From experiment it appears that the magnitude of the friction, or the resistance which the air suffers in moving along the pipes, under a like primary pressure, that is for equal initial velocity, varies with the square root of the length. The volume of gas discharged from the end of a pipe, is directly proportional to the square of its diameter, and inversely as the square root of its length; or, calling the length L, the diameter D, the cubic feet of gas discharged in an hour k; then k = D2√L. Experience likewise shows, that for a pipe 250 feet long, which transmits in an hour 200 cubic feet of gas, one inch is a sufficient diameter.
Consequently, 200 : k ∷ 1144 √250 : D2√L; and D = √k √L455,000
From this formula the following table of proportions is calculated.
| Number of cubic feet per hour. | Length of pipe, in feet. | Diameter, in inches. | |
|---|---|---|---|
| 50 | 100 | 0 | ·40 |
| 250 | 200 | 1 | ·00 |
| 500 | 600 | 1 | ·97 |
| 700 | 1000 | 2 | ·65 |
| 1000 | 1000 | 3 | ·16 |
| 1500 | 1000 | 3 | ·87 |
| 2000 | 1000 | 4 | ·47 |
| 2000 | 2000 | 5 | ·32 |
| 2000 | 4000 | 6 | ·33 |
| 2000 | 6000 | 7 | ·00 |
| 6000 | 1000 | 7 | ·75 |
| 6000 | 2000 | 9 | ·21 |
| 8000 | 1000 | 8 | ·95 |
| 8000 | 2000 | 16 | ·65 |
These dimensions are applicable to the case where the body of gas is transmitted through pipes without being let off in its way by burners, that is, to the mains which conduct the gas to the places where it is to be used. If the main sends off branches for burners, then for the same length the diameter may be reduced, or for like diameter the length may be greater. For example, if a pipe of 5·32 inches, which transmits 2000 cubic feet through a length of 2000 feet, gives off, in this space, 1000 cubic feet of gas; then the remainder of the pipe, having the same diameter, can continue to transmit the gas through a length of 2450 feet = (450,000k)2, with undiminished pressure for the purposes of lighting. Inversely, the diameter should be progressively reduced in proportion to the number of jets sent off in the length of the pipe.
Suppose for instance, the gasometer to discharge 2000 cubic feet per hour, and the last point of the jets to be at a distance of 4000 feet. Suppose also that from the gasometer to the first point of lighting, the gas proceeds through 1000 feet of close pipe, the diameter of the pipe will be here 4·47 inches; in the second 1000 feet of length, suppose the pipe to give off, at equal distances, 1000 cubic feet of gas, the diameter in this length (calculated at 1500 cubic feet for 1000 feet long) = 3·87 inches; in the third extent of 1000 feet, 600 cubic feet of gas will be given off, and the diameter (reckoning 700 cubic feet for 1000 feet long) will be 2·65 inches; in the fourth and last space (for 200 cubic feet in 1000 feet long) the pipe has a diameter of only an inch and a half, for which, in practice, a two-inch cast iron pipe is substituted; this being the smallest used in mains, into which branch pipes can be conveniently inserted.
The same relations hold with regard to branch pipes through which the gas is transmitted into buildings and other places to be illuminated. If such pipes make frequent angular turnings, whereby they retard the motion of the gas, they must be a third or a half larger in diameter. The smallest tubes of distribution are never less than one fourth of an inch in the bore.
Where, from one central gas work, a very great quantity of light is required in particular localities, there ought to be placed near these spots gasometers of distribution, which, being filled during the slack hours of the day, are ready to supply the burners at night, without making any considerable demand upon the original main pipe. Suppose the first main be required to supply 8000 cubic feet in the hour, for an illumination of 8 hours, at the distance of 2000 feet, a pipe 102⁄3 inches in diameter would be necessary; but if two or three gasometers of distribution, or station gasometers be had recourse to, into which the gas during the course of 24 hours would flow through the same distance continuously from the central gas works, the quantity required per hour from them would be only one third of 8000, = 2666·6 cubic feet; consequently the diameter for such a pipe is only 6·15 inches.
