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 = 1313.5_d^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
d = 0.05552(Q^2_l/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Bernat's formula, however, has now been generally superseded by one given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^2_l/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.
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