Exact flows are calculated for an infinite set of pipe cross-sections, each with variable corrugations, ranging from angular to smooth as a parameter varies. The results are compared with three ‘rules of thumb’ which give general but approximate formulae for the rate of flow through a pipe of given cross-sectional shape. These are (i) the Saint-Venant formula, in which the flow is related to the area and the polar moment J about the centroid of the pipe cross-section; (ii) the Aissen approximation, in which the flow is approximated in terms of the pipe cross-sectional area A and the diameters of the inscribed and circumscribed circles; and (iii) the area–perimeter or hydraulic radius approximation of various authors, which states that for a given pressure gradient and fluid viscosity the total flow rate through a pipe of given cross-section is proportional to A 3 / P 2 where P is the perimeter length of a pipe section normal...

中文翻译：

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穿过波纹管的层流：精确解和近似解的比较

计算出无限大的管道横截面的精确流量，每个横截面具有可变的波纹，随着参数的变化，波纹的变化范围从角度到平滑。将结果与三个“经验法则”进行比较，这三个“经验法则”给出了通过给定横截面形状的管道的流速的通用但近似公式。这些是（i）Saint-Venant公式，其中流量与面积和围绕管道横截面质心的极矩J有关；（ii）Aissen近似法，其中，以管道横截面面积A和内接和外切圆的直径来近似流量；（iii）不同作者的面积-周长或水力半径近似值，