以π试验设计的实验验证适用于不同阻力区段的球体沉降公式

Verification of the Theory for a Sphere Settling in Fluid With Resistance in Different Ranges by Experiment of π-Testing Design

摘要: 根据阻力系数Ｃ_Ｄ＝ｆ（Ｒｅ）的实验规律列出球体沉降中的阻力项，并建立微分方程，求得其解析解。经用π试验设计的实验进行验证：球体沉降理论公式的解与实测值间的误差为２％～２０％，而原理论公式的解的误差为１３６％～２４９％，证实了球体沉降理论公式的普遍意义。

Abstract: Based on the Diagram of Resistance Coefficient C_Ｄ versus Re , a resistance term and differential equation were formulated. Its analytical solution proved consistent with the experiment results with the error ranging from 2 %～20 %, while the solution of original differential equation has the error ranging from 136 %～249 %. That experiment was conducted with π-Testing Design. The settling equation of a sphere in fluid proved its generality in the sphere subject to resistance figuring in different ranges.