库特(Couette)剪切流准确解的一般形式

AN EXACT SOLUTION FOR COUETTE SHEAR FLOW

从N S方程出发 ,得到了轴对称异型断面管纯剪切流动速度分布的一般解 ,进而推出了纯剪切流动有限宽度矩形断面管的速度分布和流量计算公式 ,证明了库特剪切流是有限宽度矩形断面管当宽度趋向无穷大时的一种特例。并对库特剪切流流量的计算误差进行了分析 ,给出了该公式的适用范围 ,同时对有限宽度矩形断面管剪切流公式进行了曲线拟合 ,得到了便于工程使用的流量计算公式。

An exact solution of velocity distribution for Couette shear flow in a non circular conduit with axial symmetry section is obtained in this paper.From the solution,velocity and flow rate for the rectangular section conduit with finite width are obtained,and it is concluded that Couette shear flow is just a special example when the width is just infinite in the rectangular section conduit flow.Further,we analyzed the error of the solution,and the range in which the formula is suitable is given.An appropriate formula which is easy to use in engineering was obtained based on the results.