THE VISCOSITY OF GASES

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distance s from the plane which is at rest. If, with Joule, we
think of one-third of the molecules as moving in a direction which
is at right angles to the shear, then these molecules are the only
ones concerned in the transfer of momentum which is the cause
of viscosity in gases. Through a unit area of a plane separating
any two layers of fluid there will pass per second in either direc-
tion 1/QNV molecules, N being the number of molecules in a
unit volume and V their average velocity as calculated from the
kinetic energy. The molecule in passing through the given plane
comes from a distance which is equal to the molecular mean free
path L, and therefore from a plane in which the velocity is not v
but v — L in one direction and v + L in the other direction.
The molecule which diffuses into a more slowly moving layer
loses momentum represented by m(v — L), and similarly a
molecule diffusing into the more rapidly moving layer gains
momentum represented by m(v +1/), so that the total loss
of momentum is

t; - L) -

or since Nm = p

7? =

(97)

If the speed of the molecules 0 is the mean value as calculated
according to Maxwell's law of distribution, the formula for the
viscosity becomes, according to 0. E. Meyer (1889),
77 = 0.30967 QL (98)
Since the length of the mean free path varies inversely as the
pressure, whereas the density varies directly as the pressure,
it was seen at once that the viscosity of gases should be inde-
pendent of the pressure. This surprising result was confirmed
by 0. E. Meyer (1866) calculating out the measurements of
Graham, also by the measurements of Maxwell (1866) and 0. E.
Meyer (1865), and it did much to establish the kinetic theory.
With the acceptance of the kinetic theory it can be seen that vis-
cosity measurements give a very convenient and simple method
for the determination of the mean free path.