in which C is a factor dependent on the character of the material of the conduit. The values of C as given by Hazen and Williams are,
| C | Character of Material |
|---|---|
| 95 | Steel pipe under future conditions. (Riveted steel.) |
| 100 | Cast iron under ordinary future conditions and brick sewers in good condition. |
| 110 | New riveted steel, and cement pipe. |
| 120 | Smooth wood or masonry conduits under ordinary conditions. |
| 130 | Masonry conduits after some time and for very smooth pipes such as glass, brass, lead, etc., when old, and for new cast-iron pipe under ordinary conditions. |
This formula is of as general application as Kutter’s formula and is easier of solution, but being more recently in the field and because of the ease of the solution of Kutter’s formula by diagrams it is not in such general use. Exponential formulas are used more in waterworks than in sewerage practice.
Manning’s formula is in the form,
V = 1.486
nR⅔S½
in which n is the same as for Kutter’s formula. Charts for the solution of Manning’s formula are given in Eng. News-Record, Vol. 85, 1920, p. 837.
36. Solution of Formulas.—The solution of even the simplest of these formulas, such as Flamant’s, is laborious because of the exponents involved. Darcy’s and Kutter’s formulas are even more cumbersome because of the character of the coefficient. The labor involved in the solution of these formulas has resulted in the development of a number of diagrams and other short cuts. Since each formula involves three or more variables it cannot be represented by a single straight line on rectangular coordinate paper. The simplest form of diagram for the solution of three or more variables is the nomograph, an example of which is shown in Fig. 13 for the solution of Flamant’s formula. A straight-edge placed on any two points of the scales of two different vertical lines will cross the other line at a point on the scale corresponding to its correct value in the formula. Such a diagram is in common use for the solution of problems for the flow of water in cast-iron pipe.
Fig. 13.—Diagram for the Solution of Flamant’s Formula for the Flow of Water in Cast-iron Pipe.
Fig. 14 has been prepared to simplify the solution of Hazen and Williams’ formula. The scales of slope for different classes of material are shown on vertical lines to the left of the slope line. For use these scales must be projected horizontally on the slope line. The scales for other factors are shown on independent reference lines.