American Technical Society. # Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) online

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Online Library → American Technical Society → Cyclopedia of engineering : a general reference work on steam boilers, pumps, engines, and turbines, gas and oil engines, automobiles, marine and locomotive work, heating and ventilating, compressed air, refrigeration, dynamos motors, electric wiring, electric lighting, elevators, etc. (Volume 2) → online text (page 10 of 30)

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285

290

57.72

259.4

911.0

1170.4

0.1359

7.356

290

295

62.33

264.4

907.4

1171.9

0.1461

6.847

295

300

67.22

269.5

903.9

1173.4

0.1567

6.380

300

305

72.42

274.5

900.5

1175.0

0.1680

5.952

305

310

77.83

279.6

896.9

1176 5

0.1799

5.558

310

315

83.77

284.8

893.2

1178.0

0.1925

5.195

315

320

89.95

290.0

889.5

1179.5

0.2058

4861

320

325

96.48

295.2

885.9

1181.1

0.2197

4.552

325

330

103.38

300.5

882.1

1128.6

0.2343

4.267

330

335

110.66

305.7

878.4

1184.1

0.2498

4.004

335

340

118.31

310.9

874.7

1185.8

0.2660

3.760

340

345

126.43

316.1

871.1

1187.2

0.2830

3.534

345

350

134.95

321.4

867.3

1188.7

0.3008

3.324

350

355

143.91

326.6

863.6

1190.2

0.3195

3.130

355

360

153.33

331.8

859.9

1191.7

0.3391

2.949

360

365

163.22

337.1

856.2

1193.3

0.3597

2.780

365

370

173 60

342.3

852.5

1194.8

03812

2.623

370

375

184.49

347.5

848.8

1196.3

0.4038

2.476

375

380

195.91

352.8

845.0

1197.8

0.4276

2.338

380

385

207.87

358.0

841.4

1199.4

0.4521

2.212

385

390

220.39

363.2

837.7

1200.9

0.4780

2.092

390

395

233.50

368.4

834.0

12024

0.5051

1.980

395

400

247.21

373.7

830.2

1203.9

0.5336

1.874

400

405

261.65

378.9

826.6

1205.5

0.5633

1.775

405

410

276.64

384.1

822.9

1207.0

0.5945

1.682

410

415

292.21

389.4

819.1

1208.5

0.6270

1.595

415

420

308.57

394.6

816.4

1210.0

0.6610

1.612

420

425

325.65

399.8

811.8

1211.6

0.6970

1.434

425

90 THE STEAM ENGINE.

saturated steam, one varying with the temperatures, the other

with the pressures. The tables are made out in five unit inter-

vals ; intermediate points are proportional.

Example. Suppose we wish to find the total heat corre-

sponding to a pressure of 112.3 pounds (gage). We first add

14.7 to the 112.3 and get 127 pounds absolute pressure. The

total heat of 1 pound of steam at 125 pounds pressure is 1,186.9.

The total heat at 130 pounds pressure is 1,187.8.

Difference for 5 pounds = 1,187.8 1,186.9 = .9

Difference for 1 pound =.94- 5 = .18

Difference for 2 pounds = 2 X .18 = .36

The total heat for 127 pounds is :

Total heat at 125 pounds = 1,186.9

Difference for 2 pounds = .36

Total heat at 127 pounds = 1,187.26

This method is called interpolation, and in many complete

tables the differences for the intervals are given to facilitate the

work.

If steam tables are not at hand, there are several approximate

formulas that may be used for rough calculations and estimates,

but it must be borne in mind that results obtained by the use of

these equations are not strictly accurate, and should not be used

if the regular tables can be had.

Probably the relation of temperature and pressure will be

most frequently needed. If the gage pressure is between 20

pounds and 100 pounds

t = 14 v/ ~p~+ 198 approximately [3]

where t = temperature in degrees Fahrenheit

p = gage pressure in pounds per square inch.

For pressures over 100 pounds per square inch (gage) we

must modify the equation thus :

[4]

These equations will cover a range of pressures from 20 to

340 pounds, and give an error of less than 1 J in nearly all cases.

