# Reynolds Number

We know that the Reynolds Number is $R_e=\frac{\rho vd}{\eta}$ ($\rho$ density, $v$ velocity, $d$ diameter and $\eta$ the viscosity of fluid).

We also know that an ideal fluid has no viscosity which means that $\eta=0$ and what we get is $R_e=\frac{\rho vd}{0}$. Does this mean that the ideal fluid doesn't have a Reynolds Number?

In my book it says that every fluid has it's own Reynolds Number.

Can anybody help me?

Thank you!

At the moment the answer to your question is still matter of active research. In many aspects liquid helium at very low temperatures is an ideal fluid but the Reynolds number is still finite (Barenghi, 2008).

So it seems that every fluid has a finite Reynolds number and only in a gedanken experiment one can have an infinite Reynolds number.

Barenghi, C., "Is the Reynolds number infinite in superfluid turbulence?", Physica D: Nonlinear Phenomena, V. 237, 15 Aug. 2008, pp 2195–2202.

1) The Reynolds number is a combination of fluid properties, $\eta/\rho$, and flow properties, $vd$. So yes, for a given flow profile, every fluid has its own Reynolds number.