c = (a + l/n + p/i)/{1 + (a + p/i)n/[root]m},
the form of the expression for c ultimately adopted by Ganguillet and
Kutter.
For the constants a, l, p Ganguillet and Kutter obtain the values 23,
1 and 0.00155 for metrical measures, or 41.6, 1.811 and 0.00281 for
English feet. The coefficient of roughness n is found to vary from
0.008 to 0.050 for either metrical or English measures.
The most practically useful values of the coefficient of roughness n
are given in the following table:--
Nature of Sides of Channel. Coefficient of
Roughness n.
Well-planed timber 0.009
Cement plaster 0.010
Plaster of cement with one-third sand 0.011
Unplaned planks 0.012
Ashlar and brickwork 0.013
Canvas on frames 0.015
Rubble masonry 0.017
Canals in very firm gravel 0.020
Rivers and canals in perfect order, free from stones \
or weeds / 0.025
Rivers and canals in moderately good order, not \
quite free from stones and weeds / 0.030
Rivers and canals in bad order, with weeds and \
detritus / 0.035
Torrential streams encumbered with detritus 0.050
Ganguillet and Kutter's formula is so cumbrous that it is difficult to
use without the aid of tables.
Lowis D'A. Jackson published complete and extensive tables for
facilitating the use of the Ganguillet and Kutter formula (_Canal and
Culvert Tables_, London, 1878). To lessen calculation he puts the
formula in this form:--