| | | | |
| Reaction. | Diamond | Amorphous | |
| | Carbon. | Carbon. | |
|________________________________|_________|___________|________|
| | | | |
| (1) C (solid) + O . . . | 26.1 | 29.1 | ... |
| (2) C (solid) + O_2 . . . | 94.3 | 97.3 | ... |
| (3) CO + O (2 - 1) . . . | ... | ... | 68.2 |
| (4) Conversion of solid carbon | | | |
| into gas (3 - 1) . . . | 42.1 | 39.1 | ... |
| (5) C (gas) + O (1 + 4) . . | ... | ... | 68.2 |
| (6) Conversion of amorphous | | | |
| carbon to diamond . . | ... | ... | 3.0 |
| (7) C_2 + H_2 . . . . | -58.1 | -52.1 | ... |
| (8) C_2H_2 + 2-1/2O_2 . . | ... | ... | 315.7 |
|________________________________|_________|___________|________|
W. G. Mixter has determined the heat of combustion of acetylene to be 312.9 calories at constant volume, and 313.8 at constant pressure. Using Berthelot and Matignon's data given above for amorphous carbon, this represents the heat of formation to be -50.2 (Mixter himself calculates it as -51.4) calories. By causing compressed acetylene to dissociate under the influence of an electric spark, Mixter measured its heat of formation as -53.3 calories. His corresponding heats of combustion of ethylene are 344.6 calories (constant volume) and 345.8 (constant pressure); for its heat of formation he deduces a value -7.8, and experimentally found one of about -10.6 (constant pressure).
THE ACETYLENE FLAME.--It has been stated in Chapter I. that acetylene burnt in self-luminous burners gives a whiter light than that afforded by any other artificial illuminant, because the proportion of the various spectrum colours in the light most nearly resembles the corresponding proportion found in the direct rays of the sun. Calling the amount of monochromatic light belonging to each of the five main spectrum colours present in the sun's rays unity in succession, and comparing the amount with that present in the light obtained from electricity, coal-gas, and acetylene, Münsterberg has given the following table for the composition of the several lights mentioned:
| | | | | |
| | Electricity | Coal-Gas | Acetylene | |
| |________________|__________________|_______________|_______|
| Colour | | | | | | | |
| in | | | | | | With | |
| Spectrum.| Arc. | Incan- | Lumin- | Incan- | Alone.| 3 per | Sun- |
| | | descent.| ous. | descent.| | Cent. | light.|
| | | | | | | Air. | |
|__________|______|_________|________|_________|_______|_______|_______|
| | | | | | | | |
| Red | 2.09 | 1.48 | 4.07 | 0.37 | 1.83 | 1.03 | 1 |
| Yellow | 1.00 | 1.00 | 1.00 | 0.90 | 1.02 | 1.02 | 1 |
| Green | 0.99 | 0.62 | 0.47 | 4.30 | 0.76 | 0.71 | 1 |
| Blue | 0.87 | 0.91 | 1.27 | 0.74 | 1.94 | 1.46 | 1 |
| Violet | 1.08 | 0.17 | 0.15 | 0.83 | 1.07 | 1.07 | 1 |
| Ultra- | | | | | | | |
| Violet | 1.21 | ... | ... | ... | ... | ... | 1 |
|__________|______|_________|________|_________|_______|_______|_______|
These figures lack something in explicitness; but they indicate the greater uniformity of the acetylene light in its proportion of rays of different wave-lengths. It does not possess the high proportion of green of the Welsbach flame, or the high proportion of red of the luminous gas- flame. It is interesting to note the large amount of blue and violet light in the acetylene flame, for these are the colours which are chiefly concerned in photography; and it is to their prominence that acetylene has been found to be so very actinic. It is also interesting to note that an addition of air to acetylene tends to make the light even more like that of the sun by reducing the proportion of red and blue rays to nearer the normal figure.
