Actual Behaviour of Steam in the Cylinder
76. In fig. 18, we have what we may be called a first approximation to the theoretical indicator diagram of a steam-engine. In the action then described it was assumed(1) that the steam supplied was dry and saturated, and had during admission the full (uniform) pressure of the boiler P1; (2) that there was no transfer of heat to or from the steam except in the boiler and in the condenser; (3) that after more or less complete expansion all the steam was discharged by the return stroke of the piston, during which the back pressure was the (uniform) pressure in the condenser P2; (4) that the volume of the cylinder was swept through by the piston. It remains to be seen how far these assumption are untrue in practice, and how far the efficiency is affected in consequence.
The actual conditions of working differ from these in the following main respects, some of which are illustrated by the practical indicator diagram of fig. 19, which is taken from an actual engine.
77. Owing to the resistance of the ports and passages, and to the inertia of the steam. The pressure within the cylinder is less than P1 during admission and greater than P2 during exhaust.
Moreover P1 and P2 are themselves not absolutely uniform, and P2 is greater than the pressure of steam at the temperature of the condenser, on account of the presence of air in the condenser.
During admission the pressure of steam in the cylinder is less that the boiler pressure by an amount which increases as the piston advances, on account of the increased velocity of the pistons motion and the consequent increased demand for steam. When the ports and passages offer mush resistance the steam is expressively said to be throttled or "wire-drawn." Wire-drawing of steam is in fact a case of imperfectly-resisted expansion (§51). The steam is dried by the process to a small extent, and if initially dry it becomes superheated. In an indicator diagram wire-drawing causes the line of admission to lie below a line drawn at the boiler pressure, and to slope downwards. In fairly good practical instances the mean absolute pressure during admission is about nine-tenths of the pressure in the boiler.
In the same way, during the exhaust the actual back pressure exceeds the pressure in the condenser (shown by a dotted line in fig. 19) by an amount depending on the freedom with which the steam its exit from the cylinder. In condensing engines with a good vacuum the actual back pressure is from 3 to 5 _ per square inch, and in non-conducting engines it is 16 to 18 _ in place of the mere 14&Mac250;7 _ which is the pressure of the atmosphere. The excess of the back pressure may be greatly increase by the presence of water in the cylinder. The effects of wire-drawing do not stop here. The valves open and close more or less slowly; the points of cut-off and release are therefore not absolutely sharp, and the diagram has rounded corners at b and c in place of the sharp angles which mark those events in fig. 18. For this reason release is allowed in practice to occur a little before the end of the forward stroke, hence of the diagram takes a form like that shown in fig. 19. The sharpness of the cut-off, and to a less extent the sharpness of the release, depends greatly on the kind of valves and valve-gear used; valves of the Corliss type (to be described later),which are noted for the suddenness with which admission of steam is stopped, have the merit amongst others of producing a very sharply defined diagram.
78. When the piston is at either end of its stroke there is a small space left between it and the cylinder cover. This space, together with the volume of the passage or passages leading thence to the steam and exhaust valves, is called the clearance. It constitutes a volume through which the piston does not sweep, but which is nevertheless filled with steam when admission occurs, and the steam in the clearance forms a part of the whole steam which expands after the supply from the boiler is cut-off. If AC be the volume swept through by the piston up to release, OA the volume of the clearance, and AB the volume swept through during admission, the apparent ratio of expansion is AC/AB, but the real ratio is (OA+AC)/OA+AB).
Clearance must obviously be taken account of in any calculation of curves of expansion. It is conveniently allowed for in indicator diagrams by shifting the line of no volume back through a distance corresponding to the clearance (fig. 20). In actual engines OA is form 1/10 to 1/50 of the volume of the cylinder.
