Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/66



§ 31. Viscosity.—Definition.—The fundamental law of viscosity is enunciated in the form of an hypothesis to Section IX., Book II., of Newton's "Principia," as follows:—

The resistance arising from the want of lubricity in the parts of a fluid is, cæteris paribus, proportional to the velocity with which the parts of the fluid are separated from each other. The subsequent propositions li., lii., and liii., show that the expression "want of lubricity" is synonymous with the modern term "viscosity," and the motion contemplated by Newton in framing the foregoing hypothesis is motion in shear. The Newtonian law has since received ample verification at the hands of Maxwell and others.

Maxwell, in his "Theory of Heat," gives a quantitative definition of viscosity as follows:—

The viscosity of a substance is measured by the tangential force on the unit area of either of two horizontal planes at a unit distance apart one of which is fixed while the other moves with the unit of velocity, the space between being filled with the viscous distance. Or if (Fig. 26) a stratum of the substance of thickness I be contained between a fixed plane A B and the plane C D, moving from C towards D with a velocity V, then, when a steady state is established, the motion of the intervening fluid will be in the direction C to D, and its velocity at different points will be in proportion to the height above the plane A B, so that the fluid in immediate contact with the plane A B will remain at rest, and that in immediate contact with the plane C D will have the velocity V in common with it. Then, if F be the horizontal force