H. Erdmann has made somewhat similar calculation, comparing the light of acetylene with that of the Hefner (amyl acetate) lamp, and with coal-gas consumed in an Argand and an incandescent burner. Consecutively taking the radiation of the acetylene flame as unity for each of the spectrum colours, his results are:
| | | | |
| | | | Coal-Gas |
| Colour in | Wave-Lengths, | |_______________________|
| Spectrum | uu | Hefner Light | | |
| | | | Argand | Incandescent |
|___________|_______________|______________|________|______________|
| | | | | |
| Red | 650 | 1.45 | 1.34 | 1.03 |
| Orange | 610 | 1.22 | 1.13 | 1.00 |
| Yellow | 590 | 1.00 | 1.00 | 1.00 |
| Green | 550 | 0.87 | 0.93 | 0.86 |
| Blue | 490 | 0.72 | 1.27 | 0.92 |
| Violet | 470 | 0.77 | 1.35 | 1.73 |
|___________|_______________|______________|________|______________|
B. Heise has investigated the light of different flames, including acetylene, by a heterochromatic photometric method; but his results varied greatly according to the pressure at which the acetylene was supplied to the burner and the type of burner used. Petroleum affords light closely resembling in colour the Argand coal-gas flame; and electric glow-lamps, unless overrun and thereby quickly worn out, give very similar light, though with a somewhat greater preponderance of radiation in the red and yellow.
| | | |
| | Percent of Total | |
| Light. | Energy manifested | Observer. |
| | as Light. | |
|____________________________|___________________|___________________|
| | | |
| Candle, spermaceti . . | 2.1 | Thomsen |
| " paraffin . . . | 1.53 | Rogers |
| Moderator lamp . . . | 2.6 | Thomsen |
| Coal-gas . . . . . | 1.97 | Thomsen |
| " . . . . . | 2.40 | Langley |
| " batswing . . . | 1.28 | Rogers |
| " Argand . . . | 1.61 | Rogers |
| " incandesce . . | 2 to 7 | Stebbins |
| Electric glow-lamp . . | about 6 | Merritt |
| " " . . | 5.5 | Abney and Festing |
| Lime light (new) . . . | 14 | Orehore |
| " (old) . . . | 8.4 | Orehore |
| Electric arc . . . . | 10.4 | Tyndall; Nakano |
| " . . . . | 8 to 13 | Marks |
| Magnesium light . . . | 12.5 | Rogers |
| Acetylene . . . . | 10.5 | Stewart and Hoxie |
| " (No. 0 slit burner | 11.35 | Neuberg |
| " (No. 00000 . . | | |
| Bray fishtail) | 13.8 | Neuberg |
| " (No. 3 duplex) . | 14.7 | Neuberg |
| Geissler tube . . . | 32.0 | Staub |
|____________________________|___________________|___________________|
Violle and Féry, also Erdmann, have proposed the use of acetylene as a standard of light. As a standard burner Féry employed a piece of thermometer tube, cut off smoothly at the end and having a diameter of 0.5 millimetre, a variation in the diameter up to 10 per cent. being of no consequence. When the height of the flame ranged from 10 to 25 millimetres the burner passed from 2.02 to 4.28 litres per hour, and the illuminating power of the light remained sensibly proportional to the height of the jet, with maximum variations from the calculated value of ±0.008. It is clear that for such a purpose as this the acetylene must be prepared from very pure carbide and at the lowest possible temperature in the generator. Further investigations in this direction should be welcome, because it is now fairly easy to obtain a carbide of standard quality and to purify the gas until it is essentially pure acetylene from a chemical point of view.
L. W. Hartmann has studied the flame of a mixture of acetylene with hydrogen. He finds that the flame of the mixture is richer in light of short wave-lengths than that of pure acetylene, but that the colour of the light does not appear to vary with the proportion of hydrogen present.
Numerous investigators have studied the optical or radiant efficiency of artificial lights, i.e., the proportion of the total heat plus light energy emitted by the flame which is produced in the form of visible light. Some results are shown in the table on the previous page.
