22

FLUIDITY AND PLASTICITY

almost reached, and there the acceleration is very rapid. Even
when the stream lines in the main part of the capillary are linear,
it seems theoretically necessary to assume that there is a choking
together of the stream lines near the entrance as indicated at c.
It has been suggested that this effect might be prevented by
using rounded or trumpet-shaped openings as indicated at d.

At the exit of the capillary, the stream continues on into
the reservoir B for a considerable distance with its diameter
apparently unchanged. However the fall in pressure of the
liquid passing through the large tube B is negligible, so that the
flow observed just beyond the exit takes place at the expense—
not of pressure—but of kinetic energy taken up at the entrance.
There is no distortion of the stream lines just within the exit end
of the capillary, and it is not clear that any correction at this end
is necessary, under the conditions which we have depicted. If
the capillary opens into the air, there will naturally be a capil-
larity correction and the shape and material of the end of the
tube will be of importance—cf. Ronceray (1911).

That the stream should continue for some distance beyond
the exit with apparently constant diameter seems at first sight
quite surprising, as one might suppose that the stream would at
once drag along the adjacent fluid. The explanation is not far to
seek. In the first place one should remember that the velocities
even in the capillary are by no means uniform. Equation (3)
tells us that particles which at a given moment are in a plane
surface mno will after a certain time has elapsed be in a paraboloid
surface mpo. The transition from the stationary cylinder of
fluid in contact with the wall to the coaxial cylinders having
high speed is apparently abrupt. As the exit of the capillary is
passed, there is nothing to prevent the larger mass of liquid
from being drawn along except its own inertia. But the rate at
which the kinetic energy of the inner coaxial cylinders of fluid
passes out into the outer cylinders is proportional to the viscosity
of the medium and to the area of the cylinder. Thus in a fluid of
low viscosity a capillary stream will penetrate for some distance.
The stream disappears rather suddenly due probably to the
development of eddies.

Couette has attempted to evaluate the effects of the ends of
the tubes by supposing that they are equivalent to an addition to

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