Chapter V: Part 5

In closed heaters the feed water and the exhaust steam do not come into actual contact with each other. Either the steam or the water passes through tubes surrounded by the other medium, as the heater is of the steam-tube or water-tube type. A closed heater is best suited for water free from scale-forming matter, as such matter soon clogs the passages. Cleaning such heaters is costly and the efficiency drops off rapidly as scale forms. A closed heater is not advisable where the engines work intermittently, as is the case with mine hoisting engines. In this class of work the frequent coolings between operating periods and the sudden heatings when operation commences will tend to loosen the tubes or even pull them apart. For this reason, an open heater, or economizer, will give more satisfactory service with intermittently operating apparatus.

Open heaters are best suited for waters containing scale-forming matter. Much of the temporary hardness may be precipitated in the heater and the sediment easily removed. Such heaters are frequently used with a reagent for precipitating permanent hardness in the combined heat and chemical treatment of feed water. The so-called live steam purifiers are open heaters, the water being raised to the boiling temperature and the carbonates and a portion of the sulphates being precipitated. The disadvantage of this class of apparatus is that some of the sulphates remain in solution to be precipitated as scale when concentrated in the boiler. Sufficient concentration to have such an effect, however, may often be prevented by frequent blowing down.

Economizers find their largest field where the design of the boiler is such that the maximum possible amount of heat is not extracted from the gases of combustion. The more wasteful the boiler, the greater the saving effected by the use of the economizer, and it is sometimes possible to raise the temperature of the feed water to that of high pressure steam by the installation of such an apparatus, the saving amounting in some cases to as much as 20 per cent. The fuel used bears directly on the question of the advisability of an economizer installation, for when oil is the fuel a boiler efficiency of 80 per cent or over is frequently realized, an efficiency which would leave a small opportunity for a commercial gain through the addition of an economizer.

From the standpoint of space requirements, economizers are at a disadvantage in that they are bulky and require a considerable increase over space occupied by a heater of the exhaust type. They also require additional brickwork or a metal casing, which increases the cost. Sometimes, too, the frictional resistance of the gases through an economizer make its adaptability questionable because of the draft conditions. When figuring the net return on economizer investment, all of these factors must be considered.

When the feed water is such that scale will quickly encrust the economizer and throw it out of service for cleaning during an excessive portion of the time, it will be necessary to purify water before introducing it into an economizer to make it earn a profit on the investment.

From the foregoing, it is clearly indicated that it is impossible to make a definite statement as to the relative saving by heating feed water in any of the three types. Each case must be worked out independently and a decision can be reached only after an exhaustive study of all the conditions affecting the case, including the time the plant will be in service and probable growth of the plant. When, as a result of such study, the possible methods for handling the problem have been determined, the solution of the best apparatus can be made easily by the balancing of the saving possible by each method against its first cost, depreciation, maintenance and cost of operation.

Feeding of Water--The choice of methods to be used in introducing feed water into a boiler lies between an injector and a pump. In most plants, an injector would not be economical, as the water fed by such means must be cold, a fact which makes impossible the use of a heater before the water enters the injector. Such a heater might be installed between the injector and the boiler but as heat is added to the water in the injector, the heater could not properly fulfill its function.

TABLE 18

COMPARISON OF PUMPS AND INJECTORS _________________________________________________________________________ | | | | | Method of Supplying | | | | Feed-water to Boiler | Relative amount of | Saving of fuel over| | Temperature of feed-water as | coal required per | the amount required| | delivered to the pump or to | unit of time, the | when the boiler is | | injector, 60 degrees Fahren- | amount for a direct-| fed by a direct- | | heit. Rate of evaporation of | acting pump, feeding| acting pump without| | boiler, to pounds of water | water at 60 degrees | heater | | per pound of coal from and | without a heater, | Per Cent | | at 212 degrees Fahrenheit | being taken as unity| | |______________________________|_____________________|____________________| | | | | | Direct-acting Pump feeding | | | | water at 60 degrees without | | | | a heater | 1.000 | .0 | | | | | | Injector feeding water at | | | | 150 degrees without a heater | .985 | 1.5 | | Injector feeding through a | | | | heater in which the water is | | | | heated from 150 to 200 | | | | degrees | .938 | 6.2 | | | | | | Direct-acting Pump feeding | | | | water through a heater in | | | | which it is heated from 60 | | | | to 200 degrees | .879 | 12.1 | | | | | | Geared Pump run from the | | | | engine, feeding water | | | | through a heater in which it | | | | is heated from 60 to 200 | | | | degrees | .868 | 13.2 | |______________________________|_____________________|____________________|

The injector, considered only in the light of a combined heater and pump, is claimed to have a thermal efficiency of 100 per cent, since all of the heat in the steam used is returned to the boiler with the water. This claim leads to an erroneous idea. If a pump is used in feeding the water to a boiler and the heat in the exhaust from the pump is imparted to the feed water, the pump has as high a thermal efficiency as the injector. The pump has the further advantage that it uses so much less steam for the forcing of a given quantity of water into the boiler that it makes possible a greater saving through the use of the exhaust from other auxiliaries for heating the feed, which exhaust, if an injector were used, would be wasted, as has been pointed out.

In locomotive practice, injectors are used because there is no exhaust steam available for heating the feed, this being utilized in producing a forced draft, and because of space requirements. In power plant work, however, pumps are universally used for regular operation, though injectors are sometimes installed as an auxiliary method of feeding.

Table 18 shows the relative value of injectors, direct-acting steam pumps and pumps driven from the engine, the data having been obtained from actual experiment. It will be noted that when feeding cold water direct to the boilers, the injector has a slightly greater economy but when feeding through a heater, the pump is by far the more economical.

Auxiliaries--It is the general impression that auxiliaries will take less steam if the exhaust is turned into the condensers, in this way reducing the back pressure. As a matter of fact, vacuum is rarely registered on an indicator card taken from the cylinders of certain types of auxiliaries unless the exhaust connection is short and without bends, as long pipes and many angles offset the effect of the condenser. On the other hand, if the exhaust steam from the auxiliaries can be used for heating the feed water, all of the latent heat less only the loss due to radiation is returned to the boiler and is saved instead of being lost in the condensing water or wasted with the free exhaust. Taking into consideration the plant as a whole, it would appear that the auxiliary machinery, under such conditions, is more efficient than the main engines.