Figures showing the ratio of the visible light emitted by various illuminants to the amount of energy expended in producing the light and also the energy equivalent of each spherical Hefner unit evolved have been published by H. Lux, whose results follow:
| | | | | |
| | Ratio of | Ratio of | Mean | Energy |
| | Light | Light | Spherical | Equiva- |
| Light. | emitted to | emitted to | Illuminat- | lent to 1 |
| | Total | Energy | ing Power. | Spherical |
| | Radiation. | Impressed. | Hefners. | Hefner in |
| | | | | Watts. |
|____________________|____________|____________|____________|___________|
| | | | | |
| | Per Cent. | Per Cent. | | |
| Hefner lamp | 0.89 | 0.103 | 0.825 | 0.108 |
| Paraffin lamp, 14" | 1.23 | 0.25 | 12.0 | 0.105 |
| ACETYLENE, 7.2 | | | | |
| litre burner | 6.36 | 0.65 | 6.04 | 0.103 |
| Coal-gas incandes- | | | | |
| cent, upturned | 2.26-2.92 | 0.46 | 89.6 | 0.037 |
| " incandes- | | | | |
| cent, inverted | 2.03-2.97 | 0.51 | 82.3 | 0.035 |
| Carbon filament | | | | |
| glow-lamp | 3.2-2.7 | 2.07 | 24.5 | 0.085 |
| Nernst lamp | 5.7 | 4.21-3.85 | 91.9 | 0.073 |
| Tantalum lamp | 8.5 | 4.87 | 26.7 | 0.080 |
| Osram lamp | 9.1 | 5.36 | 27.4 | 0.075 |
| Direct-current arc | 8.1 | 5.60 | 524 | 0.047 |
| " " enclosed | 2.0 | 1.16 | 295 | 0.021 |
| Flame arc, yellow | 15.7 | 13.20 | 1145 | 0.041 |
| " " white | 7.6 | 6.66 | 760 | 0.031 |
| Alternating- | | | | |
| current arc | 3.7 | 1.90 | 89 | 0.038 |
| Uviol mercury | | | | |
| vapour lamp | 5.8 | 2.24 | 344 | 0.015 |
| Quartz lamp | 17.6 | 6.00 | 2960 | 0.014 |
|____________________|____________|____________|____________|___________|
CHEMICAL PROPERTIES.--It is unnecessary for the purpose of this work to give an exhaustive account of the general chemical reactions of acetylene with other bodies, but a few of the more important must be referred to. Since the gases are liable to unite spontaneously when brought into contact, the reactions between, acetylene and chlorine require attention, first, because of the accidents that have occurred when using bleaching- powder (see Chapter V.) as a purifying material for the crude gas; secondly, because it has been proposed to manufacture one of the products of the combination, viz., acetylene tetrachloride, on a large scale, and to employ it as a detergent in place of carbon tetrachloride or carbon disulphide. Acetylene forms two addition products with chlorine, C_2H_2Cl_2, and C_2H_2Cl_4. These are known as acetylene dichloride and tetrachloride respectively, or more systematically as dichlorethylene and tetrachlorethane. One or both of the chlorides is apt to be produced when acetylene comes into contact with free chlorine, and the reaction sometimes proceeds with explosive violence. The earliest writers, such as E. Davy, Wöhler, and Berthelot, stated that an addition of chlorine to acetylene was invariably followed by an explosion, unless the mixture was protected from light; whilst later investigators thought the two gases could be safely mixed if they were both pure, or if air was absent. Owing to the conflicting nature of the statements made, Nieuwland determined in 1905 to study the problem afresh; and the annexed account is chiefly based on his experiments, which, however, still fail satisfactorily to elucidate all the phenomena observed. According to Nieuwland's results, the behaviour of mixtures of acetylene and chlorine appears capricious, for sometimes the gases unite quietly, although sometimes they explode. Acetylene and chlorine react quite quietly in the dark and at low temperatures; and neither a moderate increase in temperature, nor the admission of diffused daylight, nor the introduction of small volumes of air, is necessarily followed by an explosion. Doubtless the presence of either light, air, or warmth increases the probability of an explosive reaction, while it becomes more probable still in their joint presence; but in given conditions the reaction may suddenly change from a gentle formation of addition products to a violent formation of substitution products without any warning or manifest cause. When the gases merely unite quietly, tetrachlorethane, or acetylene tetrachloride, is produced thus:
C_2H_2 + 2Cl_2 = C_2H_2Cl_4;
but when the reaction is violent some hexachlorethane is formed, presumably thus:
2C_2H_2 + 5Cl_2 = 4HCl + C_2 + C_2Cl_6.
The heat evolved by the decomposition of the acetylene by the formation of the hydrochloric acid in the last equation is then propagated amongst the rest of the gaseous mixture, accelerating the action, and causing the acetylene to react with the chlorine to form more hydrochloric acid and free carbon thus;
C_2H_2 + Cl_2 = 2HCl + C_2.
It is evident that these results do not altogether explain the mechanism of the reactions involved. Possibly the formation of substitution products and the consequent occurrence of an explosion is brought about by some foreign substance which acts as a catalytic agent. Such substance may conceivably be one of the impurities in crude acetylene, or the solid matter of a bleaching-powder purifying material. The experiments at least indicate the direction in which safety may be sought when bleaching- powder is employed to purify the crude gas, viz., dilution of the powder with an inert material, absence of air from the gas, and avoidance of bright sunlight in the place where a spent purifier is being emptied. Unfortunately Nieuwland did not investigate the action on acetylene of hypochlorites, which are presumably the active ingredients in bleaching- powder. As will appear in due course, processes have been devised and patented to eliminate all danger from the reaction between acetylene and chlorine for the purpose of making tetrachlorethane in quantity.
Acetylene combines with hydrogen in the presence of platinum black, and ethylene and then ethane result. It was hoped at one time that this reaction would lead to the manufacture of alcohol from acetylene being achieved on a commercial basis; but it was found that it did not proceed with sufficient smoothness for the process to succeed, and a number of higher or condensation products were formed at the same time. It has been shown by Erdmann that the cost of production of alcohol from acetylene through this reaction must prove prohibitive, and he has indicated another reaction which he considered more promising. This is the conversion of acetylene by means of dilute sulphuric acid (3 volumes of concentrated acid to 7 volumes of water), preferably in the presence of mercuric oxide, to acetaldehyde. The yield, however, was not satisfactory, and the process does not appear to have passed beyond the laboratory stage.
It has also been proposed to utilise the readiness with which acetylene polymerises on heating to form benzene, for the production of benzene commercially; but the relative prices of acetylene and benzene would have to be greatly changed from those now obtaining to make such a scheme successful. Acetylene also lends itself to the synthesis of phenol or carbolic acid. If the dry gas is passed slowly into fuming sulphuric acid, a sulpho-derivative results, of which the potash salt may be thrown down by means of alcohol. This salt has the formula C_2H_4O_2,S_2O_6K_2, and on heating it with caustic potash in an atmosphere of hydrogen, decomposing with excess of sulphuric acid, and distilling, phenol results and may be isolated. The product is, however, generally much contaminated with carbon, and the process, which was devised by Berthelot, does not appear to have been pursued commercially. Berthelot has also investigated the action of ordinary concentrated sulphuric acid on acetylene, and obtained various sulphonic derivatives. Schröter has made similar investigations on the action of strongly fuming sulphuric acid on acetylene. These investigations have not yet acquired any commercial significance.
If a mixture of acetylene with either of the oxides of carbon is led through a red-hot tube, or if a similar mixture is submitted to the action of electric sparks when confined within a closed vessel at some pressure, a decomposition occurs, the whole of the carbon is liberated in the free state, while the hydrogen and oxygen combine to form water. Analogous reactions take place when either oxide of carbon is led over calcium carbide heated to a temperature of 200° or 250° C., the second product in this case being calcium oxide. The equations representing these actions are:
C_2H_2 + CO = H_2O + 3C
2C_2H_2 + CO_2 = 2H_2O + 5C
CaC_2 + CO = CaO + 3C
2CaC_2 + CO_2 = 2CaO + 5C
By urging the temperature, or by increasing the pressure at which the gases are led over the carbide, the free carbon appears in the graphitic condition; at lower temperatures and pressures, it is separated in the amorphous state. These reactions are utilised in Frank's process for preparing a carbon pigment or an artificial graphite (cf. Chapter XII.).
Parallel decompositions occur between carbon bisulphide and either acetylene or calcium carbide, all the carbon of both substances being eliminated, while the by-product is either sulphuretted hydrogen or calcium (penta) sulphide. Other organic bodies containing sulphur are decomposed in the same fashion, and it has been suggested by Ditz that if carbide could be obtained at a suitable price, the process might be made useful in removing sulphur (i.e., carbon bisulphide and thiophen) from crude benzol, in purifying the natural petroleum oil which contains sulphur, and possibly in removing "sulphur compounds" from coal-gas.
COMPOUNDS WITH COPPER. By far the most important chemical reactions of acetylene in connexion with its use as an illuminant or fuel are those which it undergoes with certain metals, notably copper. It is known that if acetylene comes in contact with copper or with one of its salts, in certain conditions a compound is produced which, at least when dry, is highly explosive, and will detonate either when warmed or when struck or gently rubbed. The precise mechanism of the reaction, or reactions, between acetylene and copper (or its compounds), and also the character of the product, or products, obtained have been studied by numerous investigators; but their results have been inconclusive and sometimes rather contradictory, so that it can hardly be said that the conditions which determine or preclude the formation of an explosive compound and the composition of the explosive compound are yet known with certainty. Copper is a metal which yields two series of compounds, cuprous and cupric salts, the latter of which contain half the quantity of metal per unit of acid constituent that is found in the former. It should follow, therefore, that there are two compounds of copper with carbon, or copper carbides: cuprous carbide, Cu_2C_2, and cupric carbide, CuC_2. Acetylene reacts at ordinary temperatures with an ammoniacal solution of any cupric salt, forming a black cupric compound of uncertain constitution which explodes between 50° and 70° C. It is decomposed by dilute acids, yielding some polymerised substances. At more elevated temperatures other cupric compounds are produced which also give evidence of polymerisation. Cuprous carbide or acetylide is the reddish brown amorphous precipitate which is the ultimate product obtained when acetylene is led into an ammoniacal solution of cuprous chloride. This body is decomposed by hydrochloric acid, yielding acetylene; but of itself it is, in all probability, not explosive. Cuprous carbide, however, is very unstable and prone to oxidation; so that, given the opportunity, it combines with oxygen or hydrogen, or both, until it produces the copper acetylide, or acetylene-copper, which is explosive--a body to which Blochmann's formula C_2H_2Cu_2O is generally ascribed. Thus it should happen that the exact nature of the copper acetylene compound may vary according to the conditions in which it has been formed, from a substance that is not explosive at all at first, to one that is violently explosive; and the degree of explosiveness should depend on the greater exposure of the compound to air and moisture, or the larger amount of oxygen and moisture in the acetylene during its contact with the copper or copper salt. For instance, Mai has found that freshly made copper acetylide can be heated to 60° C. or higher without explosion; but that if the compound is exposed to air for a few hours it explodes on warming, while if warmed with oxygen it explodes on contact with acetylene. It is said by Mai and by Caro to absorb acetylene when both substances are dry, becoming so hot as to explode spontaneously. Freund and Mai have also observed that when copper acetylide which has been dried in contact with air for four or five hours at a temperature of 50° or 60° C. is allowed to explode in the presence of a current of acetylene, an explosion accompanied by light takes place; but it is always local and is not communicated to the gas, whether the latter is crude or pure. In contact with neutral or acid solutions of cuprous salts acetylene yields various double compounds differing in colour and crystallising power; but according to Chavastelon and to Caro they are all devoid of explosive properties. Sometimes a yellowish red precipitate is produced in solutions of copper salts containing free acid, but the deposit is not copper acetylide, and is more likely to be, at least in part, a copper phosphide--especially if the gas is crude. Hence acid solutions or preparations of copper salts may safely be used for the purification of acetylene, as is done in the case of frankoline, mentioned in Chapter V. It is clear that the amount of free acid in such a material is much more than sufficient to neutralise all the ammonia which may accompany the crude acetylene into the purifier until the material is exhausted in other respects; and moreover, in the best practice, the gas would have been washed quite or nearly free from ammonia before entering the purifier.
From a practical aspect the possible interaction of acetylene and metallic copper has been investigated by Gerdes and by Grittner, whose results, again, are somewhat contradictory. Gerdes exposed neat acetylene and mixtures of acetylene with oil-gas and coal-gas to a pressure of nine or ten atmospheres for ten months at ordinary summer and winter temperatures in vessels made of copper and various alloys. Those metals and alloys which resisted oxidation in air resisted the attack of the gases, but the more corrodible substances were attacked superficially; although in no instance could an explosive body be detected, nor could an explosion be produced by heating or hammering. In further experiments the acetylene contained ammonia and moisture and Gerdes found that where corrosion took place it was due exclusively to the ammonia, no explosive compounds being produced even then. Grittner investigated the question by leading acetylene for months through pipes containing copper gauze. His conclusions are that a copper acetylide is always produced if impure acetylene is allowed to pass through neutral or ammoniacal solutions of copper; that dry acetylene containing all its natural impurities except ammonia acts to an equal extent on copper and its alloys, yielding the explosive compound; that pure and dry gas does not act upon copper or its alloys, although it is possible that an explosive compound may be produced after a great length of time. Grittner has asserted that an explosive compound may be produced when acetylene is brought into contact with such alloys of copper as ordinary brass containing 64.66 per cent. of copper, or red brass containing 74.46 per cent. of copper, 20.67 per cent. of zinc, and 4.64 per cent. of tin; whereas none is obtained when the metal is either "alpaca" containing 64.44 per cent. of copper, 18.79 per cent. of nickel, and 16.33 per cent. of zinc, or britannia metal composed of 91.7 per cent. of copper and 8.3 per cent. of tin. Caro has found that when pure dry acetylene is led for nine months over sheets or filings of copper, brass containing 63.2 per cent. of copper, red brass containing 73.8 per cent., so-called "alpaca-metal" containing 65.3 per cent., and britannia metal containing 90.2 per cent. of copper, no action whatever takes place at ordinary temperatures; if the gas is moist very small quantities of copper acetylide are produced in six months, whatever metal is tested, but the yield does not increase appreciably afterwards. At high temperatures condensation occurs between acetylene and copper or its alloys, but explosive bodies are not formed.
