The work performed by steam expanded in a cylinder may be calculated by means of Hyperbolic Logarithms given in the following Table.

The temperature of expanding steam at any instant is the same as that which accompanies the pressure at that instant, according to Table 1.

Expansive-Work of Steam in a Cylinder.—If there were no clearance in a cylinder, and the total work performed by the steam during its admission be represented by 1, the additional work performed by expanding the steam to the end of the stroke, is represented by the hyperbolic logarithm of the ratio of expansion. The ratio of expansion is, if there be no clearance, expressed by the quotient obtained by dividing the length of stroke by the period of admission. Adding the work done during admission and that done during expansion together, the whole work done in one stroke is represented proportionally by

1 + Hyperbolic Logarithm of ratio of Expansion.

This expression shows the whole work done during admission to the cylinder, as well as during expansion for the remainder of the stroke, supposing the work done in admission is represented by 1. And, to find the total actual work done in any case, this expression must be multiplied by the actual work during admission. For instance, take a cylinder 12 inches diameter with 2 feet stroke, without clearance, having steam of 60 pounds pressure above the atmosphere admitted on the piston during 6 inches, or one-fourth of the stroke. Then the area of the piston is = 12 x 12 X 7854 = 1131 square inches; and the whole pressure on the piston is 1131 × 60 lbs = 678.6 pounds. The product of the whole pressure by

the ength in feet of that portion of the stroke during which steam is admitted, expresses the total work during admission, in foot-pounds = 678.6 pounds 5 foot = 339'3 foot-pounds. The ratio of expansion is 2+ 54, that is, the steam is expanded four times. The Hyperbolic Logarithm of 4 is, from Table 2 = 1.3862, and 1 +1.3862 = 2.3862, and 339′3 foot-pounds 23862 809 637 foot-pounds the total work of the stroke, x effected by the admission initially for the fourth of the stroke, showing that the work performed by the steam initially has been increased to more than 2 times its amount, by the simple act of expansion after the steam from the boiler ceased to flow into the cylinder.

=

CYLINDERS OF STEAM-ENGINES.

Condensation.-It is found in practice that nearly all steam engines use half as much more steam than is theoretically required, and this loss is mostly caused by condensation of the steam in the cylinder. When steam enters a cold cylinder, it is rapidly condensed during the operation of warming the cylinder and piston, and raising their heat up to the same temperature as the steam, because the piston will not move until both it and the surrounding surfaces are heated to a temperature approaching more or less that of the steam. Re-evaporation takes place during the whole time of exhaust. The steam, when exhausting after expansion, being lower in pressure and temperature, cools the cylinder and steam passages, and absorbs the heat. The heat thus abstracted must be restored to the metal by the entering steam, a portion of which must be condensed to restore the heat thus lost, because, as already stated, until the metal is considerably raised in temperature, the heat in the entering steam will be expended in heating the surfaces, instead of moving the piston. Condensation also goes on in the cylinder, due to the performance of work during expansion in driving the piston. The steam falls in temperature owing to its change in volume during expansion, and the temperature of the interior surfaces of the cylinder also falls during expansion, nearly with that of the steam, parting with heat to re-evaporate the water formed. Therefore, at the commencement of each stroke, a portion of the entering steam must be condensed to restore the heat lost by condensation and the cooling of the cylinder by re-evaporation during the previous expansion, as well as the heat abstracted by the steam during exhaust.

The extent to which cylinder condensation takes place depends upon the extent of the cooling surfaces opposed, and also upon the quantity of water mixed with the steam and carried with it from the boiler; but part of the water formed from the condensed steam is re-converted into steam during expansion, and the heat necessary for its re-evaporation is supplied from three sources. First, from the heat stored in the metal which was abstracted from the entering steam. Secondly, from the sensible heat given up by the

steam as it falls in pressure and temperature during expansion. Thirdly, from the latent heat given up by the steam during condensation. So that the action of condensation and re-evaporation is continually going on in the cylinder. Condensation varies as the size of cylinder, for as the diameter is increased, the condensing surfaces increase directly as the diameter; but the area and consequently the volume of steam increases as the square of the diameter; the condensing surfaces of the piston and cylinder-ends increase as the square of the diameter; but the volume of steam cut off at a given proportion of the stroke increases directly as the length of stroke, so that the loss from condensation diminishes as the diameter of cylinder and the length of stroke are increased. Condensation also varies with the rate of expansion; the weight of steam condensed increases rapidly with each increase in the ratio of expansion.

Cylinder-Condensation causes a great loss of both steam and fuel, and forms an obstacle to working expansively; in fact, unless the cylinder is protected in some way, so as to keep up the temperature of the steam during expansion the full benefit cannot be derived from working expansively. If steam could only be maintained at a suitably high temperature during expansion, without condensation, then the reduction of pressure during expansion would be the exact equivalent of the work done in expanding. It is found in practice that even in cylinders jacketed in the best manner the loss from condensation is at least from 1 to 2 lbs. per horse-power per hour, and in unjacketed but well clothed cylinders the loss from condensation is from 4 to 5 lbs. per horse-power per hour.

Leaky Pistons are another source of loss, and the amount of steam which from this cause escapes past the piston increases with the pressure of the steam and also with the age of the engine, so that a quantity of steam is continually passing through the cylinder without performing any work.

Leaky Valves also cause loss by admitting the steam after it is supposed to be cut off, and the initial work of such steam is lost, the cause of leakage being either want of stiffness in the valve, which allows it to bend into the ports in passing over them, or the surface is made so small that capillary attraction does not properly take place between the valve and its seat.