STEAM

When a given weight of a perfect gas is compressed or expanded at a constant temperature, the product of the pressure and volume is a constant. Vapors, which are liquids in aeriform condition, on the other hand, can exist only at a definite pressure corresponding to each temperature if in the saturated state, that is, the pressure is a function of the temperature only. Steam is water vapor, and at a pressure of, say, 150 pounds absolute per square inch saturated steam can exist only at a temperature 358 degrees Fahrenheit. Hence if the pressure of saturated steam be fixed, its temperature is also fixed, and _vice versa_.

Saturated steam is water vapor in the condition in which it is generated from water with which it is in contact. Or it is steam which is at the maximum pressure and density possible at its temperature. If any change be made in the temperature or pressure of steam, there will be a corresponding change in its condition. If the pressure be increased or the temperature decreased, a portion of the steam will be condensed. If the temperature be increased or the pressure decreased, a portion of the water with which the steam is in contact will be evaporated into steam. Steam will remain saturated just so long as it is of the same pressure and temperature as the water with which it can remain in contact without a gain or loss of heat. Moreover, saturated steam cannot have its temperature lowered without a lowering of its pressure, any loss of heat being made up by the latent heat of such portion as will be condensed. Nor can the temperature of saturated steam be increased except when accompanied by a corresponding increase in pressure, any added heat being expended in the evaporation into steam of a portion of the water with which it is in contact.

Dry saturated steam contains no water. In some cases, saturated steam is accompanied by water which is carried along with it, either in the form of a spray or is blown along the surface of the piping, and the steam is then said to be wet. The percentage weight of the steam in a mixture of steam and water is called the quality of the steam. Thus, if in a mixture of 100 pounds of steam and water there is three-quarters of a pound of water, the quality of the steam will be 99.25.

Heat may be added to steam not in contact with water, such an addition of heat resulting in an increase of temperature and pressure if the volume be kept constant, or an increase in temperature and volume if the pressure remain constant. Steam whose temperature thus exceeds that of saturated steam at a corresponding pressure is said to be superheated and its properties approximate those of a perfect gas.

As pointed out in the chapter on heat, the heat necessary to raise one pound of water from 32 degrees Fahrenheit to the point of ebullition is called the _heat of the liquid_. The heat absorbed during ebullition consists of that necessary to dissociate the molecules, or the _inner latent heat_, and that necessary to overcome the resistance to the increase in volume, or the _outer latent heat_. These two make up the _latent heat of evaporation_ and the sum of this latent heat of evaporation and the heat of the liquid make the _total heat_ of the steam. These values for various pressures are given in the steam tables, pages 122 to 127.

The specific volume of saturated steam at any pressure is the volume in cubic feet of one pound of steam at that pressure.

The density of saturated steam, that is, its weight per cubic foot, is obviously the reciprocal of the specific volume. This density varies as the 16/17 power over the ordinary range of pressures used in steam boiler work and may be found by the formula, D = .003027p^{.941}, which is correct within 0.15 per cent up to 250 pounds pressure.

The relative volume of steam is the ratio of the volume of a given weight to the volume of the same weight of water at 39.2 degrees Fahrenheit and is equal to the specific volume times 62.427.

As vapors are liquids in their gaseous form and the boiling point is the point of change in this condition, it is clear that this point is dependent upon the pressure under which the liquid exists. This fact is of great practical importance in steam condenser work and in many operations involving boiling in an open vessel, since in the latter case its altitude will have considerable influence. The relation between altitude and boiling point of water is shown in Table 12.

The conditions of feed temperature and steam pressure in boiler tests, fuel performances and the like, will be found to vary widely in different trials. In order to secure a means for comparison of different trials, it is necessary to reduce all results to some common basis. The method which has been adopted for the reduction to a comparable basis is to transform the evaporation under actual conditions of steam pressure and feed temperature which exist in the trial to an equivalent evaporation under a set of standard conditions. These standard conditions presuppose a feed water temperature of 212 degrees Fahrenheit and a steam pressure equal to the normal atmospheric pressure at sea level, 14.7 pounds absolute. Under such conditions steam would be generated _at_ a temperature of 212 degrees, the temperature corresponding to atmospheric pressure at sea level, _from_ water at 212 degrees. The weight of water which _would_ be evaporated under the assumed standard conditions by exactly the amount of heat absorbed by the boiler under actual conditions existing in the trial, is, therefore, called the equivalent evaporation "from and at 212 degrees."

The factor for reducing the weight of water actually converted into steam from the temperature of the feed, at the steam pressure existing in the trial, to the equivalent evaporation under standard conditions is called the _factor of evaporation._ This factor is the ratio of the total heat added to one pound of steam under the standard conditions to the heat added to each pound of steam in heating the water from the temperature of the feed in the trial to the temperature corresponding to the pressure existing in the trial. This heat added is obviously the difference between the total heat of evaporation of the steam at the pressure existing in the trial and the heat of the liquid in the water at the temperature at which it was fed in the trial. To illustrate by an example:

In a boiler trial the temperature of the feed water is 60 degrees Fahrenheit and the pressure under which steam is delivered is 160.3 pounds gauge pressure or 175 pounds absolute pressure. The total heat of one pound of steam at 175 pounds pressure is 1195.9 B. t. u. measured above the standard temperature of 32 degrees Fahrenheit. But the water fed to the boiler contained 28.08 B. t. u. as the heat of the liquid measured above 32 degrees Fahrenheit. Therefore, to each pound of steam there has been added 1167.82 B. t. u. To evaporate one pound of water under standard conditions would, on the other hand, have required but 970.4 B. t. u., which, as described, is the latent heat of evaporation at 212 degrees Fahrenheit. Expressed differently, the total heat of one pound of steam at the pressure corresponding to a temperature of 212 degrees is 1150.4 B. t. u. One pound of water at 212 degrees contains 180 B. t. u. of sensible heat above 32 degrees Fahrenheit. Hence, under standard conditions, 1150.4 - 180 = 970.4 B. t. u. is added in the changing of one pound of water into steam at atmospheric pressure and a temperature of 212 degrees. This is in effect the definition of the latent heat of evaporation.

Hence, if conditions of the trial had been standard, only 970.4 B. t. u. would be required and the ratio of 1167.82 to 970.4 B. t. u. is the ratio determining the factor of evaporation. The factor in the assumed case is 1167.82 ÷ 970.4 = 1.2034 and if the same amount of heat had been absorbed under standard conditions as was absorbed in the trial condition, 1.2034 times the amount of steam would have been generated. Expressed as a formula for use with any set of conditions, the factor is,

H - h
F = ----- (2)
970.4

Where H = the total heat of steam above 32 degrees Fahrenheit from steam
tables,
h = sensible heat of feed water above 32 degrees Fahrenheit from
Table 22.

In the form above, the factor may be determined with either saturated or superheated steam, provided that in the latter case values of H are available for varying degrees of superheat and pressures.

Where such values are not available, the form becomes,

H - h + s(t_{sup} - t_{sat})
F = ---------------------------- (3)
970.4

Where s = mean specific heat of superheated steam at the
pressure existing in the trial from saturated
steam to the temperature existing in the trial,
t_{sup} = final temperature of steam,
t_{sat} = temperature of saturated steam, corresponding to
pressure existing,
(t_{sup} - t_{sat}) = degrees of superheat.

The specific heat of superheated steam will be taken up later.

Table 19 gives factors of evaporation for saturated steam boiler trials to cover a large range of conditions. Except for the most refined work, intermediate values may be determined by interpolation.

Steam gauges indicate the pressure above the atmosphere. As has been pointed out, the atmospheric pressure changes according to the altitude and the variation in the barometer. Hence, calculations involving the properties of steam are based on _absolute_ pressures, which are equal to the gauge pressure plus the atmospheric pressure in pounds to the square inch. This latter is generally assumed to be 14.7 pounds per square inch at sea level, but for other levels it must be determined from the barometric reading at that place.

Vacuum gauges indicate the difference, expressed in inches of mercury, between atmospheric pressure and the pressure within the vessel to which the gauge is attached. For approximate purposes, 2.04 inches height of mercury may be considered equal to a pressure of one pound per square inch at the ordinary temperatures at which mercury gauges are used. Hence for any reading of the vacuum gauge in inches, G, the absolute pressure for any barometer reading in inches, B, will be (B - G) ÷ 2.04. If the barometer is 30 inches measured at ordinary temperatures and not corrected to 32 degrees Fahrenheit and the vacuum gauge 24 inches, the absolute pressure will be (30 - 24) ÷ 2.04 = 2.9 pounds per square inch.

TABLE 19

FACTORS OF EVAPORATION
CALCULATED FROM MARKS AND DAVIS TABLES

______________________________________________________________________ | | | |Feed | | |Temp- | | |erature| | |Degrees| Steam Pressure by Gauge | |Fahren-| | |heit | | |_______|______________________________________________________________| | | | | | | | | | | | 50 | 60 | 70 | 80 | 90 | 100 | 110 | |_______|________|________|________|________|________|________|________| | | | | | | | | | | 32 | 1.2143 | 1.2170 | 1.2194 | 1.2215 | 1.2233 | 1.2233 | 1.2265 | | 40 | 1.2060 | 1.2087 | 1.2111 | 1.2131 | 1.2150 | 1.2168 | 1.2181 | | 50 | 1.1957 | 1.1984 | 1.2008 | 1.2028 | 1.2047 | 1.2065 | 1.2079 | | 60 | 1.1854 | 1.1881 | 1.1905 | 1.1925 | 1.1944 | 1.1961 | 1.1976 | | 70 | 1.1750 | 1.1778 | 1.1802 | 1.1822 | 1.1841 | 1.1859 | 1.1873 | | 80 | 1.1649 | 1.1675 | 1.1699 | 1.1720 | 1.1738 | 1.1756 | 1.1770 | | 90 | 1.1545 | 1.1572 | 1.1596 | 1.1617 | 1.1636 | 1.1653 | 1.1668 | | 100 | 1.1443 | 1.1470 | 1.1493 | 1.1514 | 1.1533 | 1.1550 | 1.1565 | | 110 | 1.1340 | 1.1367 | 1.1391 | 1.1411 | 1.1430 | 1.1448 | 1.1462 | | 120 | 1.1237 | 1.1264 | 1.1288 | 1.1309 | 1.1327 | 1.1345 | 1.1359 | | 130 | 1.1134 | 1.1161 | 1.1185 | 1.1206 | 1.1225 | 1.1242 | 1.1257 | | 140 | 1.1031 | 1.1058 | 1.1082 | 1.1103 | 1.1122 | 1.1139 | 1.1154 | | 150 | 1.0928 | 1.0955 | 1.0979 | 1.1000 | 1.1019 | 1.1036 | 1.1051 | | 160 | 1.0825 | 1.0852 | 1.0876 | 1.0897 | 1.0916 | 1.0933 | 1.0948 | | 170 | 1.0722 | 1.0749 | 1.0773 | 1.0794 | 1.0813 | 1.0830 | 1.0845 | | 180 | 1.0619 | 1.0646 | 1.0670 | 1.0691 | 1.0709 | 1.0727 | 1.0741 | | 190 | 1.0516 | 1.0543 | 1.0567 | 1.0587 | 1.0606 | 1.0624 | 1.0638 | | 200 | 1.0412 | 1.0439 | 1.0463 | 1.0484 | 1.0503 | 1.0520 | 1.0535 | | 210 | 1.0309 | 1.0336 | 1.0360 | 1.0380 | 1.0399 | 1.0417 | 1.0432 | |_______|________|________|________|________|________|________|________| ______________________________________________________________________ | | | |Feed | | |Temp- | | |erature| | |Degrees| Steam Pressure by Gauge | |Fahren-| | |heit | | |_______|______________________________________________________________| | | | | | | | | | | | 120 | 130 | 140 | 150 | 160 | 170 | 180 | |_______|________|________|________|________|________|________|________| | | | | | | | | | | 32 | 1.2280 | 1.2292 | 1.2304 | 1.2314 | 1.2323 | 1.2333 | 1.2342 | | 40 | 1.2196 | 1.2209 | 1.2221 | 1.2231 | 1.2241 | 1.2250 | 1.2259 | | 50 | 1.2093 | 1.2106 | 1.2117 | 1.2128 | 1.2137 | 1.2147 | 1.2156 | | 60 | 1.1990 | 1.2003 | 1.2014 | 1.2025 | 1.2034 | 1.2044 | 1.2053 | | 70 | 1.1887 | 1.1900 | 1.1911 | 1.1922 | 1.1931 | 1.1941 | 1.1950 | | 80 | 1.1785 | 1.1797 | 1.1809 | 1.1819 | 1.1828 | 1.1838 | 1.1847 | | 90 | 1.1682 | 1.1695 | 1.1706 | 1.1717 | 1.1725 | 1.1735 | 1.1744 | | 100 | 1.1579 | 1.1592 | 1.1603 | 1.1614 | 1.1623 | 1.1633 | 1.1642 | | 110 | 1.1477 | 1.1489 | 1.1500 | 1.1511 | 1.1520 | 1.1530 | 1.1539 | | 120 | 1.1374 | 1.1386 | 1.1398 | 1.1408 | 1.1418 | 1.1427 | 1.1436 | | 130 | 1.1271 | 1.1284 | 1.1295 | 1.1305 | 1.1315 | 1.1324 | 1.1333 | | 140 | 1.1168 | 1.1181 | 1.1192 | 1.1203 | 1.1212 | 1.1221 | 1.1230 | | 150 | 1.1065 | 1.1078 | 1.1089 | 1.1099 | 1.1109 | 1.1118 | 1.1127 | | 160 | 1.0962 | 1.0975 | 1.0986 | 1.0997 | 1.1006 | 1.1015 | 1.1024 | | 170 | 1.0859 | 1.0872 | 1.0883 | 1.0893 | 1.0903 | 1.0912 | 1.0921 | | 180 | 1.0756 | 1.0768 | 1.0780 | 1.0790 | 1.0800 | 1.0809 | 1.0818 | | 190 | 1.0653 | 1.0665 | 1.0676 | 1.0687 | 1.0696 | 1.0706 | 1.0715 | | 200 | 1.0549 | 1.0562 | 1.0573 | 1.0584 | 1.0593 | 1.0602 | 1.0611 | | 210 | 1.0446 | 1.0458 | 1.0469 | 1.0480 | 1.0489 | 1.0499 | 1.0508 | |_______|________|________|________|________|________|________|________| ______________________________________________________________________ | | | |Feed | | |Temp- | | |erature| | |Degrees| Steam Pressure by Gauge | |Fahren-| | |heit | | |_______|______________________________________________________________| | | | | | | | | | | | 190 | 200 | 210 | 220 | 230 | 240 | 250 | |_______|________|________|________|________|________|________|________| | | | | | | | | | | 32 | 1.2350 | 1.2357 | 1.2364 | 1.2372 | 1.2378 | 1.2384 | 1.2390 | | 40 | 1.2267 | 1.2274 | 1.2282 | 1.2289 | 1.2295 | 1.2301 | 1.2307 | | 50 | 1.2164 | 1.2171 | 1.2178 | 1.2186 | 1.2192 | 1.2198 | 1.2204 | | 60 | 1.2061 | 1.2068 | 1.2075 | 1.2083 | 1.2089 | 1.2095 | 1.2101 | | 70 | 1.1958 | 1.1965 | 1.1972 | 1.1980 | 1.1986 | 1.1992 | 1.1998 | | 80 | 1.1855 | 1.1863 | 1.1869 | 1.1877 | 1.1883 | 1.1889 | 1.1895 | | 90 | 1.1750 | 1.1760 | 1.1766 | 1.1774 | 1.1780 | 1.1786 | 1.1792 | | 100 | 1.1650 | 1.1657 | 1.1664 | 1.1671 | 1.1678 | 1.1684 | 1.1690 | | 110 | 1.1547 | 1.1554 | 1.1562 | 1.1569 | 1.1575 | 1.1581 | 1.1587 | | 120 | 1.1444 | 1.1452 | 1.1459 | 1.1466 | 1.1472 | 1.1478 | 1.1484 | | 130 | 1.1341 | 1.1349 | 1.1356 | 1.1363 | 1.1369 | 1.1375 | 1.1381 | | 140 | 1.1239 | 1.1246 | 1.1253 | 1.1260 | 1.1266 | 1.1272 | 1.1278 | | 150 | 1.1136 | 1.1143 | 1.1150 | 1.1157 | 1.1163 | 1.1169 | 1.1176 | | 160 | 1.1033 | 1.1040 | 1.1047 | 1.1054 | 1.1060 | 1.1066 | 1.1073 | | 170 | 1.0930 | 1.0937 | 1.0944 | 1.0951 | 1.0957 | 1.0963 | 1.0969 | | 180 | 1.0826 | 1.0834 | 1.0841 | 1.0848 | 1.0854 | 1.0860 | 1.0866 | | 190 | 1.0723 | 1.0730 | 1.0737 | 1.0745 | 1.0751 | 1.0757 | 1.0763 | | 200 | 1.0620 | 1.0627 | 1.0634 | 1.0641 | 1.0647 | 1.0653 | 1.0660 | | 210 | 1.0516 | 1.0523 | 1.0530 | 1.0538 | 1.0544 | 1.0550 | 1.0556 | |_______|________|________|________|________|________|________|________|

The temperature, pressure and other properties of steam for varying amounts of vacuum and the pressure above vacuum corresponding to each inch of reading of the vacuum gauge are given in Table 20.