From 35 pounds per square inch to 100 pounds the error is gen*

erally less than one-half of one degree.

142

THE STEAM EXGINE. 91

For pressures below 20 pounds use the constant 196 instead

<rf 198.

The latent heat may be approximately expressed by the

formula,

I = 1,114 .7 * [5]

in which I = latent heat

t = temperature in degrees F.

This formula gives very good results for temperatures less

than 320 6 , corresponding to a gage pressure of about 75 pounds.

Above this pressure the formula gives slightly larger results than

are found in the steam tables. At 250 pounds (gage) the for-

mula gives 829.8 and the steam tables 825.8, so that the error

will not be large in any case.

We have defined a B. T. U. as the amount of heat necessary

to raise one pound of water from 61 F to 62 F. The specific

heat of water is nearly constant over ordinary ranges of temper-

ature and at 400 we find the heat of the liquid from the tables to

be 373.7 B. T. U. By definition, the heat of the liquid at 32 is

zero, so that a rise of 368 in temperature requires 373.7 B. T. U.

If we consider the heat of the liquid proportional to .the rise in

temperature, our error will be 5.7 units of heat in 400. At

lower temperatures the error is much smaller, so that we may

express the heat of the liquid approximately by the formula,

h = t 32 [6]

in which h = the heat of the liquid

t = temperature in degrees as before.

The total heat is equal to the sum of the last two, or

H = h + I [7]

The relation of pressure and volume of steam may be approx-

imately expressed by the equation

*

= C,orV*..

In which P = absolute pressure

V = specific volume

17

HT

C a constant =475 nearly.

n = an exponent = .

16

143

92 THE STEAM ENGINE.

We may then write the equation

This is called the equation of constant steam weight ; it may

be solved by the aid of logarithms.

The density can of course be determined from the specific

volume.

Let us apply these approximate formulas to a specific case

and see how the results compare with the actual quantities given

in the steam tables. For this purpose we will suppose steam at

70.3 pounds gage pressure or 85 pounds absolute.

Equation (3) t 14 \J~^ -j- 198

= 14 v 'Yol+ 198 = 315.40

From steam tables, temperature = 316.02

Equation (5) I = 1,114 .7 t

I = 1,114 (.7 X 315.4) = 893.2

From stea,m tables, latent heat = 892.5

Equation (6) h = t 32

= 315.6 32 = 283.4

From tables, heat in the liquid = 285.8

Equation (7) H = h -f I

= 285.8 -j- 893.2 = 1,179.0

From tables, total heat = 1,178.3

'175

Equation (8) V = Y/l!^

V = ~V/ 475 = 5.100

V "85

From tables, specific volume = 5.125.

A comparison of these results shows that these formula^ can-

not b3 used when accuracy is sought ; but if only approximate

results are desired they will be found satisfactory. Whenever

possible the steam tables should be used, in preference to any

approximations.

Superheated Vapor. We have seen that a saturated vapor

contains just enough heat to keep it in the form of a vapor; if it

144

THE STEAM ENGINE. 93

loses heat it will condense. A superheated vapor is one that has

been heated after vaporization ; it can lose this extra heat before

any condensation will take place. A vapor in contact with its

liquid is saturated; one heated after removal from the liquid is

superheated.

For saturated steam there is a fixed temperature for every

pressure. If we know either the pressure or the temperature, we

can find the other in the steam tables. For instance, if the gage

pressure of a boiler is 60.3 pounds and we wish to know the tem-

perature, we simply add atmospheric pressure and turn to our

tables and find it to be 307 (about).

With superheated steam the case is entirely different, for there

is no longer the same direct relation between the temperature and

pressure. In fact, the relation between temperature and pressure'

of superheated steam depends upon the amount of superheating.

Superheated steam at 60.3 pounds gage pressure may have a tem-

perature considerably above 307 F. At a given pressure the

temperature and volume of a given weight of superheated steam

are always greater than the temperature and volume of the same

weight of saturated steam. The properties of superheated steam

at given pressure are not constant as is the case with saturated

steam.

