The mechanical viscosity of fluids

Abstract

The experiments described in the following paper were undertaken in order to investigate the relation between shearing stress and rate of distortion in fluids which are in eddying or sinuous motion, that is, motion in which the frictional resistance, at the boundaries of the solid over which they move, varies approximately as the square of the relative velocity, as distinguished from that steady or laminar motion in which the frictional resistance is proportional to the first power of the relative speed. This shearing stress has been called by Osborne Reynolds “mechanical viscosity,” i. e ., a “viscosity arising from the molar motion of the fluid and which is not a property of the fluid independent of its motion as is its physical viscosity.” Thus, to quote Reynolds’ statement, in the eddying motion of a fluid in a parallel channel, “although the mean motion at any point taken over a sufficient time is parallel to the axis of the pipe, it is made up of a succession of motions crossing the pipe in different directions.” In this case, the shearing stress at this point on a cylindrical surface coaxial with the pipe “will include the momentum per second parallel to the pipe carried by the cross streams across the surface on which this shearing stress is measured.” On the other hand, “the coefficient of physical viscosity is the coefficient of instantaneous resistance to distortion at a point moving with the fluid.”