e._, at the inlet head of service-pipe) p_1, it
follows that p_1 - p_0 = _f_. Now the cross-section of the pipe has
an area (pi/4)_d^2_, and if _h_ represents the difference of
pressure between the two ends of the pipe per square inch of its area, it
follows that _f_ = _h(pi/4)d^2_. But since _f_ has been
found above to vary as _ldsv^2_ , it is evident that
_h(pi/4)d^2_ varies as _ldsv^2_.
Hence
_v^2_ varies as _hd/ls_,
and putting in some constant M, the value of which must be determined by
experiment, this becomes
_v^2_ = M_hd/ls_.
The value of M deduced from experiments on the friction of coal-gas in
pipes was inserted in this equation, and then taking Q = pi/4_d^2v_,
it was found that for coal-gas Q = 780(_hd/sl_)^(1/2)
This formula, in its usual form, is
Q = 1350_d^2_(_hd/sl_)^(1/2)
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.
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