In this paper, we solve the Brinkman equation for unidirectional, steady, incompressible and Newtonian flow through a duct of uniform cross-section in the shape of a regular N-gon under no-slip boundary condition on the surface of the duct in the absence of applied forces. We calculate solutions for small values of N and by analysing them we devise a recursive scheme of generating solutions for all . We obtain approximate expressions for the vortex lines for all values of N by applying a trigonometric perturbation on circular vortex lines and graphically compare them with exact vortex lines. We also graphically compare both exact and approximate vortex lines with Schwarz-Christoffel transformation.

在本文中，我们通过均匀的横截面的以规则的形状的管道解决单向的，稳定的，不可压缩的和牛顿流动布林克曼方程Ñ边形下无滑动管道的在不存在在表面上的边界条件施加的力。我们计算N 的小值的解决方案，并通过分析它们，我们设计了一个为所有 生成解决方案的递归方案。我们通过对圆形涡旋线应用三角扰动来获得所有N值的涡旋线的近似表达式，并以图形方式将它们与精确的涡旋线进行比较。我们还通过 Schwarz-Christoffel 变换以图形方式比较了精确和近似涡旋线。