This is such a widely used number in fluid dynamics that it’s easy to be embarrassed to ask questions about it. That’s a shame. As with so many things in engineering, the fine print can be confusing and is often unclear at best, uncertain at worst.
The Reynold’s number indicates the relative importance of different forms of energy in a flow: inertial and viscous, as most references will explain. Forget that for a while, and consider why we calculate it.
It is most often used to determine whether a flow is turbulent or not. This is great for flow in a circular pipe, where the length of the pipe and its diameter are the only two important dimensions. But there are so many flows that engineers wrestle with that are not in pipe – flow around an aircraft, for example. Unlike circular pipes, the relevant dimensions for such flow domains are not unique.
You should certainly know the formula for Re (it’s easy enough to remember, and you should feel embarrassed if you fumble) but the values associated with it (both the dimensions and the value that separates turbulence from laminar flows) can depend on the engineering application you’re working on.
Coda: if you’re not concerned with fluid dynamics, there’s really no reason to learn anything about this.