TABLE 20

PROPERTIES OF SATURATED STEAM FOR VARYING AMOUNTS OF VACUUM CALCULATED FROM MARKS AND DAVIS TABLES ______________________________________________________________________ | | | | | | | | | | | | Heat of | Latent | Total | | | | | Temp- | the Liquid| Heat | Heat | | | | | erature | Above | Above | Above |Density or| | | Absolute | Degrees | 32 De- | 32 De- | 32 De- |Weight per| | Vacuum | Pressure | Fahren- | grees | grees | grees |Cubic Foot| |Ins. Hg.| Pounds | heit | B. t. u. |B. t. u.|B. t. u.| Pounds | |________|__________|_________|___________|________|________|__________| | | | | | | | | | 29.5 | .207 | 54.1 | 22.18 | 1061.0 | 1083.2 | 0.000678 | | 29 | .452 | 76.6 | 44.64 | 1048.7 | 1093.3 | 0.001415 | | 28.5 | .698 | 90.1 | 58.09 | 1041.1 | 1099.2 | 0.002137 | | 28 | .944 | 99.9 | 67.87 | 1035.6 | 1103.5 | 0.002843 | | 27 | 1.44 | 112.5 | 80.4 | 1028.6 | 1109.0 | 0.00421 | | 26 | 1.93 | 124.5 | 92.3 | 1022.0 | 1114.3 | 0.00577 | | 25 | 2.42 | 132.6 | 100.5 | 1017.3 | 1117.8 | 0.00689 | | 24 | 2.91 | 140.1 | 108.0 | 1013.1 | 1121.1 | 0.00821 | | 22 | 3.89 | 151.7 | 119.6 | 1006.4 | 1126.0 | 0.01078 | | 20 | 4.87 | 161.1 | 128.9 | 1001.0 | 1129.9 | 0.01331 | | 18 | 5.86 | 168.9 | 136.8 | 996.4 | 1133.2 | 0.01581 | | 16 | 6.84 | 175.8 | 143.6 | 992.4 | 1136.0 | 0.01827 | | 14 | 7.82 | 181.8 | 149.7 | 988.8 | 1138.5 | 0.02070 | | 12 | 8.80 | 187.2 | 155.1 | 985.6 | 1140.7 | 0.02312 | | 10 | 9.79 | 192.2 | 160.1 | 982.6 | 1142.7 | 0.02554 | | 5 | 12.24 | 202.9 | 170.8 | 976.0 | 1146.8 | 0.03148 | |________|__________|_________|___________|________|________|__________|

From the steam tables, the condensed Table 21 of the properties of steam at different pressures may be constructed. From such a table there may be drawn the following conclusions.

TABLE 21

VARIATION IN PROPERTIES OF SATURATED STEAM WITH PRESSURE ___________________________________________________ | | | | | | | Pressure |Temperature | Heat of | Latent | Total | | Pounds | Degrees | Liquid | Heat | Heat | | Absolute | Fahrenheit |B. t. u. |B. t. u.|B. t. u.| |__________|____________|_________|________|________| | | | | | | | 14.7 | 212.0 | 180.0 | 970.4 | 1150.4 | | 20.0 | 228.0 | 196.1 | 960.0 | 1156.2 | | 100.0 | 327.8 | 298.3 | 888.0 | 1186.3 | | 300.0 | 417.5 | 392.7 | 811.3 | 1204.1 | |__________|____________|_________|________|________|

As the pressure and temperature increase, the latent heat decreases. This decrease, however, is less rapid than the corresponding increase in the heat of the liquid and hence the total heat increases with an increase in the pressure and temperature. The percentage increase in the total heat is small, being 0.5, 3.1, and 4.7 per cent for 20, 100, and 300 pounds absolute pressure respectively above the total heat in one pound of steam at 14.7 pounds absolute. The temperatures, on the other hand, increase at the rates of 7.5, 54.6, and 96.9 per cent. The efficiency of a perfect steam engine is proportional to the expression (t - t_{1})/t in which t and t_{1} are the absolute temperatures of the saturated steam at admission and exhaust respectively. While actual engines only approximate the ideal engine in efficiency, yet they follow the same general law. Since the exhaust temperature cannot be lowered beyond present practice, it follows that the only available method of increasing the efficiency is by an increase in the temperature of the steam at admission. How this may be accomplished by an increase of pressure is clearly shown, for the increase of fuel necessary to increase the pressure is negligible, as shown by the total heat, while the increase in economy, due to the higher pressure, will result directly from the rapid increase of the corresponding temperature.

