Scientific American Supplement, No. 275, April 9, 1881

+ p), and a temperature of 26.5° Cent. (80° Fahr.); p

= 5.24 atm., p = 5.00 atm. Hence p

– p = 0.24 atm. =0.24 x 10,334 kilogrammes per square meter (2,116 lb. per square foot); whence we obtain b

= 0.3002275. 2nd experiment: Q = 0.1586 cubic meter (5.6 cubic feet), at a pressure of ½(p

+ p), and a temperature of 26.5° Cent. (80° Fahr.); p

= 3.650 atm., p = 3.545 atm. Hence p

– p = 0.105 atm. = 0.105 x 10,334 kilogrammes per square meter (2,116 lb. per square foot); whence we obtain b

= 0.0002255. It is clear that these experiments give very small values for the coefficient. The divergence from the results which D'Aubuisson's formula would give is due to the fact that his formula was determined with very small pipes. It is probable that the coefficients corresponding to diameters of 0.15 meter (6 in.) and 0.20 meter (8 in.) for a substance as smooth as tin, would be still smaller respectively than the figures obtained above.

The divergence from the results obtained by M. Arson's formula does not arise from a difference in size, as this is taken into account. The author considers that it may be attributed to the fact that the pipes for the St. Gothard Tunnel were cast with much greater care than ordinary pipes, which rendered their surface smoother, and also to the fact that flanged joints produce much less irregularity in the internal surface than the ordinary spigot and faucet joints.

Lastly, the difference in the methods of observation and the errors which belong to them, must be taken into account. M. Stockalper, who experimented on great pressures, used metallic gauges, which are instruments on whose sensibility and correctness complete reliance cannot be placed; and moreover the standard manometer with which they were compared was one of the same kind. The author is not of opinion that the divergence is owing to the fact that M. Stockalper made his observations on an air conduit, where the pressure was much higher than in gas pipes. Indeed, it may be assumed that gases and liquids act in the same manner; and, as will be [1] explained later on, there is reason to believe that with the latter a rise of pressure increases the losses of pressure instead of diminishing them.

[Transcribers note 1: corrected from 'as will we explained']

All the pipes for supplying compressed air in tunnels and in headings of mines are left uncovered, and have flanged joints; which are advantages not merely as regards prevention of leakage, but also for facility of laying and of inspection. If a compressed air pipe had to be buried in the ground the flanged joint would lose a part of its advantages; but, nevertheless, the author considers that it would still be preferable to the ordinary joint.

It only remains to refer to the motors fed with the compressed air. This subject is still in its infancy from a practical point of view. In proportion as the air becomes hot by compression, so it cools by expansion, if the vessel containing it is impermeable to heat. Under these conditions it gives out in expanding a power appreciably less than if it retained its original temperature; besides which the fall of temperature may impede the working of the machine by freezing the vapor of water contained in the air.

If it is desired to utilize to the utmost the force stored up in the compressed air it is necessary to endeavor to supply heat to the air during expansion so as to keep its temperature constant. It would be possible to attain this object by the same means which prevent heating from compression, namely, by the circulation and injection of water. It would perhaps be necessary to employ a little larger quantity of water for injection, as the water, instead of acting by virtue both of its heat of vaporization and of its specific heat, can in this case act only by virtue of the latter. These methods might be employed without difficulty for air machines of some size. It would be more difficult to apply them to small household machines, in which simplicity is an essential element; and we must rest satisfied with imperfect methods, such as proximity to a stove, or the immersion of the cylinder in a tank of water. Consequently loss of power by cooling and by incomplete expansion cannot be avoided. The only way to diminish the relative amount of this loss is to employ compressed air at a pressure not exceeding three or four atmospheres.

