On 15 March 1883, Osborne Reynolds presented the results of ‘An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels’ to the Royal Society of London. It was first published in the Proceedings of the Royal Society (Reynolds 1883a), followed by a longer account in the Philosophical Transactions of the Royal Society (Reynolds 1883b). The longer paper incorporates the brief one as §I and contains comprehensive documentation of his experiments as well as the famous sketch of his experimental rig, which to this day is preserved at Manchester University. The historical probes into the archives of the Royal Society by Jackson & Launder (2007) showed that the referees were well aware of the significance of the contribution: Lord Rayleigh observes that ‘the paper records some well contrived experiments on a subject which has long needed investigation .’, and Sir George Stokes emphasizes that Osborne Reynolds ‘shows for the first time that the distinction between regular and eddying motion depends on a relationship between the dimensions of space and velocity’. That dimensionless relationship became later known as the Reynolds number (see von Ka´rma´n (1954) and Rott (1990) for the historical developments). For flow in a pipe, the Reynolds number is usually based on the mean flow speed U, the diameter of the pipe d and the kinematic viscosity of the fluid n,