an expression first proposed by L. M. H. Navier. The coefficient [mu]
is termed the coefficient of viscosity.
According to J. Clerk Maxwell, the value of [mu] for air at [theta]°
Fahr. in pounds, when the velocities are expressed in feet per second,
is
[mu] = 0.0000000256 (461° + [theta]);
that is, the coefficient of viscosity is proportional to the absolute
temperature and independent of the pressure.
The value of [mu] for water at 77° Fahr. is, according to H. von
Helmholtz and G. Piotrowski,
[mu] = 0.0000188,
the units being the same as before. For water [mu] decreases rapidly
with increase of temperature.
[Illustration: FIG. 2.]
§ 4. When a fluid flows in a very regular manner, as for instance when
It flows in a capillary tube, the velocities vary gradually at any
moment from one point of the fluid to a neighbouring point. The layer
adjacent to the sides of the tube adheres to it and is at rest. The
layers more interior than this slide on each other. But the resistance
developed by these regular movements is very small. If in large pipes
and open channels there were a similar regularity of movement, the
neighbouring filaments would acquire, especially near the sides, very
great relative velocities. V. J. Boussinesq has shown that the central
filament in a semicircular canal of 1 metre radius, and inclined at a
slope of only 0.0001, would have a velocity of 187 metres per second,[2]
the layer next the boundary remaining at rest. But before such a
difference of velocity can arise, the motion of the fluid becomes much
more complicated. Volumes of fluid are detached continually from the
boundaries, and, revolving, form eddies traversing the fluid in all
directions, and sliding with finite relative velocities against those
surrounding them. These slidings develop resistances incomparably
greater than the viscous resistance due to movements varying
continuously from point to point. The movements which produce the
phenomena commonly ascribed to fluid friction must be regarded as
rapidly or even suddenly varying from one point to another. The internal
resistances to the motion of the fluid do not depend merely on the
general velocities of translation at different points of the fluid (or
what Boussinesq terms the mean local velocities), but rather on the
intensity at each point of the eddying agitation. The problems of
hydraulics are therefore much more complicated than problems in which a
regular motion of the fluid is assumed, hindered by the viscosity of the
fluid.