What is meant by the inertial stress in the definition of Reynolds number? Reynolds number = Inertial stress/ viscous stress


The quick answer to your question is that the "inertial stress" as referenced in the Reynolds number definition is equivalent to a dynamic pressure $\rho v^2$, where $\rho$ and $v$ are some characteristic density and speed of the flow respectively.

Note that this isn't a unique way of defining the Reynolds number; you can do it by taking the ratio of "inertial forces" to viscous forces as in this answer. The key concept is that the Reynolds number compares the inertial effects of a flow to the viscous effects of a flow, and that can be done through any number of equivalent ratios (inertial to viscous length scales, etc.)

  • $\begingroup$ Shouldn't the dynamic pressure have a 2 in the denominat0r? $\endgroup$ – Chet Miller Jul 11 '18 at 3:18
  • $\begingroup$ For the dynamic pressure referenced in the Bernoulli equation, it would indeed carry a factor of $\frac{1}{2}$; however, the typical definition of characteristic dynamic pressure used for the definition of a Reynolds number doesn't. This is because the particular form of Reynolds number the OP describes is $Re = \frac{\rho v^2}{\mu \frac{v}{L}}$, which straightforwardly simplifies to its common form; but the addition of constant flow-independent factors is common and perfectly fine in defining Reynolds numbers as long as you do the proper book-keeping for it. $\endgroup$ – aghostinthefigures Jul 11 '18 at 3:29
  • $\begingroup$ What is dynamic pressure? Is it different than pressure? That is force/area?? And also with the characterstic density? $\endgroup$ – user182794 Jul 11 '18 at 5:44
  • $\begingroup$ This definition of dynamic pressure is proportional to a characteristic kinetic energy density of the fluid, which is naturally a function of a characteristic mass density and speed. It’s not the same thing as “normal” or mechanical pressure (which is the mean isotropic stress at a point), but note that it has the same units as pressure or force per area, so it’s the same -type- of object. $\endgroup$ – aghostinthefigures Jul 11 '18 at 5:50
  • $\begingroup$ Hello sir , sorry for being such a naive in physics, Sir can you please tell me what is this "characterstic" in the the above answers when you used characterstic density and characteristics kinetic energy density , pardon me sir again for being such a naive $\endgroup$ – user182794 Jul 11 '18 at 10:31

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