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 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.