Grittner's statement that crude acetylene, with or without ammonia, acts upon alloys of copper as well as upon copper itself, has thus been corroborated by Caro; but experience renders it tolerably certain that brass (and presumably gun-metal) is not appreciably attacked in practical conditions. Gerdes' failure to obtain an explosive compound in any circumstances may very possibly be explained by the entire absence of any oxygen from his cylinders and gases, so that any copper carbide produced remained unoxidised. Grittner's gas was derived, at least partially, from a public acetylene supply, and is quite likely to have been contaminated with air in sufficient quantity to oxidise the original copper compound, and to convert it into the explosive modification.
For the foregoing reasons the use of unalloyed copper in the construction of acetylene generators or in the subsidiary items of the plant, as well as in burner fittings, is forbidden by statute or some quasi-legal enactment in most countries, and in others the metal has been abandoned for one of its alloys, or for iron or steel, as the case may be. Grittner's experiments mentioned above, however, probably explain why even alloys of copper are forbidden in Hungary. (Cf. Chapter IV., page 127.)
When acetylene is passed over finely divided copper or iron (obtained by
reduction of the oxide by hydrogen) heated to from 130° C. to 250° C., the
gas is more or less completely decomposed, and various products, among
which hydrogen predominates, result. Ethane and ethylene are undoubtedly
formed, and certain homologues of them and of acetylene, as well as
benzene and a high molecular hydrocarbon (C_7H_6)_n termed "cuprene," have
been found by different investigators. Nearly the same hydrocarbons, and
others constituting a mixture approximating in composition to some natural
petroleums, are produced when acetylene is passed over heated nickel (or
certain other metals) obtained by the reduction of the finely divided
oxide. These observations are at present of no technical importance, but
are interesting scientifically because they have led up to the
promulgation of a new theory of the origin of petroleum, which, however,
has not yet found universal acceptance.
CHAPTER VII
MAINS AND SERVICE-PIPES--SUBSIDIARY APPARATUS
The process by which acetylene is produced, and the methods employed for purifying it and rendering it fit for consumption in dwelling-rooms, having been dealt with in the preceding pages, the present chapter will be devoted to a brief account of those items in the plant which lie between the purifier outlet and the actual burner, including the meter, governor, and pressure gauge; the proper sizes of pipe for acetylene; methods of laying it, joint-making, quality of fittings, &c.; while finally a few words will be said about the precautions necessary when bringing a new system of pipes into use for the first time.
THE METER.--A meter is required either to control the working of a complete acetylene installation or to measure the volume of gas passing through one particular pipe, as when a number of consumers are supplied through separate services under agreement from a central supply plant. The control which may be afforded by the inclusion of a meter in the equipment of a domestic acetylene generating plant is valuable, but in practice will seldom be exercised. The meter records check the yield of gas from the carbide consumed in a simple and trustworthy manner, and also serve to indicate when the material in the purifier is likely to be approaching exhaustion. The meter may also be used experimentally to check the soundness of the service-pipes or the consumption of a particular burner or group of burners. Altogether it may be regarded as a useful adjunct to a domestic lighting plant, provided full advantage is taken of it. If, however, there is no intention to pay systematic attention to the records of the meter, it is best to omit it from such an installation, and so save its initial cost and the slight loss of pressure which its use involves on the gas passing through it. A domestic acetylene lighting plant can be managed quite satisfactorily without a meter, and as a multiplication of parts is undesirable in an apparatus which will usually be tended by someone not versed in technical operations, it is on the whole better to omit the meter in such an installation. Where the plant is supervised by a technical man, a meter may advisedly be included in the equipment. Its proper position in the train of apparatus is immediately after the purifier. A meter must not be used for unpurified or imperfectly purified acetylene, because the impurities attack the internal metallic parts and ultimately destroy them. The supply of acetylene to various consumers from a central generating station entails the fixing of a meter on each consumer's service-pipe, so that the quantity consumed by each may be charged for accordingly, just as in the case of public coal-gas supplies.