If superheated steam were a perfect gas, we could determine

the relation of P, V and T by the equation PV = CT ; but super-

heated steam is not a perfect gas, hence we must modify our equa-

tion. By experiment it has been determined that the following

equation is nearly correct :

PV = 93.5 T 971 P*

In which P = absolute pressure in pounds per square foot

T = absolute temperature

V = volume of 1 pound in cubic feet.

THE STEAM ENGINE.

We have studied the action and formation of steam, and now

we shall consider its application to the steam engine. We know

that steam contains a great deal of heat, and that heat can be con-

verted into work by allowing a working substance to pass from

the high temperature of the heat generator to the lower tempera-

145

94 THE STEAM ENGINE.

ture of the refrigerator, during this change giving up heat, which

is transformed into work. There are several forms of heat engines,

all of which convert the heat contained in some substance into

work. At the present time the steam engine is the most impor-

tant. When of good size and properly designed and run, it is as

economical as any other heat engine, and it can be more easily

controlled and regulated. We shall consider first the theoretically

perfect engine and then the modifications that go to make up the

steam engine of to-day.

The theoretical engine (Fig. 3) is supposed to receive heat from

the generator at constant temperature T X until communication is

interrupted at B. The working substance expands to C without

losing or gaining any heat from external sources until the temper-

ature of the refrigerator is reached. The engine now rejects heat

at the constant temperature T 2 of the refrigerator and then com-

presses the working substance without loss or gain in the quantity

of heat until the temperature of the heat generator is reached.

These are ideal conditions, and, if fulfilled, the efficiency of the

perfect engine will depend only on the difference between the tern-

146

THE STEAM ENGINE. 95

perature at which heat is received and rejected, or, in other words,

it depends only upon the difference in temperature between the

generator and the refrigerator.

If Tj = absolute temperature of heat received and

T 2 = absolute temperature of heat rejected, then the ther-

mal efficiency, E, of the engine will be represented by the formula,

T T

~ 1

E r=

Or, in other words, the efficiency equals the absolute temper-

ature of the heat rejected, subtracted from the absolute temperature

of the heat received, and the remainder divided by the absolute

temperature of the heat received.

Suppose an engine is supplied with steam at 120 pounds

absolute pressure, and the exhaust is at atmospheric pressure.

What is the thermal efficiency ?

The absolute temperature corresponding to 120 pounds pres-

sure is 341.05 -f 461 = 802.05, and the absolute temperature of

the exhaust is 212 -f 461 = 673.

Then E = 802 f " 6T8 = .16, or 16 per cent.

802.05

In actual engines this efficiency cannot be realized, because

the difference between the heat received and the heat rejected is

not all converted into useful work. Part of it is lost by radiation,

conduction, condensation, leakage and -imperfect action of the

valves. The cylinder walls of the theoretical engine are supposed

to be made of a nonconducting material, while in the actual

engine the walls are of metal, which admits of a ready interchange

of heat between cylinder and steam. This action of the walls

cannot be overcome, and is so important that a failure to consider

its influence will lead to serious errors in computations, and no

design can be made intelligently if based on the theory of the

engine with nonconducting walls. The theoretical engine carries

on its expansion without the loss of any heat, while in the actual

engine a large amount of heat is lost by radiation. There is also

a considerable loss of pressure between the boiler and engine, due

to resistance of flow through pipes and passages. In a slow-speed

engine with large and direct ports and valves this trouble may be

147

96 THE STEAM ENGINE.

minimized. The imperfect action of valve gears may also be

lessened with due care, but the action of the cylinder walls still

remains to be overcome.

In the theoretical card, admission is at constant boiler pres-

sure, cut-off is sharp and expansion complete, that is, expansion

continues until the temperature falls to that of the condenser and

the exhaust is at condenser pressure. The piston also sweeps the

full length of the cylinder.