79. Clearance affects the thermodynamic efficiency of the engine chiefly by altering the consumption of steam per stoke, and its influence depends materially on the compression (§72). If during the back stroke the process of exhausts is discontinued before the end, and the remaining steam is compressed, this cushion of steam will finally fill the volume of the clearance; and by a proper selection of the point at which compression begins the pressure of the cushion may be made to rise just up to the pressure at which steam is admitted when the valve opens. This may be called complete compression, and when it occurs the existence of clearance has no direct effect on the consumption of steam nor on the efficiency; the whole fluid in the cylinder may then be thought of as consisting of two parts,a permanent cushion which is alternately expanded and compressed without net gain or loss of work, and the working part proper, which on admission fills the volume AB (fig. 20), and which enters and leaves the cylinder in each stroke. But if compression be incomplete or absent there is on the opening of the admission valve, an inrush of steam to fill up to the clearance space. This increase the consumption to an extent which is only partly counterbalanced by the increased area of the diagram, and the result is that the efficiency is reduced. The action is, in fact, a case of unresisted expansion (§ 51), and consequently tends, so far as its direct effects go, to make the engine less than ever reversible. It is to be noted, however, that by such unresisted expansion the entering steam is dried to some extent, and this helps in a measure to counteract the cause of loss which will be described below. Compression has the mechanical advantage that it obviates the shock which the admission of steam would otherwise cause, and that by giving the piston work to do while its velocity is being rapidly reduced it reduces those stresses in the mechanism which are due to the inertia of the reciprocating parts.
80. The third and generally by far the most important element of difference between the action of a real engine and that of our hypothetical engine is that alluded to at the end of chap. I., the difference which proceeds from the fact that the cylinder and piston are not-conductors. As the steam fluctuates in temperature there is a complex give-and-take of heat between it and the metal it touches, and the effects of this, though not very conspicuous on the indicator diagram, have an enormous influence in reducing the efficiency by increasing the consumption of steam. Attention was drawn to this action by Mr. D.K. Clark as early as 1855 (Railway Machinery, or art. STEAM-ENGINE, Ency. Brit., 8th edition1), and the results of his experiments on locomotives were confirmed some years later by Mr. Isherwoods trials of the engines of the United States steamer "Michigan." Rankine in his classical work on the steam-engine notices the subject only very briefly, and takes no account of the action of the cylinder walls in his calculations. Its importance has now been established beyond dispute, notably by the experiments of Messrs Loring and Emery on the engines of certain revenue steamers of the United Stated, and by a protracted series of investigation carried out by M. Hallauer and other Alsatian engineers under the direction of Hirn,3 whose name should be specially associated with the rational analysis of engine tests. In the next chapter some account will be given of how steam-engines are experimentally examined and how (following Hirn) we may deduce the exchanges of heat which occur between the steam and the cylinder throughout the stroke. The following is, in general terms, what experiments with actual engines show to take place.
81. When steam is admitted at the beginning of the stroke, it finds the metallic surfaces of the cylinder and piston chilled by having been in contact with low-pressure steam during the exhaust of the previous stroke. A portion of it is therefore liquefied, and, as the piston advances, more and more of the chilled cylinder surface is exposed and more and more of the hot steam is condensed. At the end of the admission, when communication with the boiler is cut 0ff, the cylinder consequently contains a film of water spread over the exposed surface, in addition to saturated steam. The boiler has therefore been drawn upon for a supply greater than that corresponding to the volume of steam in the admission space. The importance of this will be obvious from the fact, demonstrated by experiment that the steam which is thus condensed during admission frequently amounts to 30 and even 50 per cent. of the whole quantity that comes over from the boiler.
82. Then, as expansion begins, more cold metal is uncovered, and some of the remaining steam is condensed upon it. But the pressure of the steam now falls, and the layer of water which has been previously deposited begins to be re-evaporated as soon as the temperature of the expanding steam falls below that of the liquid layer. On the whole, then, the amount of water present will increase during the earliest part of the expansion, but a stage will soon be reached when the condensation which occurs on the newly exposed metal is balanced by re-evaporation of older portions of the layer. The percentage of water present is then a maximum; and from this point onwards the steam becomes more and more dried by re-evaporation of the layer.
