipe, oval pipes with different semi-axes ratios, rectangular pipes with different width-depth ratios and ring-like pipes with different ratios of inner diameter and external diameter） and laminar channel flow（flow in open channels with different width-depth ratios） are calculated in this paper. The results show that the mechanical energy loss of circular pipe is less than those of other pipes and open channels when the Reynolds numbers are equal.