The only real practical advance made in this matter is M. Mékarski's compressed air engine for tramways. In this engine the air is made to pass through a small boiler containing water at a temperature of about 120° Cent. (248° Fahr.), before entering the cylinder of the engine. It must be observed that in order to reduce the size of the reservoirs, which are carried on the locomotive, the air inside them must be very highly compressed; and that in going from the reservoir into the cylinder it passes through a reducing valve or expander, which keeps the pressure of admission at a definite figure, so that the locomotive can continue working so long as the supply of air contained in the reservoir has not come down to this limiting pressure. The air does not pass the expander until after it has gone through the boiler already mentioned. Therefore, if the temperature which it assumes in the boiler is 100° Cent. (212° Fahr.), and if the limiting pressure is 5 atm., the gas which enters the engine will be a mixture of air and water vapor at 100° Cent.; and of its total pressure the vapor of water will contribute I atm. and the air 4 atm. Thus this contrivance, by a small expenditure of fuel, enables the air to act expansively without injurious cooling, and even reduces the consumption of compressed air to an extent which compensates for part of the loss of power arising from the preliminary expansion which the air experiences before its admission into the engine. It is clear that this same contrivance, or what amounts to the same thing, a direct injection of steam, at a sufficient pressure, for the purpose of maintaining the expanding air at a constant temperature, might be tried in a fixed engine worked by compressed air with some chance of success.

Whatever method is adopted it would be advantageous that the losses of pressure in the pipes connecting the compressors with the motors should be reduced as much as possible, for in this case that loss would represent a loss of efficiency. If, on the other hand, owing to defective means of reheating, it is necessary to remain satisfied with a small amount of expansion, the loss of pressure in the pipe is unimportant, and has only the effect of transferring the limited expansion to a point a little lower on the scale of pressures. If W is the net disposable force on the shaft of the engine which works the compressor, v

the volume of air at the compressor, p

. given by the compressor, and at the temperature of the surrounding air, and p

the atmospheric pressure, the efficiency of the compressor, assuming the air to expand according to Boyle's law, is given by the well-known formula–

. Let p

be the value to which the pressure is reduced by the loss of pressure at the end of the conduit, and v

the volume which the air occupies at this pressure and at the same temperature; the force stored up in the air at the end of its course through the conduit is p

v

log(p

/p

); consequently, the efficiency of the conduit is

, a fraction that may be reduced to the simple form

, if there is no leakage during the passage of the air, because in that cause p

v

= p

v

. Lastly, if W

is the net disposable force on the shaft of the compressed air motor, the efficiency of this engine will be,

and the product of these three partial efficiencies is equal to W

/W, the general efficiency of the transmission.

III. Transmission by Pressure Water.–As transmission of power by compressed air has been specially applied to the driving of tunnels, so transmission by pressure water has been specially resorted to for lifting heavy loads, or for work of a similar nature, such as the operations connected with the manufacture of Bessemer steel or of cast-iron pipes. The author does not propose to treat of transmissions established for this special purpose, and depending on the use of accumulators at high pressure, as he has no fresh matter to impart on this subject, and as he believes that the remarkable invention of Sir William Armstrong was described for the first time, in the "Proceedings of the Institution of Mechanical Engineers." His object is to refer to transmissions applicable to general purposes.

The transmission of power by water may occur in another form. The motive force to be transmitted may be employed for working pumps which raise the water, not to a fictitious height in an accumulator, but to a real height in a reservoir, with a channel from this reservoir to distribute the water so raised among several motors arranged for utilizing the pressure. The author is not aware that works have been carried out for this purpose. However, in many towns a part of the water from the public mains serves to supply small motors–consequently, if the water, instead of being brought by a natural fall, has been previously lifted artificially, it might be said that a transmission of power is here grafted on to the ordinary distribution of water.

Unless a positive or negative force of gravity is introduced into the problem, independently of the force to be transmitted, the receivers of the water pressure must be assumed to be at the same level as the forcing pumps, or more correctly, the water discharged from the receivers to be at the same level as the surface of the water from which the pumps draw their supply. In this case the general efficiency of transmission is the product of three partial efficiencies, which correspond exactly to those mentioned with regard to compressed air. The height of lift, contained in the numerator of the fraction which expresses the efficiency of the pumps, is not to be taken as the difference in level between the surface of the water in the reservoir and the surface of the water whence the pumps draw their supply; but as this difference in level, plus the loss of pressure in the suction pipe, which is usually very short, and plus the loss in the channel to the reservoir, which may be very long. A similar loss of initial pressure affects the efficiency of the discharge channel. The reservoir, if of sufficient capacity, may become an important store of power, while the compressed air reservoir can only do so to a very limited extent.

