When dealing with coal-gas, it is highly important to bear in mind that the ordinary distributing formulæ apply directly only when the pipe or main is horizontal, and that a rise in the pipe will be attended by an increase of pressure at the upper end. But as the increase is greater the lower the density of the gas, the disturbing influence of a moderate rise in a pipe is comparatively small in the case of a gas of so high a density as acetylene. Hence in most instances it will be unnecessary to make any allowance for increase of pressure due to change of level. Where the change is very great, however, allowance may advisedly be made on the following basis: The pressure of acetylene in pipes increases by about one-tenth of an inch (head of water) for every 75 feet rise in the pipe. Hence where acetylene is supplied from a gasholder on the ground-level to all floors of a house 75 feet high, a burner at the top of the house will ordinarily receive its supply at a pressure greater by one-tenth of an inch than a burner in the basement. Such a difference, with the relatively high pressures used in acetylene supplies, is of no practical moment. In the case of an acetylene-supply from a central station to different parts of a mountainous district, the variations of pressure with level should be remembered.
The distributing formulæ also assume that the pipe is virtually straight; bends and angles introduce disturbing influences. If the bend is sharp, or if there is a right-angle, an allowance should be made if it is desired to put in pipes of the smallest permissible dimensions. In the case of the most usual sizes of pipes employed for acetylene mains or services, it will suffice to reckon that each round or square elbow is equivalent in the resistance it offers to the flow of gas to a length of 5 feet of pipe of the same diameter. Hence if 5 feet is added to the actual length of pipe to be laid for every bond or elbow which will occur in it, and the figure so obtained is taken as the value of l in formulæ (i), (ii), or (iii), the values then found for Q, d, or h will be trustworthy for all practical purposes.
It may now be useful to give an example of the manner of using the foregoing formulæ when the tables of sizes of pipes are not available. Let it be supposed that an institution is being equipped for acetylene lighting; that 50 burners consuming 0.70 cubic foot, and 50 consuming 1.00 cubic foot of acetylene per hour may be required in use simultaneously; that a pressure of at least 2-1/2 inches is required at all the burners; that for sufficient reasons it is considered undesirable to use a higher distributing pressure than 4 inches at the gasholder, outlet of the purifiers, or initial governor (whichever comes last in the train of apparatus); that the gasholder is located 100 feet from the main building of the institution, and that the trunk supply-pipe through the latter must be 250 feet in length, and the supplies to the burners, either singly or in groups, be taken from this trunk pipe through short lengths of tubing of ample size. What should be the diameter of the trunk pipe, in which it will be assumed that ten bonds or elbows are necessary?
In the first instance, it is convenient to suppose that the trunk pipe may be of uniform diameter throughout. Then the value of l will be 100 (from gasholder to main building) + 250 (within the building) + 50 (equivalent of 10 elbows) = 400. The maximum value of Q will be (50 x 0.7) + (50 x 1.0) = 85; and the value of h will be 1 - 2.5 - 1.5. Then using formula (i), we have:
d = 0.045122((85^2 x 400)/1.5)^(1/5) = 0.045122(1,926,667)^(1/5)
= 0.045122 x 18.0713 = 0.8154.
The formula, therefore, shows that the pipe should have an internal diameter of not less than 0.8154 inch, and consequently 1 inch (the next size above 0.8154 inch) barrel should be used. If the initial pressure (i.e., at outlet of purifiers) could be conveniently increased from 4 to 4.8 inches, 3/4 inch barrel could be employed for the service-pipe. But if connexions for burners were made immediately the pipe entered the building, these burners would then be supplied at a pressure of 4.2 inches, while those on the extremity of the pipe would, when all burners were in use, be supplied at a pressure of only 2.5 inches. Such a great difference of pressure is not permissible at the several burners, as no type of burner retains its proper efficiency over more than a very limited range of pressure. It is highly desirable in the case of the ordinary Naphey type of burner that all the burners in a house should be supplied at pressures which do not differ by more than half an inch; hence the pipes should, wherever practicable, be of such a size that they will pass the maximum quantity of gas required for all the burners which will ever be in use simultaneously, when the pressure at the first burner connected to the pipe after it enters the house is not more than half an inch above the pressure at the burner furthermost removed from the first one, all the burner-taps being turned on at the time the pressures are observed. If the acetylene generating plant is not many yards from the building to be supplied, it is a safe rule to calculate the size of pipes required on the basis of a fall of pressure of only half an inch from the outlet of the purifiers or initial governor to the farthermost burner. The extra cost of the larger size of pipe which the application of this rule may entail will be very slight in all ordinary house installations.
VELOCITY OF FLOW IN PIPES.--For various purposes, it is often desirable to know the mean speed at which acetylene, or any other gas, is passing through a pipe. If the diameter of the pipe is d inches, its cross-sectional area is d^2 x 0.7854 square inches; and since there are 1728 cubic inches in 1 cubic foot, that quantity of gas will occupy in a pipe whose diameter is d inches a length of
1728/(d^2 x 0.7854) linear inches or 183/d^2^ linear feet.
If the gas is in motion, and the pipe is delivering Q cubic feet per hour, since there are 3600 seconds of time in one hour, the mean speed of the gas becomes