Stationary incompressible Newtonian fluid flow governed by external force and external pressure is considered in a thin rough pipe. The transversal size of the pipe is assumed to be of the order \(\varepsilon \), i.e., cross-sectional area is about \(\varepsilon ^{2}\), and the wavelength in longitudinal direction is modeled by a small parameter \(\mu \). Under general assumption \(\varepsilon ,\mu \rightarrow 0\), the Poiseuille law is obtained. Depending on \(\varepsilon ,\mu \)-relation (\(\varepsilon \ll \mu \), \(\varepsilon /\mu \sim \mathrm {constant}\), \(\varepsilon \gg \mu \)), different cell problems describing the local behavior of the fluid are deduced and analyzed. Error estimates are presented.

在细的粗管中考虑了受外力和外压控制的固定不可压缩牛顿流体流。假定管道的横向尺寸为\（\ varepsilon \），即截面积约为\（\ varepsilon ^ {2} \），并且纵向波长由一个小模型建模。参数\（\ mu \）。在一般假设\（\ varepsilon，\ mu \ rightarrow 0 \）下，获得了Poiseuille定律。取决于\（\ varepsilon，\ mu \）关系（\（\ varepsilon \ ll \ mu \），\（\ varepsilon / \ mu \ sim \ mathrm {constant} \），\（\ varepsilon \ gg \ mu \）），推导并分析了描述流体局部行为的不同单元问题。给出误差估计。