TABLE 22

HEAT UNITS PER POUND AND WEIGHT PER CUBIC FOOT OF WATER BETWEEN 32 DEGREES FAHRENHEIT AND 340 DEGREES FAHRENHEIT _________________________________ | | | | |Temperature|Heat Units| Weight | | Degrees | per | per | | Fahrenheit| Pound |Cubic Foot| |___________|__________|__________| | | | | | 32 | 0.00 | 62.42 | | 33 | 1.01 | 62.42 | | 34 | 2.01 | 62.42 | | 35 | 3.02 | 62.43 | | 36 | 4.03 | 62.43 | | 37 | 5.04 | 62.43 | | 38 | 6.04 | 62.43 | | 39 | 7.05 | 62.43 | | 40 | 8.05 | 62.43 | | 41 | 9.05 | 62.43 | | 42 | 10.06 | 62.43 | | 43 | 11.06 | 62.43 | | 44 | 12.06 | 62.43 | | 45 | 13.07 | 62.42 | | 46 | 14.07 | 62.42 | | 47 | 15.07 | 62.42 | | 48 | 16.07 | 62.42 | | 49 | 17.08 | 62.42 | | 50 | 18.08 | 62.42 | | 51 | 19.08 | 62.41 | | 52 | 20.08 | 62.41 | | 53 | 21.08 | 62.41 | | 54 | 22.08 | 62.40 | | 55 | 23.08 | 62.40 | | 56 | 24.08 | 62.39 | | 57 | 25.08 | 62.39 | | 58 | 26.08 | 62.38 | | 59 | 27.08 | 62.37 | | 60 | 28.08 | 62.37 | | 61 | 29.08 | 62.36 | | 62 | 30.08 | 62.36 | | 63 | 31.07 | 62.35 | | 64 | 32.07 | 62.35 | | 65 | 33.07 | 62.34 | | 66 | 34.07 | 62.33 | | 67 | 35.07 | 62.33 | | 68 | 36.07 | 62.32 | | 69 | 37.06 | 62.31 | | 70 | 38.06 | 62.30 | | 71 | 39.06 | 62.30 | | 72 | 40.05 | 62.29 | | 73 | 41.05 | 62.28 | | 74 | 42.05 | 62.27 | | 75 | 42.05 | 62.26 | | 76 | 44.04 | 62.26 | | 77 | 45.04 | 62.25 | | 78 | 46.04 | 62.24 | | 79 | 47.04 | 62.23 | | 80 | 48.03 | 62.22 | | 81 | 49.03 | 62.21 | | 82 | 50.03 | 62.20 | | 83 | 51.02 | 62.19 | | 84 | 52.02 | 62.18 | | 85 | 53.02 | 62.17 | | 86 | 54.01 | 62.16 | | 87 | 55.01 | 62.15 | | 88 | 56.01 | 62.14 | | 89 | 57.00 | 62.13 | | 90 | 58.00 | 62.12 | | 91 | 59.00 | 62.11 | | 92 | 60.00 | 62.09 | | 93 | 60.99 | 62.08 | | 94 | 61.99 | 62.07 | | 95 | 62.99 | 62.06 | | 96 | 63.98 | 62.05 | | 97 | 64.98 | 62.04 | | 98 | 65.98 | 62.03 | | 99 | 66.97 | 62.02 | | 100 | 67.97 | 62.00 | | 101 | 68.97 | 61.99 | | 102 | 69.96 | 61.98 | | 103 | 70.96 | 61.97 | | 104 | 71.96 | 61.95 | | 105 | 72.95 | 61.94 | | 106 | 73.95 | 61.93 | | 107 | 74.95 | 61.91 | | 108 | 75.95 | 61.90 | | 109 | 76.94 | 61.88 | | 110 | 77.94 | 61.86 | | 111 | 78.94 | 61.85 | | 112 | 79.93 | 61.83 | | 113 | 80.93 | 61.82 | | 114 | 81.93 | 61.80 | | 115 | 82.92 | 61.79 | | 116 | 83.92 | 61.77 | | 117 | 84.92 | 61.75 | | 118 | 85.92 | 61.74 | | 119 | 86.91 | 61.72 | | 120 | 87.91 | 61.71 | | 121 | 88.91 | 61.69 | | 122 | 89.91 | 61.68 | | 123 | 90.90 | 61.66 | | 124 | 91.90 | 61.65 | | 125 | 92.90 | 61.63 | | 126 | 93.90 | 61.61 | | 127 | 94.89 | 61.59 | | 128 | 95.89 | 61.58 | | 129 | 96.89 | 61.56 | | 130 | 97.89 | 61.55 | | 131 | 98.89 | 61.53 | | 132 | 99.88 | 61.52 | | 133 | 100.88 | 61.50 | | 134 | 101.88 | 61.49 | | 135 | 102.88 | 61.47 | | 136 | 103.88 | 61.45 | | 137 | 104.87 | 61.43 | | 138 | 105.87 | 61.41 | | 139 | 106.87 | 61.40 | | 140 | 107.87 | 61.38 | | 141 | 108.87 | 61.36 | | 142 | 109.87 | 61.34 | | 143 | 110.87 | 61.33 | | 144 | 111.87 | 61.31 | | 145 | 112.86 | 61.29 | | 146 | 113.86 | 61.27 | | 147 | 114.86 | 61.25 | | 148 | 115.86 | 61.24 | | 149 | 116.86 | 61.22 | | 150 | 117.86 | 61.20 | | 151 | 118.86 | 61.18 | | 152 | 119.86 | 61.16 | | 153 | 120.86 | 61.14 | | 154 | 121.86 | 61.12 | | 155 | 122.86 | 61.10 | | 156 | 123.86 | 61.08 | | 157 | 124.86 | 61.06 | | 158 | 125.86 | 61.04 | | 159 | 126.86 | 61.02 | | 160 | 127.86 | 61.00 | | 161 | 128.86 | 60.98 | | 162 | 129.86 | 60.96 | | 163 | 130.86 | 60.94 | | 164 | 131.86 | 60.92 | | 165 | 132.86 | 60.90 | | 166 | 133.86 | 60.88 | | 167 | 134.86 | 60.86 | | 168 | 135.86 | 60.84 | | 169 | 136.86 | 60.82 | | 170 | 137.87 | 60.80 | | 171 | 138.87 | 60.78 | | 172 | 139.87 | 60.76 | | 173 | 140.87 | 60.73 | | 174 | 141.87 | 60.71 | | 175 | 142.87 | 60.69 | | 176 | 143.87 | 60.67 | | 177 | 144.88 | 60.65 | | 178 | 145.88 | 60.62 | | 179 | 146.88 | 60.60 | | 180 | 147.88 | 60.58 | | 181 | 148.88 | 60.56 | | 182 | 149.89 | 60.53 | | 183 | 150.89 | 60.51 | | 184 | 151.89 | 60.49 | | 185 | 152.89 | 60.47 | | 186 | 153.89 | 60.45 | | 187 | 154.90 | 60.42 | | 188 | 155.90 | 60.40 | | 189 | 156.90 | 60.38 | | 190 | 157,91 | 60.36 | | 191 | 158.91 | 60.33 | | 192 | 159.91 | 60.31 | | 193 | 160.91 | 60.29 | | 194 | 161.92 | 60.27 | | 195 | 162.92 | 60.24 | | 196 | 163.92 | 60.22 | | 197 | 164.93 | 60.19 | | 198 | 165.93 | 60.17 | | 199 | 166.94 | 60.15 | | 200 | 167.94 | 60.12 | | 201 | 168.94 | 60.10 | | 202 | 169.95 | 60.07 | | 203 | 170.95 | 60.05 | | 204 | 171.96 | 60.02 | | 205 | 172.96 | 60.00 | | 206 | 173.97 | 59.98 | | 207 | 174.97 | 59.95 | | 208 | 175.98 | 59.93 | | 209 | 176.98 | 59.90 | | 210 | 177.99 | 59.88 | | 211 | 178.99 | 59.85 | | 212 | 180.00 | 59.83 | | 213 | 181.0 | 59.80 | | 214 | 182.0 | 59.78 | | 215 | 183.0 | 59.75 | | 216 | 184.0 | 59.73 | | 217 | 185.0 | 59.70 | | 218 | 186.1 | 59.68 | | 219 | 187.1 | 59.65 | | 220 | 188.1 | 59.63 | | 221 | 189.1 | 59.60 | | 222 | 190.1 | 59.58 | | 223 | 191.1 | 59.55 | | 224 | 192.1 | 59.53 | | 225 | 193.1 | 59.50 | | 226 | 194.1 | 59.48 | | 227 | 195.2 | 59.45 | | 228 | 196.2 | 59.42 | | 229 | 197.2 | 59.40 | | 230 | 198.2 | 59.37 | | 231 | 199.2 | 59.34 | | 232 | 200.2 | 59.32 | | 233 | 201.2 | 59.29 | | 234 | 202.2 | 59.27 | | 235 | 203.2 | 59.24 | | 236 | 204.2 | 59.21 | | 237 | 205.3 | 59.19 | | 238 | 206.3 | 59.16 | | 239 | 207.3 | 59.14 | | 240 | 208.3 | 59.11 | | 241 | 209.3 | 59.08 | | 242 | 210.3 | 59.05 | | 243 | 211.4 | 59.03 | | 244 | 212.4 | 59.00 | | 245 | 213.4 | 58.97 | | 246 | 214.4 | 58.94 | | 247 | 215.4 | 58.91 | | 248 | 216.4 | 58.89 | | 249 | 217.4 | 58.86 | | 250 | 218.5 | 58.83 | | 260 | 228.6 | 58.55 | | 270 | 238.8 | 58.26 | | 280 | 249.0 | 57.96 | | 290 | 259.3 | 57.65 | | 300 | 269.6 | 57.33 | | 310 | 279.9 | 57.00 | | 320 | 290.2 | 56.66 | | 330 | 300.6 | 56.30 | | 340 | 311.0 | 55.94 | |___________|__________|__________|