In the actual engine there is a considerable loss of pressure

between boiler and engine, and the wire-drawing of the ports

and valves tends to cause a sloping steam line. Condensation

at the beginning of the stroke causes the real expansion line to

fall below the theoretical, while re-evaporation causes it to rise

above the theoretical toward the end of expansion. In the actual

Fig. 4.

engine, release takes place before the end of the stroke, expan-

sion is not complete, that is, the pressure at release is above

that of the condenser, and the resistance of exhaust ports causes

the back pressure to be above the actual condenser pressure.

Moreover, the piston does not sweep the full length of the

cylinder, and the clearance space must be filled with steam, which

does little or no work. The theoretical and actual cards are

shown in Fig. 4.

EFFICIENCY OF THE ACTUAL ENGINE.

We have seen that the efficiency of the theoretical engine is

purely a thermal consideration ; the efficiency of the actual engine,

148

THE STEAM ENGINE. 97

however, is a mechanical matter. The measure of the activity of

work is the horse-power which corresponds to the development

of 33,000 foot-pounds per minute. As 778 foot-pounds are equiv-

alent to one B. T. U., 33,000 foot-pounds, or one horse-power, is

equivalent to 33,000 -4- 778 = 42.42 B. T. U. Now if a certain

engine uses 84.84 B. T. U. per horse-power per minute, it is evi-

dent that its efficiency would only be |- or 50 per cent, because

42.42 -f- 84.84 = | . Hence* we may say that the efficiency of

the actual engine is equal to _ _. This

B. T. U. per H. P. per minute

efficiency is always much less than that of the perfect engine.

Let us now discuss the effects of some of the losses.

In the first place, the metal, being a good conductor of heat,

becGmes heated by the steam within and transmits this heat by

conduction and radiation to the air or external bodies. With the

cylinder well lagged much less heat is lost by radiation. If the

lagging were perfect and the temperature of the cylinder remained

the same as the temperature of the steam throughout the stroke,

there would be no loss by radiation, but we should still lose heat

by conduct' on to the different parts of the engine.

During expansion, the temperature and pressure of the steam

decrease as the volume increases, and the temperature at exhaust,

is much less than tho temperature at admission. In the perfect

engine the working substance after exhaust is compressed to the

temperature at admission, but in the actual engine much of this

steam is lost and the compression of a part of it is incomplete, so

that its temperature is less than the temperature at admission.

Suppose an engine is running with admission at 100 pounds

absolute and exhaust at 18 pounds absolute. Then from steam

tables we find the temperature at admission to be 327.6, and at

exhaust 222.4. The metal walls of the cylinder, being good con-

ductors and radiators of heat, are cooled by the low temperature

of exhaust, so that the entering steam comes through ports and into

a cylinder that is more than 100 cooler than the steam. This

means that heat must flow from steam to metal until botli are of

the same temperature. Th?s causes the steam to give up part of

its latent heat, and as saturated t team cannot lose any of its heat

without condensation, we find the cylinder walls covered with a

149

THE STEAM ENGINE.

film of moisture known as initial condensation. This conden-

sation in simple unjacketed engines working under fair conditions

may easily be 25 per cent or more of the entering steam. The

moisture in the cylinder has of course the same temperature as

the steam ; it has simply lost its heat of vaporization.

Although metal is a good conductor of heat it cannot give

up nor absorb heat instantly ; consequently during expansion

the temperature of the steam falls more rapidly than that of the

cylinder. This allows heat to flow from the cylinder walls to

the moisture on them. As fast as the steam expands so that the

pressure in the cylinder becomes less, this condensation will begin

to evaporate. As the pressure falls it requires less and less heat

to form steam, and therefore more and more of this moisture will

be evaporated. At release the pressure drops suddenly, and more

heat at once flows from the cylinder walls, and re-evaporation con-

tinues throughout the exhaust. Probably all of the water remain-

ing in the cylinder at release is now re-evaporated, blows out into

the air or the condenser, and is lost so far as useful work is

concerned.

