Demonstration of Reversibility of Laminar Flow [video]
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See around the 13 minute mark: https://www.youtube.com/watch?v=51-6QCJTAjU
If you sit down and non-dimensionalize the Navier-Stokes equations, you end up combining viscosity, density, a representative velocity and some representative distance into what we call the Reynolds number (Re). There's two smart places you can put it, and for very slow flows that's in front of the nonlinear term. When Re << 1 you can neglect that term, and you get the Stokes equation, which is time-reversible. If you can grok what the convective derivative really means, this starts to make intuitive sense.
I said there's another place you can put the Reynolds number, and that's 1/Re in front of the viscous term. So if you have an extremely fast flow, you can neglect viscosity, which also makes intuitive sense. Such inviscid flows are the gateway into understanding turbulence.