The gain due to superheat cannot be predicted from the formula for the efficiency of a perfect steam engine given on page 119. This formula is not applicable in cases where superheat is present since only a relatively small amount of the heat in the steam is imparted at the maximum or superheated temperature.

The advantage of the use of high pressure steam may be also indicated by considering the question from the aspect of volume. With an increase of pressure comes a decrease in volume, thus one pound of saturated steam at 100 pounds absolute pressure occupies 4.43 cubic feet, while at 200 pounds pressure it occupies 2.29 cubic feet. If then, in separate cylinders of the same dimensions, one pound of steam at 100 pounds absolute pressure and one pound at 200 pounds absolute pressure enter and are allowed to expand to the full volume of each cylinder, the high-pressure steam, having more room and a greater range for expansion than the low-pressure steam, will thus do more work. This increase in the amount of work, as was the increase in temperature, is large relative to the additional fuel required as indicated by the total heat. In general, it may be stated that the fuel required to impart a given amount of heat to a boiler is practically independent of the steam pressure, since the temperature of the fire is so high as compared with the steam temperature that a variation in the steam temperature does not produce an appreciable effect.

The formulae for the algebraic expression of the relation between saturated steam pressures, temperatures and steam volumes have been up to the present time empirical. These relations have, however, been determined by experiment and, from the experimental data, tables have been computed which render unnecessary the use of empirical formulae. Such formulae may be found in any standard work of thermo-dynamics. The following tables cover all practical cases.

Table 22 gives the heat units contained in water above 32 degrees Fahrenheit at different temperatures.

Table 23 gives the properties of saturated steam for various pressures.

Table 24 gives the properties of superheated steam at various pressures and temperatures.

These tables are based on those computed by Lionel S. Marks and Harvey N. Davis, these being generally accepted as being the most correct.