Clearance between the piston and the cylinder-covers, and the space occupied by the steam-passages, cause considerable loss, because these spaces are emptied of steam at each exhaust, and have to be re-filled at the beginning of each stroke, and the steam thus used does no work during admission, although it is not altogether lost, because it acts by expansion during the stroke.

Compression. The loss due to clearance and waste-room in the steam passages may be avoided by compressing the steam; this is accomplished by closing the exhaust-port a little before the termination of the return stroke, and the advancing piston compresses the confined steam against the cylinder-end. This is motion against resistance, and the work lost by the piston is imparted as heat to the steam, the compression of which raises its

temperature, and its pressure can thus be raised up to its initial pressure, and heat will be applied to the cylinder-covers and piston, which would otherwise be abstracted from the steam from the boiler, and condensation is prevented to that extent.

Cushioning. Another great advantage from compression is that the compressed steam acts as a cushion to the piston, and prevents a sudden shock at the end and beginning of each stroke, when the motion of the piston is reversed, and the power used in compressing the steam (with the exception of loss from friction) is returned by the re-expansion of the compressed steam on the reversal of the piston. By properly adjusting the quantity of cushion, the momentum of the piston may be balanced, and the engine may be made to run smoothly and noiselessly.

Back-Pressure causes loss of power, the extent of which depends upon the quantity of water mixed with the exhaust-steam, and also upon the amount of resistance opposed to the escape of the exhaust-steam from the cylinder, in the shape of contracted ports and passages and bent exhaust pipes. Bends and elbows in the exhaust-pipe cause great back-pressure, but in non-condensing engines the back-pressure is never less than the pressure of the atmosphere, plus the power required to expel the exhaust steam from the cylinder. In condensing-engines, the condenser and airpump are employed to remove the back-pressure or pressure of the atmosphere, but as a perfect vacuum is never obtained and there is always some resistance to the escape of the steam from the cylinder, there is always a back-pressure of at least 2 lbs. per square inch in condensing-engines.

Ratio of Expansion.-In order to obtain all the available power, the steam should be brought on to the piston at its highest pressure and cut off quickly, so that the pressure does not fall during the closing of the port, as expansion cannot begin properly until the port is closed, and the full expansive force of the steam should be used as nearly as possible to the end of the stroke, and then exhausted freely, therefore the steam must be cut off at such a part of the stroke that it will expand to the lowest practicable point before exhausting. In practice the best results have been obtained by expanding the steam 6 times in single-cylinder steam-jacketed condensing-engines; 4 times in single-cylinder condensing-engines without steam jackets; 3 times in single-cylinder steam-jacketed non-condensing engines; 3 times in single cylinder non-condensing engines without steam jackets, but with well-clothed cylinders; 8 times in double-expansion condensing steam-jacketed engines; 6 times in double-expansion condensing engines without jackets, but with well-clothed cylinders; 10 times in tripleexpansion surface-condensing engines: and 12 times in quadruple expansion surface-condensing engines. In all cases the utmost feasible ratio of expansion is the number of times the total back pressure is contained in the total initial pressure.

Lowest Absolute Terminal-Pressure.-In non-condensing engines, the exhaust port being open to the atmosphere, there is a back pressure of

15 lbs. per square inch, plus the power necessary to drive the engine against its own friction, and to expel the exhaust steam from the cylinder, which is on an average 5 lbs. ; so that the lowest terminal absolute pressure to which steam can be economically expanded is 20 lbs. In condensing engines, there is always a pressure in the condenser to be provided against, as well as the resistance to the escape of the steam from the cylinder, and the power necessary to drive the engine against its own friction, so that the lowest terminal absolute pressure to which steam can be economically expanded, is 8 lbs. per square inch. When the steam is expanded to a lower terminal pressure than this, the result will be loss of power.

Economical Working.-To secure the utmost economy, it is necessary to work at a good rate of expansion with dry steam, and this can only be obtained by keeping the steam in the cylinder at such a point, that it will be as nearly as possible totally free from condensation; for this purpose the steam jacket was designed.

Steam-Jackets.-The object of the steam-jacket is to maintain a uniform temperature in the cylinder, and obtain dry steam throughout the stroke, by preventing condensation in the cylinder. The effect of the jacket is to remove the condensation from the inside of the cylinder, where it retards the effective working of the piston, to the outside of the cylinder into the jacket, whence it can easily be drained off and returned to the boiler as feed-water. To enable the jacket to work properly, means must be provided to keep it clear of both air and water, otherwise they will destroy its action. It is essential to supply the jacket with dry steam, of a

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Fig. 15.-Steam-Jacket.

temperature not less than that of the steam on entering the cylinder, and the jacket should be drained automatically by a steam-trap. Exhaust-steam should not be used for heating the jacket, as the cylinder would be enveloped in steam of a less temperature than that inside the cylinder, and the heat would flow from the hotter to the colder steam and cause loss of power.

A simple form of steam-jacket, cast in one piece with the cylinder, as shown in Fig. 15; the cylinder covers are also jacketed. The jackets of the cylinder and cover should be connected by at least 6 holes, and care must be used in making the joint to prevent these holes from being filled up with red lead, but pieces of tube screwed into the cylinder-cover effectually prevents this taking place. The jacket is filled with steam from the boiler, and condensation in the cylinder during expansion is prevented by the heat passing from the jacket to the expanding steam.