d = 0.05552(Q^2l/h)^(1/5)
Bernat's formula, however, has now been generally superseded by one given by Morel, which has been found to be more in accordance with the actual results observed in the practical distribution of acetylene. Morel's formula is
D = 1.155(Q^2l/h)^(1/5)
in which D = the diameter of the pipe in centimetres, Q = the number of cubic metres of gas passing per hour, l = the length of pipe in metres, and h = the loss of pressure between the two ends of the pipe in millimetres. On converting tins formula into terms of the English system of measures (i.e., l feet, Q cubic feet, and h and d inches) it becomes
(i) d = 0.045122(Q^2l/h)^(1/5)
At first sight this formula does not appear to differ greatly from Bernat's, the only change being that the constant is 0.045122 instead of 0.05552, but the effect of this change is very great--for instance, other factors remaining unaltered, the value of Q by Morel's formula will be 1.68 times as much as by Bernat's formula. Transformations of Morel's formula which may sometimes be more convenient to apply than (i) are:
(ii) Q = 2312.2(hd^5/l)^(1/2)
(iii) h = 0.000000187011(Q^2l/d^5)
and (iv) l = 5,346,340(hd^5/Q^2)
In order to avoid as far as possible expenditure of time and labour in repeating calculations, tables have been drawn up by the authors from Morel's formulæ which will serve to give the requisite information as to the proper sizes of pipes to be used in those cases which are likely to be met with in ordinary practice. These tables are given at the end of this chapter.