Acetylene, The Principles Of Its Generation And Use

F >> F. H. Leeds and W. J. Atkinson Butterfield >> Acetylene, The Principles Of Its Generation And Use

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GASHOLDER PRESSURE.--In drawing up the specification or scheme of an
acetylene installation, it is frequently necessary either to estimate the
pressure which a bell gasholder of given diameter and weight will throw,
or to determine what should be the weight of the bell of a gasholder of
given diameter when the gas is required to be delivered from it at a
particular pressure. The gasholder of an acetylene installation serves
not only to store the gas, but also to give the necessary pressure for
driving it through the posterior apparatus and distributing mains and
service-pipes. In coal-gas works this office is generally given over
wholly or in part to a special machine, known as the exhauster, but this
machine could not be advantageously employed for pumping acetylene unless
the installation were of very great magnitude. Since, therefore,
acetylene is in practice always forced through mains and service-pipes in
virtue of the pressure imparted to it by the gasholder and since, for
reasons already given, only the rising-bell type of gasholder can be
regarded as satisfactory, it becomes important to know the relations
which subsist between the dimensions and weight of a gasholder bell and
the pressure which it "throws" or imparts to the contained gas.

The bell must obviously be a vessel of considerable weight if it is to
withstand reasonable wear and tear, and this weight will give a certain
hydrostatic pressure to the contained gas. If the weight of the bell is
known, the pressure which it will give can be calculated according to the
general law of hydrostatics, that the weight of the water displaced must
be equal to the weight of the floating body. Supposing for the moment
that there are no other elements which will have to enter into the
calculation, then if _d_ is the diameter in inches of the
(cylindrical) bell, the surface of the water displaced will have an area
of _d^2_ x 0.7854. If the level of the water is depressed _p_
inches, then the water displaced amounts to _p_(_d^2_ x 0.7854)
cubic inches, and its weight will be (at 62 deg. F.):

(0.7854_pd^2_ x 0.03604) = 0.028302_pd^2_ lb.

Consequently a bell which is _d_ inches in diameter, and gives a
pressure of _p_ inches of water, will weigh 0.028302_pd^2_ lb.
Or, if W = the weight of the bell in lb., the pressure thrown by it will
be W/0.028302_d^2_ or 35.333W/_d^2_. This is the fundamental
formula, which is sometimes given as _p_ = 550W/_d^2_, in which
W = the weight of the bell in tons, and _d_ the diameter in feet.
This value of _p_, however, is actually higher than the holder would
give in practice. Reductions have to be made for two influences, viz.,
the lifting power of the contained gas, which is lighter than air, and
the diminution in the effective weight of so much of the bell as is
immersed in water. The effect of these influences was studied by Pole,
who in 1839 drew up some rules for calculating the pressure thrown by a
gasholder of given dimensions and weight. These rules form the basis of
the formula which is commonly used in the coal-gas industry, and they may
be applied, _mutatis mutandis_, to acetylene holders. The
corrections for both the influences mentioned vary with the height at
which the top of the gasholder bell stands above the level of the water
in the tank. Dealing first with the correction for the lifting power of
the gas, this, according to Pole, is a deduction of _h_(1 -
_d_)/828 where _d_ is the specific gravity of the gas and
_h_ the height (in inches) of the top of the gasholder above the
water level. This strictly applies only to a flat-topped bell, and hence
if the bell has a crown with a rise equal to about 1/20 of the diameter
of the bell, the value of _h_ here must be taken as equal to the
height of the top of the sides above the water-level (= _h'_), plus
the height of a cylinder having the same capacity as the crown, and the
same diameter as the bell, that is to say, _h_=_h'_ +
_d_/40 where _d_ = the diameter of the bell. The specific
gravity of commercially made acetylene being constantly very nearly 0.91,
the deduction for the lifting power of the gas becomes, for acetylene
gasholders, 0.0001086_h_ + 0.0000027_d_, where _h_ is the
height in inches of the top of the sides of the bell above the water-
level, and _d_ is the diameter of the bell. Obviously this is a
negligible quantity, and hence this correction may be disregarded for all
acetylene gasholders, whereas it is of some importance with coal-gas and
other gases of lower specific gravity. It is therefore wrong to apply to
acetylene gasholders formulae in which a correction for the lifting power
of the gas has been included when such correction is based on the average
specific gravity of coal-gas, as is the case with many abbreviated
gasholder pressure formulae.

