42 FLUIDITY AND PLASTICITY
and the logarithms of the mean velocities as ordinates. For
tubes 4 and 5, Reynolds obtained the curves given in Fig. 13.
Linear flow exists along the line ABC, or A'B'C', the hydraulic
regime exists along the line BDEF or B'D'E'F'. It is evident now
that n is constant for each part of the curves for the two tubes
and that it is the same for both, i.e. the curves can be exactly
superimposed by merely a rectangular shift. The line ABC is
inclined at an angle of 45° so that n = 1, and the line BDEF is
inclined at an angle 30°-8' so that n = 1.723. Except for
the unstable region BCD, the formula P = KIn will represent the
viscosity in both regimes, it being necessary to merely change
the value of n in passing from one regime to the other.
In passing from B to C it is evident that the linear flow becomes
increasingly unstable, and thus is explained why the eddies
appear suddenly and full-fledged, when the disturbance is
sufficiently great. The more undisturbed the liquid is, the
farther is it possible to go from B.
\ The points along the curve CD (or C'D') correspond to the
mixed regime where the flashing occurs, the turbulent movement
alternating with the linear. Light has been thrown upon the
cause of the flashing by Couette (1890) and Brillouin (1907),
using a horizontal tube opening directly into the air. At high
pressures the surface of the jet had a sheet-glass appearance
indicating that the flow was hydraulic but the amplitude of the
jet was constant. As the pressure was lowered the velocity fell
to a point where linear flow began. But as the resistance was
much less in linear flow, the velocity increased as shown by the
increased amplitude of the jet, and the condition of hydraulic
flow was reestablished. The rapidity of these fluctuations
i | gradually increased as the pressure was further reduced, passed
through a maximum and gradually declined as the linear flow
came to predominate. Finally the jet became regular with a
plate glass surface.
It has been suggested that there are really three regimes, one
for velocities with which only linear flow can exist, a second for
velocities with which only turbulent flow can exist, and a third
where linear and turbulent flow alternate. The linear regime is
sharply marked off from the hydraulic regime by the point B
where the lines ABC and BDE intersect. While the period of