Various formulae for the flow of steam through pipes have been advanced,
all having their basis upon Bernoulli's theorem of the flow of water
through circular pipes with the proper modifications made for the
variation in constants between steam and water. The loss of energy due
to friction in a pipe is given by Unwin (based upon Weisbach) as
f 2 v² W L
E_{f} = ---------- (37)
gd
where E is the energy loss in foot pounds due to the friction of W units
of weight of steam passing with a velocity of v feet per second through
a pipe d feet in diameter and L feet long; g represents the acceleration
due to gravity (32.2) and f the coefficient of friction.
Numerous values have been given for this coefficient of friction, f,
which, from experiment, apparently varies with both the diameter of pipe
and the velocity of the passing steam. There is no authentic data on the
rate of this variation with velocity and, as in all experiments, the
effect of change of velocity has seemed less than the unavoidable errors
of observation, the coefficient is assumed to vary only with the size of
the pipe.
Unwin established a relation for this coefficient for steam at a
velocity of 100 feet per second,
/ 3 \
f = K| 1 + --- | (38)
\ 10d /
where K is a constant experimentally determined, and d the internal
diameter of the pipe in feet.