There are two types of gas-meter in common use, either of which may, without essential alteration, be employed for measuring the volume of acetylene passing through a pipe. It is unnecessary to refer here at length to their internal mechanism, because their manufacture by other than firms of professed meter-makers is out of the question, and the user will be justified in accepting the mechanism as trustworthy and durable. Meters can always be had stamped with the seal of a local authority or other body having duly appointed inspectors under the Sales of Gas Act, and the presence of such a stamp on a meter implies that it has been officially examined and found to register quantities accurately, or not varying beyond 2 per cent. in favour of the seller, or 3 per cent, in favour of the consumer. [Footnote: It may be remarked that when a meter-- wet or dry--begins to register incorrectly by reason of old age or want of adjustment, its error is very often in the direction that benefits the customer, i.e., more gas passes through it than the dials record.] Hence a "stamped" meter may be regarded for practical purposes as affording a correct register of the quantities of gas passing through it.
Except that the use of unalloyed copper in any part of the meter where it may come in contact with the gas must be wholly avoided, for the reason that copper is inadmissible in acetylene apparatus (see Chapter VI.), the meters ordinarily employed for coal-gas serve quite well for acetylene. Obviously, however, since so very much less acetylene than coal-gas is consumed per burner, comparatively small meters only will be required even for large installations of acetylene lighting. This fact is now recognised by meter-makers, and meters of all suitable sizes can be obtained. It is desirable, if an ordinary coal-gas meter is being bought for use with acetylene, to have it subjected to a somewhat more rigorous test for soundness than is customary before "stamping" but the makers would readily be able to carry out this additional test.
The two types of gas-meter are known as "wet" and "dry." The case of the wet meter is about hall-filled with water or other liquid, the level of which has to be maintained nearly constant. Several ingenious devices are in use for securing this constancy of level over a more or less extended period, but the necessity for occasional inspection and adjustment of the water-level, coupled with the stoppage of the passage of gas in the event of the water becoming frozen, are serious objections to the employment of the wet meter in many situations. The trouble of freezing may be avoided by substituting for the simple water an aqueous solution of glycerin, or mixture of glycerin with water, suitable strengths for which may be deduced from the table relating to the use of glycerin in holder seals given at the close of Chapter III. The dry meter, on the other hand, is very convenient, because it is not obstructed by the effects of frost, and because it acts for years without requiring attention. It is not susceptible of adjustment for measuring with so high a degree of accuracy as a good wet meter, but its indications are sufficiently correct to fall well within the legalised deviations already mentioned. Such errors, perhaps, are somewhat large for so costly and powerful a gas as acetylene, and they would be better reduced; but it is not so very often that a dry meter reaches its limit of inaccuracy. Whether wet or dry, the meter should be fixed in a place where the temperature is tolerably uniform, otherwise the volumes registered at different times will not bear the same ratio to the mass of gas (or volume at normal temperature), and the registrations will be misleading unless troublesome corrections to compensate for changes of temperature are applied.
