Kutter’s formula was derived by the Swiss engineers, Ganguillet and Kutter, as the result of a series of experimental observations. It was introduced into the United States by Rudolph Hering and its derivation is given in Hering and Trautwine’s translation of “The Flow of Water in Open Channels by Ganguillet and Kutter.” In English units it is,
in which n is a factor expressing the character of the surface of the conduit and the other notation is as in the Chezy formula. V is the velocity in feet per second, S is the slope ratio, and R the hydraulic radius in feet. The values of n to be used in all cases are not agreed upon, but in general the values shown below are used in practice.
| Values of n in Kutter’s Formula | ||
|---|---|---|
| n | Character of the Materials | |
| 0.009 | Well-planed timber. | |
| 0.010 | Neat cement or very smooth pipe. | |
| 0.012 | Unplaned timber. Best concrete. | |
| 0.013 | Smooth masonry or brickwork, or concrete sewers under ordinary conditions. | |
| 0.015 | Vitrified pipe or ordinary brickwork. | |
| 0.017 | Rubble masonry or rough brickwork. | |
| 0.020 0.035 | } | Smooth earth. |
| 0.030 0.050 | } | Rough channels overgrown with grass. |
Kutter’s formula is of general application to all classes of material and to all shapes of conduits. It is the most generally used formula in sewerage design.
The cumbersomeness of Kutter’s formula is caused somewhat by the attempt to allow for the effect of the low slopes of the Mississippi River experiments on the coefficients. The correctness of these experiments has not been well established and the slopes are so flat that the omission of the term 0.0028
S will have no appreciable effect on the value of V ordinarily used in sewer design. The difference between the value of V determined by the omission of this term and the value of V found by including it is less than 1 per cent for all slopes greater than 1 in 1,000 for 8 inch pipe (R = 0.167 feet). As the diameter of the pipe or the hydraulic radius of the channel increases up to a diameter of 13.02 feet (R = 3.28 feet), the difference becomes less and at this value of R there is no difference whether the slope is included or not. For larger pipes the difference increases slowly. For a 16 foot pipe (R = 4 feet) on a slope of 1 in 1,000 the difference is less than 0.2 per cent, and on a slope of 1 in 10,000 the difference is approximately 1 per cent. Flatter slopes than these are seldom used in sewer design, except for very large sewers where careful determinations of the hydraulic slope are necessary. It is therefore safe in sewer design to use Kutter’s formula in the modified form shown below in which the term .0028
S has been omitted.
Bazin’s formula is
in which α and β are constants for different classes of material. For cast-iron pipe α is 0.00007726 and β is 0.00000647. This formula is seldom used in sewerage design.