v = [root](2g/[zeta]) [root](mi) = c [root](mi),
Ganguillet and Kutter proceeded in a purely empirical way. They found
that an expression of the form
c = [alpha]/(1 + [beta]/[root]m)
could be made to fit the experiments somewhat better than Darcy's
expression. Inverting this, we get
1/c = 1/[alpha] + [beta]/[alpha] [root]m,
an equation to a straight line having 1/[root]m for abscissa, 1/c for
ordinate, and inclined to the axis of abscissae at an angle the
tangent of which is [beta]/[alpha].
Plotting the experimental values of 1/c and 1/[root]m, the points so
found indicated a curved rather than a straight line, so that [beta]
must depend on [alpha]. After much comparison the following form was
arrived at--
c = (A + l/n)/(1 + An/[root]m),
where n is a coefficient depending only on the roughness of the sides
of the channel, and A and l are new coefficients, the value of which
remains to be determined. From what has been already stated, the
coefficient c depends on the inclination of the stream, decreasing as
the slope i increases.