40

FLUIDITY AND PLASTICITY

velocity is increased the surface takes on a sheet glass appearance
due to the sinuous motions, and finally the stream breaks into
eddies and is lost to view (cf. Collected Papers 2, 158).

Reynolds reasoned from the equations of motion that the
birth of eddies should depend upon a definite value of

pRI<p

where R is a single linear parameter, as the radius of the tube,
and I is a single velocity parameter, as the mean velocity of flow
along the tube. Reynolds found the value of the constant to be
approximately 1,000, hence, the maximum mean velocity in
centimeters per second for which we may expect linear flow, may
be taken to be

1,000

i =

(14)

In Table XIV we have calculated the value of the product
pRIp from some of Reynolds' observations near the critical
velocity.

TABLE XIV. — CALCULATION OF THE CRITICAL VELOCITY CONSTANT

Flow
Temperature
p
R centimeters
<p
J centimeters per
PRI<P

second

Steady .....
9
1.00
0.3075
74.4
44.26
1,012

Unsteady. . .
8
1.00
0.3075
72.4
48.65
1,113

Steady ......
5
1.00
0.3075
66.2
51.06
1,039

Unsteady. . .
5
1.00
0.3075
66.2
54.33
1,106

Steady ......
8
1.00
0.6350
72.4
22.60
1,039

Unsteady . . .
8
1.00
0.6350
72.4
22.60
1,039

Reynolds tried plotting the mean velocity against the fall in
pressure per unit length of the tube as shown in Fig. 12. It is
to be observed that the resistance increases as a linear function
of the velocity according to Poiseuille's law up to a certain definite
point, and that from that point on the resistance varies as some
higher power of the velocity. This power as we shall see is
constant and is, according to Reynolds equal to 1.723 over a
wide range of pressures. Formulated this relation becomes
P = KI" (15)