The steam that is first condensed in the cylinder does no

work ; its heat is used to warm up the cylinder, and later, when

it is re-evaporated, it works only during a part of the expansion

and at a reduced efficiency, because it is re-evaporated at a pres-

sure and consequently at a temperature very much lower than

that of admission. If the cut-off is short, perhaps 20 per cent of

the steam condensed may be re-evaporated during expansion ; if the

cut-off is long, 10 per cent may be re-evaporated, the rest remaining

in the cylinder at release still in the form of moisture. Thus

some of the entering steam passes through the cylinder as

moisture, until after cut-off, and still more passes clear through

without doing any work at all.

Suppose an engine is using 30 pounds of steam per horse-

power per hour and admission is at 100 pounds absolute. The

latent heat of vaporization at this pressure is 884 B. T. U. per

pound. If the condensation amounts to 331 p er cent, then 10

pounds are condensed and we lose 10 times 884, equals 8,840

B. T. U. per hour, or 147.3 per minute ; and since 42.42 B. T. U.

represents 1 horse-power, we shall lose by condensation 147.3

150

THE STEAM ENGINE.

divided by 42.42, equals 3* horse-power (nearly). If the cut-off is

shortened, the condensation increases and may amount to 50 per

cent at very short cut-off. Of course we use very much less

steam at short cut-off than with long cut-off, and doubtless in

many cases 50 per cent of the steam at short cut-off is not as

great an absolute quantity as 30 per cent at long cutoff. Never-

theless, in all cases it is the percentages that go to make up the

efficiency.

In addition to the actual loss from condensation in the cylinder

there is still another loss due to the re-evaporation. Suppose, as

before, that 10 pounds of steam are condensed in the cylinder,

and that 20 per cent of this is re-evaporated during expansion.

This will leave 8 pounds to be re-evaporated during exhaust.

Suppose the exhaust is at 3 pounds above atmospheric pressure,

or 18 pounds absolute (about). Then the heat of vaporization is

958.5 B. T. U. per pound of steam, and it will require 8 times

958.5, which equals 7668.0 B. T. U., to evaporate the 8 pounds.

All of this heat is taken from the cylinder, leaving the engine

much cooler than it would be were it not for this re-evaporatioiv

This gives some idea of the great amount of heat passing away at

exhaust, which is known as the exhaust waste.

In all cylinders it is necessary to have a little space between

the cylinder cover and the piston when at the end of the stroke.

In vertical engines the space is greater at the bottom than at the

top. The volume of this space, together with the volume of the

steam ports, is called the clearance. It varies from 1 to 20 per

cent, depending upon the type and speed of the engine ; the higher

the speed, the greater the clearance. This clearance space must

be filled with steam before the piston receives full pressure, but

this steam does no work except in expanding, and the volume of

the clearance offers additional surface for condensation.

Another important loss is that due to friction. We know that

it takes considerable power to move an unloaded engine; if fitted

with a pLun, unbalanced slide valve, the power necessary to move

the valve alone is considerable. The piston is made steam tight

by packing rings, and leakage around the piston rod is prevented

by stuffing boxes. All these devices cause friction as well as wear

at the joints. The amount of power wasted in friction varies

151

100 THE STEAM ENGINE.

greatly, depending upon the kind of valves, general workman-

ship, state of repair and lubrication.

MULTIPLE EXPANSION.

Two engines may be used together on the same shaft, partly

expanding the steam in one of the cylinders, and then passing it

over to the other to finish the expansion. One advantage from

this arrangement is that the parts can be made lighter. The high-

pressure cylinder can be of much less diameter than would be

possible if the entire expansion were to take place in one cylinder.

This, of course, makes the pressure exerted on the piston rod

much less, and the piston rod and connecting rod can thus be

made much lighter. The low-pressure cylinder must be larger

than it otherwise would be, but its parts need not be much heavier,

because the pressure per square inch is always low.

This arrangement gives not only the advantage of lighter

parts, but a decided increase of economy over the single cylinder

type. If attention is given to the matter, a loss of economy would

be expected, because the steam is exposed to a much larger surface

through which to lose heat, but the gain comes from another

source, and is sufficient to entirely counterbalance the effect of

a larger cylinder surface.

