The Meaning of Viscometry in Fluid Dynamics

Of Navier-Stokes equations Lamb (1895, §326) wrote that they embodied the simplest hypothesis we can frame and, citing authority of Reynolds, that this hypothesis has been put to a severe test in experiments of Poiseuille and others, [so that] we can hardly hesitate to accept equations in question as a complete statement of laws of viscosity. The particular consequence of Navier-Stokes theory which the experiments of Poiseuille and others tested under a very wide range of values of rates of distortion is law of fourth power for discharge D of an incompressible fluid of shear viscosity J1 from a circular pipe of radius R through which it is driven by a pressure gradient a: