as been found and some
explanation of its derivation obtained. Taking the simplest possible
section, namely, a circle, it is found that at low velocities the loss
of head is directly proportional to the velocity and the fluid flows in
straight stream lines or the motion is direct. This motion is in exact
accordance with the theoretical equations of the motion of a viscous
fluid and constitutes almost a direct proof that the fundamental
assumptions on which these equations are based are correct. When,
however, the velocity exceeds a value which is determinable for any size
of tube, the direct or stream line motion breaks down and is replaced by
an eddy or mixing flow. In this flow the head loss by friction is
approximately, although not exactly, proportional to the square of the
velocity. No explanation of this has ever been found in spite of the
fact that the subject has been treated by the best mathematicians and
physicists for years back. It is to be assumed that the heat transferred
during the mixing flow would be at a much higher rate than with the
direct or stream line flow, and Professors Croker and Clement[86] have
demonstrated that this is true, the increase in the transfer being so
marked as to enable them to determine the point of critical velocity
from observing the rise in temperature of water flowing through a tube
surrounded by a steam jacket.

The formulae given apply only to a mixing flow and inasmuch as, from
what has just been stated, this form of motion does not exist from zero
velocity upward, it follows that any expression for the heat transfer
rate that would make its value zero when the velocity is zero, can
hardly be correct. Below the critical velocity, the transfer rate seems
to be little affected by change in velocity and Nusselt,[87] in another
paper which mathematically treats the direct or stream line flow,
concludes that, while it is approximately constant as far as the
velocity is concerned in a straight cylindrical tube, it would vary from
point to point of the tube, growing less as the surface passed over
increased.

It should further be noted that no account in any of this experimental
work has been taken of radiation of heat from the gas. Since the common
gases absorb very little radiant heat at ordinary temperatures, it has
been assumed that they radiate very little at any temperature. This may
or may not be true, but certainly a visible flame must radiate as well
as absorb heat. H