When very high pressure steam and a great ratio of expan-

sion is used, the difference between the temperature of the enter-

ing and that of the exhaust steam is great. For instance, suppose

steam at 160 pounds (gage) pressure enters the cylinder and the

exhaust pressure is 2 pounds (gage), the difference in temperature

is, from steam tables,

370.5 218.1= 152.4

This difference becomes nearly 230 if the steam is con-

densed to about three pounds absolute pressure. The cylinder and

ports of the engine are cooled to the low temperature of the

exhaust steam, and, as we have seen, a considerable quantity

of the entering steam is condensed to give up heat enough to

raise the temperature of the cylinder to that of the entering

steam. As the ratio of expansion increases, the difference in

temperature increases, and consequently the amount of steam

thus condensed also increases. To keep this initial condensation

152

THE STEAM ENGINE. 101

as small as possible we must limit the temperature, that is, we

must not have as great a difference between admission and

exhaust. To do this we must divide the expansion between two

or more cylinders.

It will be remembered that the great trouble Watt found with

Newcomen's engine was its great amount of condensation, and he

stated as the law which all engines should try to approach, " that

the cylinder should be kept as hot as the steam which enters it."

This is to avoid condensation when steam first comes in. If,

instead of expanding the steam in one cylinder, we expand it

partly in one and then finish the expansion in another, we shall

have passed it out of the first cylinder before its temperature falls

a great deal, and consequently the cylinder walls will be hotter

than they would be if we had expanded it entirely in one cylinder.

This would then reduce the amount of steam condensed. The

importance of this may not be evident at first, but it makes a

great difference in the economy of the engine. If there is less

condensation, there will be less moisture to re-evaporate, and con-

sequently less exhaust waste ; hence we shall save in two ways at

the same time.

In a compound engine we admit the steam first to the smaller

or high-pressure cylinder, and exhaust it to the larger or low-

pressure.

Suppose steam at 160 pounds (gage) pressure is admitted

to a cylinder, and the ratio of expansion is such that the steam

is exhausted at about 60 pounds (g a g e ) pressure; then the dif-

ference of temperature is

370.5 307 = 63.5.

If, now, the steam when exhausted from the first cylinder

290

57.72

259.4

911.0

1170.4

0.1359

7.356

290

295

62.33

264.4

907.4

1171.9

0.1461

6.847

295

300

67.22

269.5

903.9

1173.4

0.1567

6.380

300

305

72.42

274.5

900.5

1175.0

0.1680

5.952

305

310

77.83

279.6

896.9

1176 5

0.1799

5.558

310

315

83.77

284.8

893.2

1178.0

0.1925

5.195

315

320

89.95

290.0

889.5

1179.5

0.2058

4861

320

325

96.48

295.2

885.9

1181.1

0.2197

4.552

325

330

103.38

300.5

882.1

1128.6

0.2343

4.267

330

335

110.66

305.7

878.4

1184.1

0.2498

4.004

335

340

118.31

310.9

874.7

1185.8

0.2660

3.760

340

345

126.43

316.1

871.1

1187.2

0.2830

3.534

345

350

134.95

321.4

867.3

1188.7

0.3008

3.324

350

355

143.91

326.6

863.6

1190.2

0.3195

3.130

355

360

153.33

331.8

859.9

1191.7

0.3391

2.949

360

365

163.22

337.1

856.2

1193.3

0.3597

2.780

365

370

173 60

342.3

852.5

1194.8

03812

2.623

370

375

184.49

347.5

848.8

1196.3

0.4038

2.476

375

380

195.91

352.8

845.0

1197.8

0.4276

2.338

380

385

207.87

358.0

841.4

1199.4

0.4521

2.212

385

390

220.39

363.2

837.7

1200.9

0.4780

2.092

390

395

233.50

368.4

834.0

12024

0.5051

1.980

395

400

247.21

373.7

830.2

1203.9

0.5336

1.874

400

405

261.65

378.9

826.6

1205.5

0.5633

1.775

405

410

276.64

384.1

822.9

1207.0

0.5945

1.682

410

415

292.21

389.4

819.1

1208.5

0.6270

1.595

415

420

308.57

394.6

816.4

1210.0

0.6610

1.612

420

425

325.65

399.8

811.8

1211.6

0.6970

1.434

425

90 THE STEAM ENGINE.

saturated steam, one varying with the temperatures, the other

with the pressures. The tables are made out in five unit inter-

vals ; intermediate points are proportional.