83. If the amount of initial condensation has been small this re-evaporation may be complete before release occurs. Very usually, however, there is still an undried layer at the end of the forward stroke, and the process of re-evaporation continues during the return stroke, while exhaust is taking place. In extreme cases, if the amount of initial condensation has been very great, the cylinder walls may fall to become quite dry even during the exhaust, and a residue of the layer of condensed water may either be carried over as water into the condenser, or, if the exhaust valves are so badly arranged as to prevent its discharge, this unevaporated residue may gather in the cylinder, requiring perhaps the drain-cocks to be left open to allow of its escape. When any water is retained in this way the initial condensation is enormously increased, for the hot steam then meets not only cold metal but cold water. The latter causes much condensation, partly because of its high specific heat, and partly because it is brought into intimate mixture with the entering steam.
84. Apart, however, from this extreme case, whatever water is re-evaporated during expansion and exhaust takes heat from the metal of the cylinder, and so brings it into a state that makes condensation inevitable when steam is next admitted from the boiler. Mere contact with low-pressure steam during the exhaust stroke would cool the metal but little; the cooling which actually occurs is due mainly to the re-evaporation of the condensed water. Thus if an engine were set in action, after being heated beforehand to the boiler temperature, the cylinder would be only slightly cooled during the first exhaust stroke, and little condensation would occur during the next admission. But the metal would be more cooled in the subsequent expansion and exhaust, since it would part with heat in re-evaporating this water. In the third admission more still would be condensed, and so on, until a permanent regime would be established in which condensation and re-evaporation were exactly balanced. The same permanent regime is reached when the engine starts cold.
85. The wetness of the working fluid to which the action of the walls of the cylinder gives rise is essentially superficial. A film of water forms on the walls, but except for this the body of the steam remains dry, until (by adiabatic or nearly adiabatic expansion) it becomes wet throughout its volume. The water formed by the act of expansion takes form as a mist diffused throughout the steam, and on it the sides of the cylinder exert practically no influences. This latter wetness is in fact increasing while the substance, as a whole, is getting dried by the re-evaporation of the liquid film. During expansion the working substance may be regarded as made up two parts,a core of steam, which is expanding adiabatically but is at the same time receiving additions to its amount in the form of saturated steam from the liquid layer, and a liquid layer which is turning into steam.
86. From a thermodynamic point of view all initial condensation of the steam is bad, for, however early the film be re-evaporated, this can take only after its temperature has cooled below that of the boiler. The process consequently involves a misapplication of heat, since the substance, after parting with high temperature heat, takes it up again at a temperature lower than the top of its range. This causes a loss of efficiency (chap. II.), and the loss is greater the later in the stroke re-evaporation occurs. The heat that is drawn from the cylinder by re-evaporation of the condensed film becomes less and less effective for doing work as the end of the expansion is approached, and finally, whatever evaporation continues during the back stroke is an unmitigated source of waste. The heat is take from the cylinder does no work; its only effect, indeed, is to increase the back pressure by augmenting the volume of steam to be expelled. A small amount of initial condensation reduces the efficiency of the engine but little; a large amount causes a much more than proportionally larger loss.
87. The action of the cylinder walls is increased by any loss of heat which the engine suffers by radiation and conduction from its external surface. The entering has then to give up enough heat to provide for this waste, as well as enough to produce the subsequent re-evaporation of the condensed film. The consequence is that more steam is initially condensed. The loss of efficiency due to this cause will therefore be greater in an unprotected cylinder than in one which is well lagged or covered with non-conducting material. On the other hand, if the engines have a steam-jacket the deleterious action of the wall is reduced. The working substance is then on the whole gaining instead of losing heat by conduction during its passage through the cylinder. The jacket accelerates the process of re-evaporation and tends to make it finish at a point in the stroke when the temperature of the steam is still comparatively high. When the process is complete the cylinder walls give up very little additional heat to the steam during the remainder of the expansion and exhaust, for the conduction and radiation between dry steam and the metal of the cylinder are incompetent to cause any considerable exchange of heat. The earlier, therefore, that evaporation is complete the less is the metal chilled, and the less is the subsequence condensation. Moreover, after this stage in the stroke has passed, a steam-jacket continues to give heat to the metal during the remainder of the double stroke, and warms it to a temperature more nearly equal to that of the boiler steam before the next admission takes place.
