METHODS OF MEASUREMENT 5
decreases. At this point the regime of turbulent or hydraulic
flow begins. This will be studied in detail at a later point in
the development of the subject. There are substances, on the
other hand, for which the value of the above ratio increases
indefinitely as soon as the deforming force falls below a certain
minimum. These substances are said to be plastic. In plastic
flow it is generally understood that a definite shearing force is
required before any deformation takes place. But whether this
is strictly true or not has not been established.
The Coefficient of Viscosity.—Consider two parallel planes A
and B, s being their distance apart. If a shearing force F per
unit area give the plane A a velocity v in reference to B, the
velocity of each stratum, between A and B, as was first pointed
out by Newton, will be proportional to its distance from B.
The rate of shear dv/ds is therefore constant throughout a
homogeneous fluid under the above conditions. The possibility
that it may not be constant near a boundary surface will be
considered later. Since the force F is required to maintain a
uniform velocity, this force must be opposed by another which
is equal in amount due to the internal friction. The ratio of
this force to the rate of shear is called the coefficient of viscosity
and is usually denoted by the symbol rj
Fs m
>?=T (1)
The dimensions of viscosity are [MLrlT~1]. The definition of
viscosity due to Maxwell may be stated as follows: The vis-
cosity of a substance is measured by the tangential force on a
unit area of either of two horizontal planes at a unit distance apart
required to move one plane with unit velocity in reference to
the other plane, the space between being filled with the viscous
substance. The coefficient of fluidity is the reciprocal of the
coefficient of viscosity, so that if the former is denoted by <t> we
have <t> = -• The coefficient of fluidity may be independently
defined as the velocity given to either of two horizontal planes
in respect to the other by a unit tangential force per unit area,
when the planes are a unit distance apart and the space between
them is filled with the viscous substance.