Stokes’ hypothesis states that the bulk viscosity of a Newtonian fluid can be set to zero. Although not valid for many fluids, it is common practice to invoke this hypothesis in the study of low-Mach-number, variable-density flows. Based on scaling arguments, we provide a necessary condition for neglecting the bulk viscous pressure from the governing equations. More specifically, we show that the Reynolds number defined with respect to the bulk viscosity must be very large. We further show that even when this condition is not satisfied, the bulk viscous pressure does not need to be taken explicitly into account in the computation of the velocity field because it can be combined with the hydrodynamic pressure.

中文翻译：

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斯托克斯假设对低马赫数流的适用性

斯托克斯的假设指出，牛顿流体的体粘度可以设置为零。尽管不适用于许多流体，但通常的做法是在研究低马赫数，可变密度流时引用此假设。基于比例论证，我们为从控制方程式中忽略总粘性压力提供了必要条件。更具体地说，我们表明相对于本体粘度定义的雷诺数必须非常大。我们进一步表明，即使不满足该条件，在速度场的计算中也不需要明确考虑整体粘性压力，因为它可以与流体动力压力相结合。