88. Thus a steam-jacket, though in itself a thermodynamically imperfect contrivance, inasmuch as its object is to supply heat to the working substance at a temperature lower than the source, acts beneficially by counteracting, to some extent , the more serious misapplication of heat which occurs through cooling and heating of the cylinder walls. The heat which a jacket communicates to working steam often increases the power of an engine to an extent far greater than corresponds to the extra supply of heat which the jacket itself requires. Besides its thermodynamic effect a jacket has the drawback that it increases wastes by external radiation, since it both enlarges the area of radiating surface and raises its temperature; notwithstanding this, however many experiments have shown that in large and specially in slow-running engines, the influence of a steam-jacket on the efficiency is, in general, good; and this is to be ascribed to the fact that it reduces, though it does not entirely remove, the evils of initial condensation. To be effective, however, jackets must be well drained and kept full of "live" steam, instead of being, as many are, traps for condensed water or fro air.
89. It is interesting to notice, in general terms, the effects which certain variations of the conditions of working may be expected to produce on the loss that occurs through the action of the cylinder walls. Initial condensation will be increased by anything that augments the range of temperature through which the inner surface of the cylinder fluctuates in each stroke, or that expose a larger surface of metal to the action a quantity of steam, or that prolongs the contacts in which heat is exchanged. The influence of time is especially important; for it must be done in mind that the whole action depends on the rate at which heat is conducted into the substance of the metal. The changes of temperature which the metal undergoes are in every case mainly superficial; the alternate heating and cooling of the inner surface initiates waves pf high and low temperature in the iron whose effects are sensible only to a small depth; and the faster the alternate states succeed each other the more superficial are the effects. In an engine making an indefinitely large number of strokes per minute the cylinder side would behave like non-conductors and the action of the working substance would be adiabatic.
We may conclude, then, that in general an engine running at a high speed will have a higher thermodynamic efficiency than the same engine running at a low speed, all the other conditions of working being the same in both cases.
Again, as regards range of temperature, the influence of the cylinder walls will be greater (other things being equal) with high than with low pressure steam, and in condensing than in non-condensing engines. On the other hand, high pressure has the good effects of reducing the surface of metal exposed to the action of each pound of steam.
In large engines the action of the walls will be less than in small engines, since the proportion of wall surface to cylinder volume is less. This conclusion agrees with the well-known fact that no small engines achieve the economy that is easily with larger form, especially with large marine engines, which eclipse all other in the matter of size.
Cylinder condensation is increased when the ratio of expansion is increased, all the other circumstances of working being left unaltered. The metal is then brought into more prolonged contract with low-temperature steam. The volume of admission is reduced to a greater extent than the surface that is exposed to the entering steam, since that surface include tow constant quantities, the surface of the cylinder cover and of the piston. For these and perhaps other reasons, we may conclude that with an early cut-off the initial condensation is relatively large; and this conclusion is amply borne out by experiment. An important result is that increase expansion does not, beyond a certain limit, involve increase of thermodynamic efficiency; when that limit is passed the augmentation of waste through the action of the cylinder walls more than balances the increased economy to which, on general principles, expansion should give rise, and the result is a net loss. With a given engine, boiler pressure, and speed, a certain ratio of which this maximum depends are too complex to admit of theoretical solution; the best ratio can be determined only by experiment. It may even happen that an engine which is required to work at a specified power will give better results, in point of efficiency, with moderate steam-pressure and moderate expansion, than with high steam-pressure and a very early cut-off.
90. The effect of increased expansion in augmenting the action of the sides and so reducing the efficiency, when carried beyond a certain moderate grade, is well illustrated by the American and Alsatian experiments alluded to above. The following figures (Table III.), relating to a single-cylinder Corliss engine, are reduced from one of Hallauers papers:1
OF STEAM IN CYLINDER.]
Expansion. Percentage of Water present Consumption of steam per indicated Horse-Power per hour.
At End of
Admission. At End of
7&Mac250;3 24&Mac250;2 17&Mac250;8 17&Mac250;8
9&Mac250;4 30&Mac250;8 18&Mac250;6 17&Mac250;6
15&Mac250;1 37&Mac250;5 20&Mac250;8 17&Mac250;7
Here a maximum of efficiency lies between the extreme grades of expansion to which the test extends. In the American experiments the best results were obtained with even more moderations of expansion. The compound engines of the United States revenue steamer "Bache," when tested with steam in the jacket of a large cylinder, with the boiler pressure nearly uniform of 80 _ by gauge, or 95 _ per square inch absolute, and the speed not greatly varied, gave the results shown in Table IV. Here the efficiency is very little affected by a large variation in the cut-off, but when the ratio of expansion becomes excessive a distinct loss is incurred.
Ratio of Total
Steam per I.H.P.
Experiments with engines, in the conditions which hold in ordinary practice, show that it is not unusual to find 20 or 30 per cent. of the steam that comes over from the cylinder condensed during admission. In favorable cases the amount is less than this; occasionally, on the other hand, the amount condensed is as much as half, or even more than half, the whole steam supply.
91. The action of the cylinder walls is reduced(1) by jacketing, (2) by superheating, and (3) by using compound expansion. The advantage of the steam-jacket has been already mentioned. In high-speed engines its bacterial effect is necessarily small, and in certain cases the benefit may be even more than neutralized by the drawbacks which have been alluded to above (§ 88). In general, however, the steam-jacket forms a valuable means of reducing the wasteful action of the cylinder walls, especially when the ratio of expansion is considerable. Experiments made with and without a jacket, on the same engine, have shown that jacketing may increase the efficiency by 20 or 25 per cent. When a jacket is working properly it uses, in a single-cylinder engine, 4 to 5 per cent., and in a compound engine 8 to 12 per cent., of the whole steam supply.
92. Superheating the steam before its admission reduces the amount of initial condensation, by lessening the quantity of steam needed to give up a specified amount of heat, and this in its turn lessens the subsequent cooling by re-evaporation. That it has a marked advantage in this respect has been experimentally demonstrated by Hirn. On general thermodynamic grounds superheating is good, because it extends the range of temperature through which the working substance is carried. In modern practice superheating (to any considerable extent) is seldom attempted. It occurs to a small extent whenever dry steam is throttled, and a slight superheating is occasionally given to steam in its passage from the high-pressure to the low-pressure cylinder of a compound engine. In former years superheated steam was a common feature of marine practice, but serious practical difficulties caused engineers to abandon its use and to seek economy rather by increasing the initial pressure and using compound expansion. In those days, however, the theoretical advantage of superheating was less understood than it is now. The economy of fuel which its employment would probably secure is so great as to warrant a fresh and energetic attempt to overcome the mechanical difficulties of construction and lubrication stood in the way.
93. The most important means of preventing cylinder condensation from becoming excessive is the use of compound expansion. If the vessels were non-conductors of heat it would be, from the thermodynamic point of view, a matter of indifference whether expansion was completed in a single vessel of divided between two or more, provided the passage of steam from one to the other was performed without introducing unresisted expansion (§ 51).
But with actual materials the compound system has the important merit that is
subjects each cylinder to a greatly reduced range of temperature variation. For this reason the amount initially condensed in the high-pressure cylinder is greatly less than if admission were to take at once into the low-pressure cylinder and the whole expansion were to be performed there. Further, the steam which is re-evaporated from the first cylinder during its exhaust does work in the second, and it is only the re-evaporation that occurs during the exhaust form the second cylinder that is absolutely wasteful. The exact advantage of this division of range, as compared with expansion (through the same ratio) in a single cylinder, would be hard to calculate; but it is easy to see in a general way that an advantage is to be anticipated, and (though there are isolated instances to the contrary) experience bears out this conclusion. In large engines, working with high pressure, much expansion, and a slow stroke, the fact that compound engines are in general more efficient than single engines cannot be doubted. Additional evidence to the same effect is furnished when a compound engine is tested first with compound expansion and then as a simple engine with the same grade of expansion in the large cylinder alone. Thus in the American experiments the compound engine of the "Bache" when worked as a simple engine used 24 _ of steam per I.H.P per hour, as compared with about 20 _ when the engine worked compound, with the same boiler pressure, the same total expansion, and steam in the jacket in both cases. The necessity for compounding, if efficiency is to be secured, becomes greater with every increase of boiler pressure. So long as the initial pressure is less than about 100 _ per square inch (absolute) it suffices to reduce the range of temperature into two parts by employing two-cylinder compound engines; with the higher pressures now common in marine practice triple and even quadruple expansion is being introduced.
