16 FLUIDITY AND PLASTICITY

But the force due to the frictional resistance on the outside of
the cylinder must be exactly balanced by a force due to the pres-
sure and this is

- 7rr2pg

where p is the pressure in grams per square centimeter and g is
the acceleration due to gravity. The negative sign is used
because this force acts from left to right. We have then that

*=-!*

but v = 0 when r = R, therefore the constant of integration K
can be evaluated

VSS_ r

From Eq. (3) we may obtain the velocity in centimeters per
second at any point in the capillary. It follows that the liquid
flowing through the capillary in a given time has the volume of
a paraboloid of revolution. If the volume per second is U, then

=0 r = 0

which is the Law of Poiseuille. If V is the total volume of efflux
in the time £, the formula becomes

The mean velocity of the fluid, in cubic centimeters per second
passing through the tube, I, is

Summary. — The simple law of Poiseuille was first discovered
experimentally, after which its theoretical deduction was quickly
made; There is, however, a considerable amount of data for
which the simple law is not sufficient. The law may be given
far greater usefulness by adding certain correction terms, which
are the subject of discussion in the following chapter.