The correction for the immersion of the sides of the bell is of greater
magnitude, and has an important practical significance. Let H be the
total height in inches of the side of the gasholder, _h_ the height
in inches of the top of the sides of the gasholder above the water-level,
and _w_ = the weight of the sides of the gasholder in lb.; then, for
any position of the bell, the proportion of the total height of the sides
immersed (H - _h_)/H, and the buoyancy is (H - _h_)/H x
_w_/S + pi/4_d^2_, in which S = the specific gravity of the
material of which the bell is made. Assuming the material to be mild
steel or wrought iron, having a specific gravity of 7.78, the buoyancy is
(4_w_(H - _h_)) / (7.78Hpi_d^2_) lb. per square inch
(_d_ being inches and _w_ lb.), which is equivalent to
(4_w_(H - _h_)) / (0.03604 x 7.78Hpi_d^2_) =
(4.54_w_(H - _h_)) / (H_d^2_) inches of water. Hence the
complete formula for acetylene gasholders is:

_p_ = 35.333W / _d^2_ - 4.54_w_(H - _h_) /
H_d^2_

It follows that _p_ varies with the position of the bell, that is to
say, with the extent to which it is filled with gas. It will be well to
consider how great this variation is in the case of a typical acetylene
holder, as, if the variation should be considerable, provision must be
made, by the employment of a governor on the outlet main or otherwise, to
prevent its effects being felt at the burners.

Now, according to the rules of the "Acetylen-Verein" (_cf._ Chapter
IV.), the bells of holders above 53 cubic feet in capacity should have
sides 1.5 mm. thick, and crowns 0.5 mm. thicker. Hence for a holder from
150 to 160 cubic feet capacity, supposing it to be 4 feet in diameter and
about 12 feet high, the weight of the sides (say of steel No. 16 S.W.G. =
2.66 lb. per square foot) will be not less than 12 x 4pi x 2.66 = 401 lb.
The weight of the crown (say of steel No. 14 S.W.G. = 3.33 lb. per square
foot) will be not less than about 12.7 x 3.33 = about 42 lb. Hence the
total weight of holder = 401 + 42 = 443 lb. Then if the holder is full,
_h_ is very nearly equal to H, and _p_ = (35.333 x 443) / 48^2
= 6.79 inches. If the holder stands only 1 foot above the water-level,
then _p_ = 6.79 - (4.54 x 401 (144 - 12)) / (144 x 48^2) = 6.79 -
0.72 = 6.07 inches. The same result can be arrived at without the direct
use of the second member of the formula:

For instance, the weight of the sides immersed is 11 x 4pi x 2.66 = 368
lb., and taking the specific gravity of mild steel at 7.78, the weight of
water displaced is 368 / 7.78 = 47.3 lb. Hence the total effective weight
of the bell is 443 - 47.3 = 395.7 lb., and _p_ = (35.333 x 395.7) /
48^2 = 6.07 inches. [Footnote: If the sealing liquid in the gasholder
tank is other than simple water, the correction for the immersion of the
sides of the bell requires modification, because the weight of liquid
displaced will be _s'_ times as great as when the liquid is water,
if _s'_ is the specific gravity of the sealing liquid. For instance,
in the example given, if the sealing liquid were a 16 per cent. solution
of calcium chloride, specific gravity 1.14 (_vide_ p. 93) instead of
water, the weight of liquid displaced would be 1.14 (368 / 7.78) = 53.9
lb., and the total effective weight of the bell = 443 - 53.9 = 389.1 lb.
Therefore _p_ becomes = (35.333 x 389.1) / 48^2 = 5.97 inches,
instead of 6.07 inches.]

The value of _p_ for any position of the bell can thus be arrived
at, and if the difference between its values for the highest and for the
lowest positions of the bell exceeds 0.25 inch, [Footnote: This figure is
given as an example merely. The maximum variation in pressure must be
less than one capable of sensibly affecting the silence, steadiness, and
economy of the burners and stoves, &c., connected with the installation.]
a governor should be inserted in the main leading from the holder to the
burners, or one of the more or less complicated devices for equalising
the pressure thrown by a holder as it rises and falls should be added to
the holder. Several such devices were at one time used in connexion with
coal-gas holders, and it is unnecessary to describe them in this work,
especially as the governor is practically the better means of securing
uniform pressure at the burners.

