208 
MESSRS. T. E. STANTON AND J. R. PANNELL ON SIMILARITY OF 
for either fluid, in any of the four pipes, from its mean value does not exceed 2*0 per 
cent., so that the similarity of the motions over this range is fully demonstrated. 
Below vd/v = 2500 there is a sudden fall in the value of the ordinate showing that 
a change in the character of the motion is taking place—a change which is revealed 
to the observer by the rapid fluctuations which take place in the resistance and render 
accurate determinations practically impossible. It appears that the fluctuations are 
due to the steepness of the curve in this region, so that small fluctuations of speeds of 
flow which would produce no appreciable effect on the resistance when the motion 
was fully eddying, cause such a relatively large change in the resistance that steady 
readings cannot be obtained. 
When this fall in the value of the ordinate occurs, it will be seen that a relatively 
small reduction in the value of the abscissae brings all the plotted points on the 
theoretical curve for stream-line resistance. As the theory of this type of motion is 
well known and its results have been constantly checked by observations of the 
resistance, it has not been considered necessary in the case of the air and water 
experiments to extend the curve further back than to values corresponding to 
vd/v — 1250. 
It will be noticed from the results plotted in fig. 3 that the values of vd/v at which 
the motion changes from sinuous to stream-line in character is practically constant 
for all the pipes except the smallest (0'361 cm. diameter). In the case of this small 
pipe, and to a much smaller but perceptible degree in the 07125 and 1'255 cm. pipes, 
it was found that, both for air and water, under the conditions of admission to the 
pipe, the stream-line motion tended to persist when the critical (2500) value of vd/v 
had been exceeded, until at some value of vd/v depending on the nature of the orifice 
and the amount of disturbance of the air at the inlet and possibly other factors the 
value of Ji/pV 2 suddenly rose to the value attained in the other pipes under similar 
conditions. 
In explanation of the apparently anomalous behaviour of this small pipe it may be 
recalled that Osborne Reynolds defined two critical velocities in pipes. One is the 
velocity at which a fluid, which enters a pipe in a high state of turbulence, passes 
from eddying motion to stream-line motion, and which is well defined in all the pipes 
used in these experiments except the small one under discussion. The other refers to 
the case in which a perfectly undisturbed fluid enters a pipe in stream-line motion 
which persists until, with considerable care, a velocity of about seven times that of the 
former critical velocity can be reached before it breaks down into eddying motion. 
If slight disturbances are present this breakdown occurs earlier. 
It is evident that the behaviour of the small pipe in these experiments is analogous 
to the second case of critical velocity mentioned by Reynolds, and that the 
turbulence existing outside the orifice to this pipe was not sufficiently violent to 
correspond to turbulent flow, whereas in the case of the other pipes it was so. 
Further confirmation of this was found in the fact that by fitting a bell mouth-piece 
