MEASUREMENT OF FLOWING WATER. 129
have
a wide range. This formula, however, has been considered the simplest,
and has been used by many engineers, different values being given to c, varying
from 84' to 100 for large streams, and being as low as 68 for small
streams. " Though there is abundant evidence," says Higham (p. 5), "
that the latter is much too high for low values of v in earthen
channels, and that 100 is too low for very large rivers, as high a
value as 254.4 having been deduced from the Mississippi observations."
D'Arcy
and Bazin, by their experiments on channels of moderate section with
limited variation of grades, proved that the coefficient c involved not only r and s, but
also a constant for the different degrees of roughness of the channel,
the formula being applicable within certain limits of inclination and
values of r.
Humphreys
and Abbot make the velocity vary with the fourth root of the
inclination, while Hagen assumes the velocity to vary with the sixth
root.
Ganguillet and Kutter considered that the Chezy formula,
was the correct point of departure, but
that the coefficient should be made variable, involving not only r and s, but likewise a constant for different degrees of roughness in the bed or channel.
The
final formula adopted by Ganguillet and Kutter, which within certain
limits of inclination, and especially in regular channels, will give
very satisfactory results, is the following:
