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.

Let

A = a + p/i.

Then

c = (a + l/n + p/i) / {1 + (a + p/i) n/√ 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 timber0.009
Cement plaster0.010
Plaster of cement with one-third sand0.011
Unplaned planks0.012
Ashlar and brickwork0.013
Canvas on frames0.015
Rubble masonry0.017
Canals in very firm gravel0.020
Rivers and canals in perfect order, free from stones or weeds0.025
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 detritus0.035
Torrential streams encumbered with detritus0.050

Ganguillet and Kutter’s formula is so cumbrous that it is difficult to use without the aid of tables.