It is frequently necessary to add weight to the bell of a small gasholder
in order to obtain a sufficiently high pressure for the distribution of
acetylene. It is best, having regard to the steadiness of the bell, that
any necessary weighting of it should be done near its bottom rim, which
moreover is usually stiffened by riveting to it a flange or curb of
heavier gauge metal. This flange may obviously be made sufficiently stout
to give the requisite additional weighting. As the flange is constantly
immersed, its weight must not be added to that of the sides in computing
the value of _w_ for making the correction of pressure in respect of
the immersion of the bell. Its effective weight in giving pressure to the
contained gas is its actual weight less its actual weight divided by its
specific gravity (say 7.2 for cast iron, 7.78 for wrought iron or mild
steel, or 11.4 for lead). Thus if _x_ lb. of steel is added to the
rim its weight in computing the value of W in the formula _p_ =
35.333W / _d_^2 should be taken as x - x / 7.78. If the actual
weight is 7.78 lb., the weight taken for computing W is 7.78 - 1 = 6.78
lb.

THE PRESSURE GAUGE.--The measurement of gas pressure is effected by means
of a simple instrument known as a pressure gauge. It comprises a glass U-
tube filled to about half its height with water. The vacant upper half of
one limb is put in communication with the gas-supply of which the
pressure is to be determined, while the other limb remains open to the
atmosphere. The difference then observed, when the U-tube is held
vertical, between the levels of the water in the two limbs of the tube
indicates the difference between the pressure of the gas-supply and the
atmospheric pressure. It is this _difference_ that is meant when the
_pressure_ of a gas in a pipe or piece of apparatus is spoken of,
and it must of necessity in the case of a gas-supply have a positive
value. That is to say, the "pressure" of gas in a service-pipe expresses
really by how much the pressure in the pipe _exceeds_ the
atmospheric pressure. (Pressures less than the atmospheric pressure will
not occur in connexion with an acetylene installation, unless the
gasholder is intentionally manipulated to that end.) Gas pressures are
expressed in terms of inches head or pressure of water, fractions of an
inch being given in decimals or "tenths" of an inch. The expression
"tenths" is often used alone, thus a pressure of "six-tenths" means a
pressure equivalent to 0.6 inch head of water.

The pressure gauge is for convenience provided with an attached scale on
which the pressures may be directly read, and with a connexion by which
the one limb is attached to the service-pipe or cock where the pressure
is to be observed. A portable gauge of this description is very useful,
as it can be attached by means of a short piece of flexible tubing to any
tap or burner. Several authorities, including the British Acetylene
Association, have recommended that pressure gauges should not be directly
attached to generators, because of the danger that the glass might be
fractured by a blow or by a sudden access of heat. Such breakage would be
followed by an escape of gas, and might lead to an accident. Fixed
pressure gauges, however, connected with every item of a plant are
extremely useful, and should be employed in all large installations, as
they afford great aid in observing and controlling the working, and in
locating the exact position of any block. All danger attending their use
can be obviated by having a stopcock between the gauge inlet and the
portion of the plant to which it is attached; the said stopcock being
kept closed except when it is momentarily opened to allow of a reading
being taken. As an additional precaution against its being left open, the
stopcock may be provided with a weight or spring which automatically
closes the gas-way directly the observer's hand is removed from the tap.
In the best practice all the gauges will be collected together on a board
fastened in some convenient spot on the wall of the generator-house, each
gauge being connected with its respective item of the plant by means of a
permanent metallic tube. The gauges must be filled with pure water, or
with a liquid which does not differ appreciably in specific gravity from
pure water, or the readings will be incorrect. Greater legibility will be
obtained by staining the water with a few drops of caramel solution, or
of indigo sulphate (indigo carmine); or, in the absence of these dyes,
with a drop or two of common blue-black writing ink. If they are not
erected in perfectly frost-free situations, the gauges may be filled with
a mixture of glycerin and pure alcohol (not methylated spirit), with or
without a certain proportion of water, which will not freeze at any
winter temperature. The necessary mixture, which must have a density of
exactly 1.00, could be procured from any pharmacist.

It is the pressure as indicated by the pressure gauge which is referred
to in this book in all cases where the term "pressure of the gas" or the
like is used. The quantity of acetylene which will flow in a given time
from the open end of a pipe is a function of this pressure, while the
quantity of acetylene escaping through a tiny hole or crack or a burner
orifice also depends on this total pressure, though the ratio in this
instance is not a simple one, owing to the varying influence of friction
between the issuing gas and the sides of the orifice. Where, however,
acetylene or other gas is flowing through pipes or apparatus there is a
loss of energy, indicated by a falling off in the pressure due to
friction, or to the performance of work, such as actuating a gas-meter.
The extent of this loss of energy in a given length of pipe or in a meter
is measured by the difference between the pressures of the gas at the two
ends of the pipe or at the inlet and outlet of the meter. This difference
is the "loss" or "fall" of pressure, due to friction or work performed,
and is spoken of as the "actuating" pressure in regard to the passage of
gas through the stretch of pipe or meter. It is a measure of the energy
absorbed in actuating the meter or in overcoming the friction. (Cf.
footnote, Chapter II., page 54.)