THE GOVERNOR, which can be dispensed with in most ordinary domestic acetylene lighting installations provided with a good gasholder of the rising-bell type, is designed to deliver the acetylene to a service-pipe at a uniform pressure, identical with that under which the burners develop their maximum illuminating efficiency. It must therefore both cheek the pressure anterior to it whenever that is above the determined limit to which it is set, and deliver to the efferent service-pipe acetylene at a constant pressure whether all or any number of the burners down to one only are in use. Moreover, when the pressure anterior to the governor falls to or below the determined limit, the governor should offer no resistance--entailing a loss of pressure to the passage of the acetylene. These conditions, which a perfect governor should fulfil, are not absolutely met by any simple apparatus at present in use, but so far as practical utility is concerned service governors which are readily obtainable are sufficiently good. They are broadly of two types, viz., those having a bell floating in a mercury seal, and those having a diaphragm of gas-tight leather or similar material, either the bell or the diaphragm being raised by the pressure of the gas. The action is essentially the same in both cases: the bell or the diaphragm is so weighted that when the pressure of the gas exceeds the predetermined limit the diaphragm or bell is lifted, and, through an attached rod and valve, brings about a partial closure of the orifice by which the gas flows into the bell or the diaphragm chamber. The valve of the governor, therefore, automatically throttles the gas-way more or less according to the difference in pressure before and after the apparatus, until at any moment the gas-way is just sufficient in area to pass the quantity of gas which any indefinite number of burners require at their fixed working pressure; passing it always at that fixed working pressure irrespective of the number of burners, and maintaining it constant irrespective of the amount of pressure anterior to the governor, or of any variations in that anterior pressure. In most patterns of service governor weights may be added when it is desired to increase the pressure of the effluent gas. It is necessary, in ordering a governor for an acetylene-supply, to state the maximum number of cubic feet per hour it will be required to pass, and approximately the pressure at which it will be required to deliver the gas to the service-pipe. This will usually be between 3 and 5 inches (instead of about 1 inch in the case of coal-gas), and if the anterior pressure is likely to exceed 10 inches, this fact should be stated also. The mercury-seal governors are usually the more trustworthy and durable, but they are more costly than those with leather diaphragms. The seal should have twice or thrice the depth it usually has for coal-gas. The governor should be placed where it is readily accessible to the man in charge of the installation, but where it will not be interfered with by irresponsible persons. In large installations, where a number of separate buildings receive service-pipes from one long main, each service-pipe should be provided with a governor.
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° F.):
(0.7854pd^2 x 0.03604) = 0.028302pd^2 lb.
Consequently a bell which is d inches in diameter, and gives a pressure of p inches of water, will weigh 0.028302pd^2 lb. Or, if W = the weight of the bell in lb., the pressure thrown by it will be W/0.028302d^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, 0.0001086h + 0.0000027d, 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 formulæ 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 formulæ.
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/4d^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 (4w(H - h)) / (7.78Hpid^2) lb. per square inch (d being inches and w lb.), which is equivalent to (4w(H - h)) / (0.03604 x 7.78Hpid^2) = (4.54w(H - h)) / (Hd^2) inches of water. Hence the complete formula for acetylene gasholders is:
p = 35.333W / d^2 - 4.54w(H - h) / Hd^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., pild); (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 pild, 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 = Mhd/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/4d^2v, it was found that for coal-gas Q = 780(hd/sl)^(1/2)
This formula, in its usual form, is
Q = 1350d^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 = 0.001253d^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
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.
When dealing with coal-gas, it is highly important to bear in mind that the ordinary distributing formulæ 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.
The distributing formulæ also assume that the pipe is virtually straight; bends and angles introduce disturbing influences. If the bend is sharp, or if there is a right-angle, an allowance should be made if it is desired to put in pipes of the smallest permissible dimensions. In the case of the most usual sizes of pipes employed for acetylene mains or services, it will suffice to reckon that each round or square elbow is equivalent in the resistance it offers to the flow of gas to a length of 5 feet of pipe of the same diameter. Hence if 5 feet is added to the actual length of pipe to be laid for every bond or elbow which will occur in it, and the figure so obtained is taken as the value of l in formulæ (i), (ii), or (iii), the values then found for Q, d, or h will be trustworthy for all practical purposes.
It may now be useful to give an example of the manner of using the foregoing formulæ when the tables of sizes of pipes are not available. Let it be supposed that an institution is being equipped for acetylene lighting; that 50 burners consuming 0.70 cubic foot, and 50 consuming 1.00 cubic foot of acetylene per hour may be required in use simultaneously; that a pressure of at least 2-1/2 inches is required at all the burners; that for sufficient reasons it is considered undesirable to use a higher distributing pressure than 4 inches at the gasholder, outlet of the purifiers, or initial governor (whichever comes last in the train of apparatus); that the gasholder is located 100 feet from the main building of the institution, and that the trunk supply-pipe through the latter must be 250 feet in length, and the supplies to the burners, either singly or in groups, be taken from this trunk pipe through short lengths of tubing of ample size. What should be the diameter of the trunk pipe, in which it will be assumed that ten bonds or elbows are necessary?