Omitting the subject of the pumps, and passing on at once to the discharge main, the author may first point out that the distinction between the ascending and descending mains of the system is of no importance, for two reasons: first, that nothing prevents the motors being supplied direct from the first alone; and second, that the one is not always distinct from the other. In fact, the reservoir may be connected by a single branch pipe with the system which goes from the pumps to the motors; it may even be placed at the extreme end of this system beyond the motors, provided always that the supply pipe is taken into it at the bottom. The same formula may be adopted for the loss of initial pressure in water pipes as for compressed air pipes, viz.,

; h being the difference of level between the two ends of the portion of conduit of length, L, and the sign + or – being used according as the conduit rises or falls. The specific weight, δ, is constant, and the quotients, p

/δ and p/δ, represent the heights, z and z

, to which the water could rise above the pipes, in vertical tubes branching from it, at the beginning and end of the transit. The values assigned to the coefficient b

in France, are those determined by D'Arcy. For new cast-iron pipes he gives b

– 0.0002535 + 1/D 0.000000647; and recommends that this value should be doubled, to allow for the rust and incrustation which more or less form inside the pipes during use. The determination of this coefficient has been made from experiments where the pressure has not exceeded four atmospheres; within these limits the value of the coefficient, as is generally admitted, is independent of the pressure. The experiments made by M. Barret, on the pressure pipes of the accumulator at the Marseilles docks, seem to indicate that the loss of pressure would be greater for high pressures, everything else being equal. This pipe, having a diameter of 0.127 m. (5 in.), was subjected to an initial pressure of 52 atmospheres. The author gives below the results obtained for a straight length 320 m. (1050 ft) long; and has placed beside them the results which D'Arcy's formula would give.

Moreover, these results would appear to indicate a different law from that which is expressed by the formula b

u

, as is easy to see by representing them graphically. It would be very desirable that fresh experiments should be made on water pipes at high pressure, and of various diameters. Of machines worked by water pressure the author proposes to refer only to two which appear to him in every respect the most practical and advantageous. One is the piston machine of M. Albert Schmid, engineer at Zurich. The cylinder is oscillating, and the distribution is effected, without an eccentric, by the relative motion of two spherical surfaces fitted one against the other, and having the axis of oscillation for a common axis. The convex surface, which is movable and forms part of the cylinder, serves as a port face, and has two ports in it communicating with the two ends of the cylinder. The concave surface, which is fixed and plays the part of a slide valve, contains three openings, the two outer ones serving to admit the pressure water, and the middle one to discharge the water after it has exerted its pressure. The piston has no packing. Its surface of contact has two circumferential grooves, which produce a sort of water packing acting by adhesion. A small air chamber is connected with the inlet pipe, and serves to deaden the shocks. This engine is often made with two cylinders, having their cranks at right angles.

The other engine, which is much less used, is a turbine on Girard's system, with a horizontal axis and partial admission, exactly resembling in miniature those which work in the hydraulic factory of St. Maur, near Paris. The water is introduced by means of a distributer, which is fitted in the interior of the turbine chamber, and occupies a certain portion of its circumference. This turbine has a lower efficiency than Schmid's machine, and is less suitable for high pressures; but it possesses this advantage over it, that by regulating the amount of opening of the distributer, and consequently the quantity of water admitted, the force can be altered without altering the velocity of rotation. As it admits of great speeds, it could be usefully employed direct, without the interposition of spur wheels or belts for driving magneto-electric machines employed for the production of light, for electrotyping, etc.

In compressed air machines the losses of pressure due to incomplete expansion, cooling, and waste spaces, play an important part. In water pressure machines loss does not occur from these causes, on account of the incompressibility of the liquid, but the frictions of the parts are the principal causes of loss of power. It would be advisable to ascertain whether, as regards this point, high or low pressures are the most advantageous. Theoretical considerations would lead the author to imagine that for a piston machine low pressures are preferable. In conclusion, the following table gives the efficiencies of a Girard turbine, constructed by Messrs. Escher Wyss & Co., of Zurich, and of a Schmid machine, as measured by Professor Fliegnor, in 1871:

It will be observed that these experiments relate to low pressures; it would be desirable to extend them to higher pressures.