The action of the cylinder walls would be greatly reduced if it were practicable to use a non-conducting material as n internal lining to the cylinder and to the exposed surfaces of the piston. No cure for the evils of initial condensation would be so effectual at this; and in view of the economy of heat which would result, it is a matter of some surprise that the use of a non-conducting lining has not received more serious attention.
94. The principal reasons have now been named which make the actual results of engine performance differ from the results which would be obtained if the steam conformed in every respect to the simple theory stated in chap. III. It remains to state, very shortly, a few of the results of recent practice as to the actual efficiency of steam-engines considered as heat-engines.
The performance of a steam-engine, as regards economy in its consumption of heat, may be stated in a number of ways. In some of these the engine alone is treated as an independent machine; in others the engine, boiler, and furnace are considered as a whole.
The performance of the engine alone is best expressed by stating either (1) the number of thermal units used per horse-power per minute. These terms require a short explanation. The "efficiency" of a heat-engine has already been defined as the ratio of the work done to the heat supplied. The "work done" ought in strictness to be reckoned as the net work done by the working substance in passing through a complete cycle of operations; it should be determined by subtracting from the work which the substance does in the cylinder the work which is spent upon the substance in the feed-pump. The latter is a comparatively small quantity, and engineers generally neglect it in their calculations of thermodynamic efficiency. In making comparison, however, between the efficiency which is actually realized and the efficiency of a perfect engine or of an engine working under any assumed conditions, account should be taken of the negative work done in the feed-pump. Account should also in strictness be taken of that part of the work spent in driving the air-pump which is done upon the working substance, as distinguished from the water of injection. The "heat supplied" is the total heat of the steam delivered to the engine, less the heat contained in the corresponding amount of feed-water. This quantity depends on the amount of steam used, on the temperature of the feed, on the boiler pressure, and on the extent to which the boiler "primes." Priming is the delivery by the boiler of water mixed with the steam. Except where there is actual superheating the steam supply is always more or less wet; in a badly designed or overworked boiler large volumes of water may be carried over with the steam, but in a good boiler of adequate size the amount of priming is less (often much less) than 5 per cent. of the whole supply. The effect of priming is, of course, to reduce the supply of heat per _ of the working substance.
One horse-power is the mechanical equivalent of 42&Mac250;75 thermal units per minute. The relation between the above two methods of stating engine performance is therefore expressed by the equation
Efficiency = 42&Mac250;75 .
Number of T.U. per I.H.P. per minute
Another very common is to give the number of pound of steam supplied per horse-power per hour. This is unsatisfactory, even as a method of stating the comparative economy of different engines, or of one engine in different conditions, for several reasons. It ignores variations in boiler pressure, in feed-water temperature, and in the dryness of the supply, although each of these things affects the amount of heat required for the production of pound of steam. But the total of dry steam does not vary greatly within the limits of practical pressures; moreover, since (in condensing engines) feed-water is generally taken from the hot-well, its temperature does not differ much from that of the air-pump discharge, or (say), 100&Mac251; F. Finally, in many comparative trails the amount of priming is nearly if not quite constant. Hence it happens that this mode of statement often furnishes a fairly accurate test of the economy of engines, and it and it has the advantage of putting results in a way that is easy to understand and remember.