Example. Suppose we wish to find the total heat corre-

sponding to a pressure of 112.3 pounds (gage). We first add

14.7 to the 112.3 and get 127 pounds absolute pressure. The

total heat of 1 pound of steam at 125 pounds pressure is 1,186.9.

The total heat at 130 pounds pressure is 1,187.8.

Difference for 5 pounds = 1,187.8 1,186.9 = .9

Difference for 1 pound =.94- 5 = .18

Difference for 2 pounds = 2 X .18 = .36

The total heat for 127 pounds is :

Total heat at 125 pounds = 1,186.9

Difference for 2 pounds = .36

Total heat at 127 pounds = 1,187.26

This method is called interpolation, and in many complete

tables the differences for the intervals are given to facilitate the

work.

If steam tables are not at hand, there are several approximate

formulas that may be used for rough calculations and estimates,

but it must be borne in mind that results obtained by the use of

these equations are not strictly accurate, and should not be used

if the regular tables can be had.

Probably the relation of temperature and pressure will be

most frequently needed. If the gage pressure is between 20

pounds and 100 pounds

t = 14 v/ ~p~+ 198 approximately [3]

where t = temperature in degrees Fahrenheit

p = gage pressure in pounds per square inch.

For pressures over 100 pounds per square inch (gage) we

must modify the equation thus :

[4]

These equations will cover a range of pressures from 20 to

340 pounds, and give an error of less than 1 J in nearly all cases.

From 35 pounds per square inch to 100 pounds the error is gen*

erally less than one-half of one degree.

142

THE STEAM EXGINE. 91

For pressures below 20 pounds use the constant 196 instead

<rf 198.

The latent heat may be approximately expressed by the

formula,

I = 1,114 .7 * [5]

in which I = latent heat

t = temperature in degrees F.

This formula gives very good results for temperatures less

than 320 6 , corresponding to a gage pressure of about 75 pounds.

Above this pressure the formula gives slightly larger results than

are found in the steam tables. At 250 pounds (gage) the for-

mula gives 829.8 and the steam tables 825.8, so that the error

will not be large in any case.

We have defined a B. T. U. as the amount of heat necessary

to raise one pound of water from 61 F to 62 F. The specific

heat of water is nearly constant over ordinary ranges of temper-

ature and at 400 we find the heat of the liquid from the tables to

be 373.7 B. T. U. By definition, the heat of the liquid at 32 is

zero, so that a rise of 368 in temperature requires 373.7 B. T. U.

If we consider the heat of the liquid proportional to .the rise in

temperature, our error will be 5.7 units of heat in 400. At

lower temperatures the error is much smaller, so that we may

express the heat of the liquid approximately by the formula,

h = t 32 [6]

in which h = the heat of the liquid

t = temperature in degrees as before.

The total heat is equal to the sum of the last two, or

H = h + I [7]

The relation of pressure and volume of steam may be approx-

imately expressed by the equation

*

= C,orV*..

In which P = absolute pressure

V = specific volume

17

HT

C a constant =475 nearly.

n = an exponent = .

16

143

92 THE STEAM ENGINE.

We may then write the equation

This is called the equation of constant steam weight ; it may

be solved by the aid of logarithms.

The density can of course be determined from the specific

volume.

Let us apply these approximate formulas to a specific case

and see how the results compare with the actual quantities given

in the steam tables. For this purpose we will suppose steam at

70.3 pounds gage pressure or 85 pounds absolute.

