in which l = the length of main in yards instead of in feet. This is known as Pole's formula, and has been generally used for determining the sizes of mains for the supply of coal-gas.
For the following reasons, among others, it becomes prudent to revise Pole's formula before employing it for calculations relating to acetylene. First, the friction of the two gases due to the sides of a pipe is very different, the coefficient for coal-gas being 0.003, whereas that of acetylene, according to Ortloff, is 0.0001319. Secondly, the mains and service-pipes required for acetylene are smaller, cateria paribus, than those needed for coal-gas. Thirdly, the observed specific gravity of acetylene is 0.91, that of air being unity, whereas the density of coal-gas is about 0.40; and therefore, in the absence of direct information, it would be better to base calculations respecting acetylene on data relating to the flow of air in pipes rather than upon such as are applicable to coal-gas. Bernat has endeavoured to take these and similar considerations into account, and has given the following formula for determining the sizes of pipes required for the distribution of acetylene:
Q = 0.001253d^2(hd/sl)^(1/2)
in which the symbols refer to the same quantities as before, but the constant is calculated on the basis of Q being stated in cubic metres, l in metres, and d and h in millimetres. It will be seen that the equation has precisely the same shape as Pole's formula for coal-gas, but that the constant is different. The difference is not only due to one formula referring to quantities stated on the metric and the other to the same quantities stated on the English system of measures, but depends partly on allowance having been made for the different physical properties of the two gases. Thus Bernat's formula, when merely transposed from the metric system of measures to the English (i.e., Q being cubic feet per hour, l feet, and d and h inches) becomes
Q = 1313.5d^2(hd/sl)^(1/2)
or, more simply,
Q = 1313.4(hd^5/sl)^(1/2)
But since the density of commercially-made acetylene is practically the same in all cases, and not variable as is the density of coal-gas, its value, viz., 0.91, may be brought into the constant, and the formula then becomes
Q = 1376.9(hd^5/l)^(1/2)
Bernat's formula was for some time generally accepted as the most trustworthy for pipes supplying acetylene, and the last equation gives it in its simplest form, though a convenient transposition is