95. None of these modes of statement include the efficiency of the boiler and furnace. The performance of a boiler is most usually expressed by giving the number of pounds of water at a stated temperature converted into steam at a stated pressure by the combustion of 1_ of coal. the temperature commonly chosen is 212&Mac251; F., and the water is supposed to be evaporated under atmospheric pressure; the result may then be stated as so many pounds of water evaporated from and at 212&Mac251; F., per 1 _ of coal. But the term "efficiency" may also be applied to a boiler and furnace (considered as one apparatus) in the sense of the ratio between the heat that is utilized and the potential energy that is contained in the fuel. This ratio is, in good boilers, about 0&Mac250;7. Thus, for example 1 _ of Welsh coal contains about 15,500 thermal units of potential energy, an amount which is equal to the heat of production (L) of about 16 _ of steam from and at 212&Mac251;. In practice, however, 11 _ of water under less condition, or about 9&Mac250;5 _ when the feed-water enters at 100&Mac251; F. and the absolute pressure is 100 _ per square inch.
The efficiency of the engine multiplied by that of the furnace and boiler gives a number which expresses the ratio between the heats covered into work and the potential energy of fuel,a engine, boiler and furnace considered as a whole. Instead, however, of expressing this idea by the use of the term efficiency, engineers are more usually in the habit of stating the performance of the complete system by giving the number of pounds of coal consumed per horse-power per hour. It must be borne in mind that this quantity depends on the performance of the boiler as much as on that of the engine, and that the difference in thermal value between one kind of coal and another makes it, at the best, a rough way of specifying economy. It is, however, an easy quantity to measure; and to most users of engines the size of the coal-bill is a matter of greater interest than any results of thermodynamic analysis. Still another expression for engine performance, similar to this last, is the now nearly absolute term "duty, "or number of foot-pounds of work done for every 1 cwt. of coal consumed. Its relation to the pounds of coal per house-poser per hour is this
Duty = 112 x 33000 x 60 .
Number of _s. of coal per I.H.P. per hour
A good condensing engine of large size, supplied by good boilers, consumes about 2 _ of coal per horse-power per hour; its duty is then about 110 millions.
96. To illustrate the subject of this chapter more fully the following summary is given of the results of tests of pumping engines by Mr. J. G. Mair, described in two excellent papers in Min. Pro. Inst. Civ. Eng. (vols Ixx. and lxxix.). The first group (Table V.) refers to single cylinder beam rotative engines, all of the same type, working at about 120 horse-powers (in all except the last trial there were steam-jacket in use) :
Lbs. of Dry
48 6&Mac250;8 44 22&Mac250;1 0&Mac250;099
57 4&Mac250;3 29 22&Mac250;1 0&Mac250;099
59 3&Mac250;2 22 21&Mac250;3 0&Mac250;102
59 1&Mac250;9 15 223&Mac250;6 0&Mac250;093
56 3&Mac250;8 37 26&Mac250;5 0&Mac250;083
In these engines, which ran at the slow speed of about 20 revolutions per minute, the influence of steam jacketing was very marked. In the trials made with jackets in action, the percentage of water present at cut-off, when placed in relation to the ratio of expansion, gives a diagram is sensibly a straight line; by drawing this line it may be seen that with an expansion of 3&Mac250;8 in a similar jacketed cylinder there would be about 25 per cent. of initial condensation instead of the much greater amount (37 per cent.) which the absence of a jacket caused in the last trial.
The next group of tests (Table VI.) refers to compound engines of the types named (for explanation of the terms see chap VI.): 1
Abs. Total Ratio of
Expansion. Number of
per Minute. Percentage
Cut-off. Lbs. of Dry
I.H.P. per Hour. Efficiency.
Woolf beam, without jackets.. 58 9&Mac250;3 18 51 26&Mac250;6 0&Mac250;082
,, with jackets....... 62 15&Mac250;8 20 41 17&Mac250;3 0&Mac250;126
,, without jackets. 89 7&Mac250;8 34 34 19&Mac250;2 0&Mac250;113
,, ,, ........ 68 11&Mac250;9 18 25 15&Mac250;6 0&Mac250;139
,, ,, ........ 78 16&Mac250;5 28 31 15&Mac250;5 0&Mac250;140
,, ,, ....... 75 13&Mac250;2 27 29 15&Mac250;1 0&Mac250;144
Woolf tandem, without jackets 86 11&Mac250;5 80 43 21&Mac250;6 0&Mac250;101
Receiver beam, with jackets... 76 13&Mac250;6 24 34 14&Mac250;8 0&Mac250;147
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