DIMENSIONS OF MAINS.--The diameter of the mains and service-pipes for an
acetylene installation must be such that the main or pipe will convey the
maximum quantity of the gas likely to be required to feed all the burners
properly which are connected to it, without an excessive actuating
pressure being called for to drive the gas through the main or pipe. The
flow of all gases through pipes is of course governed by the same general
principles; and it is only necessary in applying these principles to a
particular gas, such as acetylene, to know certain physical properties of
the gas and to make due allowance for their influence. The general
principles which govern the flow of a gas through pipes have been
exhaustively studied on account of their importance in relation to the
distribution of coal-gas and the supply of air for the ventilation of
places where natural circulation is absent or deficient. It will be
convenient to give a very brief reference to the way in which these
principles have been ascertained and applied, and then to proceed to the
particular case of the distribution of acetylene through mains and
service-pipes.

The subject of "The Motion of Fluids in Pipes" was treated in a lucid and
comprehensive manner in an Essay by W. Pole in the _Journal of Gas
Lighting_ during 1852, and his conclusions have been generally adopted
by gas engineers ever since. He recapitulated the more important points
of this essay in the course of some lectures delivered in 1872, and one
or other of these two sources should be consulted for further
information. Briefly, W. Pole treated the question in the following
manner:

The practical question in gas distribution is, what quantity of gas will
a given actuating pressure cause to flow along a pipe of given length and
given diameter? The solution of this question allows of the diameters of
pipes being arranged so that they will carry a required quantity of gas a
given distance under the actuating pressure that is most convenient or
appropriate. There are five quantities to be dealt with, viz.:

(1) The length of pipe = _l_ feet.

(2) The internal diameter of the pipe = _d_ inches.

(3) The actuating pressure = _h_ inches of head of water. (4) The
specific gravity or density of the gas = _d_ times that of air.

(5) The quantity of gas passing through the pipe--Q cubic feet per hour.
This quantity is the product of the mean velocity of the gas in the pipe
and the area of the pipe.

The only work done in maintaining the flow of gas along a pipe is that
required to overcome the friction of the gas on the walls of the pipe,
or, rather, the consequential friction of the gas on itself, and the laws
which regulate such friction have not been very exhaustively
investigated. Pole pointed out, however, that the existing knowledge on
the point at the time he wrote would serve for the purpose of determining
the proper sizes of gas-mains. He stated that the friction (1) is
proportional to the area of rubbing surface (viz., pi_ld_); (2)
varies with the velocity, in some ratio greater than the first power, but
usually taken as the square; and (3) is assumed to be proportional to the
specific gravity of the fluid (viz., _s_).

Thus the force (_f_) necessary to maintain the motion of the gas in
the pipe is seen to vary (1) as pi_ld_, of which pi is a constant;
(2) as _v^2_, where _v_ = the velocity in feet per hour; and
(3) as _s_. Hence, combining these and deleting the constant pi, it
appears that

_f_ varies as _ldsv^2_.

Now the actuating force is equal to _f_, and is represented by the
difference of pressure at the two ends of the pipe, _i.e._, the
initial pressure, viz., that at the place whence gas is distributed or
issues from a larger pipe will be greater by the quantity _f_ than
the terminal pressure, viz., that at the far end of the pipe where it
branches or narrows to a pipe or pipes of smaller size, or terminates in
a burner. The terminal pressure in the case of service-pipes must be
settled, as mentioned in Chapter II., broadly according to the pressure
at which the burners in use work best, and this is very different in the
case of flat-flame burners for coal-gas and burners for acetylene. The
most suitable pressure for acetylene burners will be referred to later,
but may be taken as equal to p_0 inches head of water. Then, calling the
initial pressure (_i.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 0.003, 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 = 0.001253_d^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 = 1313.5_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. 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^2_l/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^2_l/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 formulae 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.

When dealing with coal-gas, it is highly important to bear in mind that
the ordinary distributing formulae 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.

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