TABLE 23

PROPERTIES OF SATURATED STEAM

REPRODUCED BY PERMISSION FROM MARKS AND DAVIS "STEAM TABLES AND DIAGRAMS" (Copyright, 1909, by Longmans, Green & Co.) ____________________________________________________________________ |Pressure,| Temper- |Specific Vol-|Heat of |Latent Heat|Total Heat| | Pounds |ature De-| ume Cu. Ft. |the Liquid,| of Evap., |of Steam, | |Absolute |grees F. | per Pound | B. t. u. | B. t. u. | B. t. u. | |_________|_________|_____________|___________|___________|__________| | 1 | 101.83 | 333.0 | 69.8 | 1034.6 | 1104.4 | | 2 | 126.15 | 173.5 | 94.0 | 1021.0 | 1115.0 | | 3 | 141.52 | 118.5 | 109.4 | 1012.3 | 1121.6 | | 4 | 153.01 | 90.5 | 120.9 | 1005.7 | 1126.5 | | 5 | 162.28 | 73.33 | 130.1 | 1000.3 | 1130.5 | | 6 | 170.06 | 61.89 | 137.9 | 995.8 | 1133.7 | | 7 | 176.85 | 53.56 | 144.7 | 991.8 | 1136.5 | | 8 | 182.86 | 47.27 | 150.8 | 988.2 | 1139.0 | | 9 | 188.27 | 42.36 | 156.2 | 985.0 | 1141.1 | | 10 | 193.22 | 38.38 | 161.1 | 982.0 | 1143.1 | | 11 | 197.75 | 35.10 | 165.7 | 979.2 | 1144.9 | | 12 | 201.96 | 32.36 | 169.9 | 976.6 | 1146.5 | | 13 | 205.87 | 30.03 | 173.8 | 974.2 | 1148.0 | | 14 | 209.55 | 28.02 | 177.5 | 971.9 | 1149.4 | | 15 | 213.0 | 26.27 | 181.0 | 969.7 | 1150.7 | | 16 | 216.3 | 24.79 | 184.4 | 967.6 | 1152.0 | | 17 | 219.4 | 23.38 | 187.5 | 965.6 | 1153.1 | | 18 | 222.4 | 22.16 | 190.5 | 963.7 | 1154.2 | | 19 | 225.2 | 21.07 | 193.4 | 961.8 | 1155.2 | | 20 | 228.0 | 20.08 | 196.1 | 960.0 | 1156.2 | | 22 | 233.1 | 18.37 | 201.3 | 956.7 | 1158.0 | | 24 | 237.8 | 16.93 | 206.1 | 953.5 | 1159.6 | | 26 | 242.2 | 15.72 | 210.6 | 950.6 | 1161.2 | | 28 | 246.4 | 14.67 | 214.8 | 947.8 | 1162.6 | | 30 | 250.3 | 13.74 | 218.8 | 945.1 | 1163.9 | | 32 | 254.1 | 12.93 | 222.6 | 942.5 | 1165.1 | | 34 | 257.6 | 12.22 | 226.2 | 940.1 | 1166.3 | | 36 | 261.0 | 11.58 | 229.6 | 937.7 | 1167.3 | | 38 | 264.2 | 11.01 | 232.9 | 935.5 | 1168.4 | | 40 | 267.3 | 10.49 | 236.1 | 933.3 | 1169.4 | | 42 | 270.2 | 10.02 | 239.1 | 931.2 | 1170.3 | | 44 | 273.1 | 9.59 | 242.0 | 929.2 | 1171.2 | | 46 | 275.8 | 9.20 | 244.8 | 927.2 | 1172.0 | | 48 | 278.5 | 8.84 | 247.5 | 925.3 | 1172.8 | | 50 | 281.0 | 8.51 | 250.1 | 923.5 | 1173.6 | | 52 | 283.5 | 8.20 | 252.6 | 921.7 | 1174.3 | | 54 | 285.9 | 7.91 | 255.1 | 919.9 | 1175.0 | | 56 | 288.2 | 7.65 | 257.5 | 918.2 | 1175.7 | | 58 | 290.5 | 7.40 | 259.8 | 916.5 | 1176.4 | | 60 | 292.7 | 7.17 | 262.1 | 914.9 | 1177.0 | | 62 | 294.9 | 6.95 | 264.3 | 913.3 | 1177.6 | | 64 | 297.0 | 6.75 | 266.4 | 911.8 | 1178.2 | | 66 | 299.0 | 6.56 | 268.5 | 910.2 | 1178.8 | | 68 | 301.0 | 6.38 | 270.6 | 908.7 | 1179.3 | | 70 | 302.9 | 6.20 | 272.6 | 907.2 | 1179.8 | | 72 | 304.8 | 6.04 | 274.5 | 905.8 | 1180.4 | | 74 | 306.7 | 5.89 | 276.5 | 904.4 | 1180.9 | | 76 | 308.5 | 5.74 | 278.3 | 903.0 | 1181.4 | | 78 | 310.3 | 5.60 | 280.2 | 901.7 | 1181.8 | | 80 | 312.0 | 5.47 | 282.0 | 900.3 | 1182.3 | | 82 | 313.8 | 5.34 | 283.8 | 899.0 | 1182.8 | | 84 | 315.4 | 5.22 | 285.5 | 897.7 | 1183.2 | | 86 | 317.1 | 5.10 | 287.2 | 896.4 | 1183.6 | | 88 | 318.7 | 5.00 | 288.9 | 895.2 | 1184.0 | | 90 | 320.3 | 4.89 | 290.5 | 893.9 | 1184.4 | | 92 | 321.8 | 4.79 | 292.1 | 892.7 | 1184.8 | | 94 | 323.4 | 4.69 | 293.7 | 891.5 | 1185.2 | | 96 | 324.9 | 4.60 | 295.3 | 890.3 | 1185.6 | | 98 | 326.4 | 4.51 | 296.8 | 889.2 | 1186.0 | | 100 | 327.8 | 4.429 | 298.3 | 888.0 | 1186.3 | | 105 | 331.4 | 4.230 | 302.0 | 885.2 | 1187.2 | | 110 | 334.8 | 4.047 | 305.5 | 882.5 | 1188.0 | | 115 | 338.1 | 3.880 | 309.0 | 879.8 | 1188.8 | | 120 | 341.3 | 3.726 | 312.3 | 877.2 | 1189.6 | | 125 | 344.4 | 3.583 | 315.5 | 874.7 | 1190.3 | | 130 | 347.4 | 3.452 | 318.6 | 872.3 | 1191.0 | | 135 | 350.3 | 3.331 | 321.7 | 869.9 | 1191.6 | | 140 | 353.1 | 3.219 | 324.6 | 867.6 | 1192.2 | | 145 | 355.8 | 3.112 | 327.4 | 865.4 | 1192.8 | | 150 | 358.5 | 3.012 | 330.2 | 863.2 | 1193.4 | | 155 | 361.0 | 2.920 | 332.9 | 861.0 | 1194.0 | | 160 | 363.6 | 2.834 | 335.6 | 858.8 | 1194.5 | | 165 | 366.0 | 2.753 | 338.2 | 856.8 | 1195.0 | | 170 | 368.5 | 2.675 | 340.7 | 854.7 | 1195.4 | | 175 | 370.8 | 2.602 | 343.2 | 852.7 | 1195.9 | | 180 | 373.1 | 2.533 | 345.6 | 850.8 | 1196.4 | | 185 | 375.4 | 2.468 | 348.0 | 848.8 | 1196.8 | | 190 | 377.6 | 2.406 | 350.4 | 846.9 | 1197.3 | | 195 | 379.8 | 2.346 | 352.7 | 845.0 | 1197.7 | | 200 | 381.9 | 2.290 | 354.9 | 843.2 | 1198.1 | | 205 | 384.0 | 2.237 | 357.1 | 841.4 | 1198.5 | | 210 | 386.0 | 2.187 | 359.2 | 839.6 | 1198.8 | | 215 | 388.0 | 2.138 | 361.4 | 837.9 | 1199.2 | | 220 | 389.9 | 2.091 | 363.4 | 836.2 | 1199.6 | | 225 | 391.9 | 2.046 | 365.5 | 834.4 | 1199.9 | | 230 | 393.8 | 2.004 | 367.5 | 832.8 | 1200.2 | | 235 | 395.6 | 1.964 | 369.4 | 831.1 | 1200.6 | | 240 | 397.4 | 1.924 | 371.4 | 829.5 | 1200.9 | | 245 | 399.3 | 1.887 | 373.3 | 827.9 | 1201.2 | | 250 | 401.1 | 1.850 | 375.2 | 826.3 | 1201.5 | |_________|_________|_____________|___________|___________|__________|

TABLE 24

PROPERTIES OF SUPERHEATED STEAM