Equation (3) t 14 \J~^ -j- 198

= 14 v 'Yol+ 198 = 315.40

From steam tables, temperature = 316.02

Equation (5) I = 1,114 .7 t

I = 1,114 (.7 X 315.4) = 893.2

From stea,m tables, latent heat = 892.5

Equation (6) h = t 32

= 315.6 32 = 283.4

From tables, heat in the liquid = 285.8

Equation (7) H = h -f I

= 285.8 -j- 893.2 = 1,179.0

From tables, total heat = 1,178.3

'175

Equation (8) V = Y/l!^

V = ~V/ 475 = 5.100

V "85

From tables, specific volume = 5.125.

A comparison of these results shows that these formula^ can-

not b3 used when accuracy is sought ; but if only approximate

results are desired they will be found satisfactory. Whenever

possible the steam tables should be used, in preference to any

approximations.

Superheated Vapor. We have seen that a saturated vapor

contains just enough heat to keep it in the form of a vapor; if it

144

THE STEAM ENGINE. 93

loses heat it will condense. A superheated vapor is one that has

been heated after vaporization ; it can lose this extra heat before

any condensation will take place. A vapor in contact with its

liquid is saturated; one heated after removal from the liquid is

superheated.

For saturated steam there is a fixed temperature for every

pressure. If we know either the pressure or the temperature, we

can find the other in the steam tables. For instance, if the gage

pressure of a boiler is 60.3 pounds and we wish to know the tem-

perature, we simply add atmospheric pressure and turn to our

tables and find it to be 307 (about).

With superheated steam the case is entirely different, for there

is no longer the same direct relation between the temperature and

pressure. In fact, the relation between temperature and pressure'

of superheated steam depends upon the amount of superheating.

Superheated steam at 60.3 pounds gage pressure may have a tem-

perature considerably above 307 F. At a given pressure the

temperature and volume of a given weight of superheated steam

are always greater than the temperature and volume of the same

weight of saturated steam. The properties of superheated steam

at given pressure are not constant as is the case with saturated

steam.

If superheated steam were a perfect gas, we could determine

the relation of P, V and T by the equation PV = CT ; but super-

heated steam is not a perfect gas, hence we must modify our equa-

tion. By experiment it has been determined that the following

equation is nearly correct :

PV = 93.5 T 971 P*

In which P = absolute pressure in pounds per square foot

T = absolute temperature

V = volume of 1 pound in cubic feet.

THE STEAM ENGINE.

We have studied the action and formation of steam, and now

we shall consider its application to the steam engine. We know

that steam contains a great deal of heat, and that heat can be con-

verted into work by allowing a working substance to pass from

the high temperature of the heat generator to the lower tempera-

145

94 THE STEAM ENGINE.

ture of the refrigerator, during this change giving up heat, which

is transformed into work. There are several forms of heat engines,

all of which convert the heat contained in some substance into

work. At the present time the steam engine is the most impor-

tant. When of good size and properly designed and run, it is as

economical as any other heat engine, and it can be more easily

controlled and regulated. We shall consider first the theoretically

perfect engine and then the modifications that go to make up the

steam engine of to-day.

The theoretical engine (Fig. 3) is supposed to receive heat from

the generator at constant temperature T X until communication is

interrupted at B. The working substance expands to C without

losing or gaining any heat from external sources until the temper-

ature of the refrigerator is reached. The engine now rejects heat

at the constant temperature T 2 of the refrigerator and then com-

presses the working substance without loss or gain in the quantity

of heat until the temperature of the heat generator is reached.

These are ideal conditions, and, if fulfilled, the efficiency of the

perfect engine will depend only on the difference between the tern-

146

THE STEAM ENGINE. 95

perature at which heat is received and rejected, or, in other words,

it depends only upon the difference in temperature between the

generator and the refrigerator.

If Tj = absolute temperature of heat received and

T 2 = absolute temperature of heat rejected, then the ther-

mal efficiency, E, of the engine will be represented by the formula,

T T

~ 1

E r=

Or, in other words, the efficiency equals the absolute temper-

ature of the heat rejected, subtracted from the absolute temperature

of the heat received, and the remainder divided by the absolute

temperature of the heat received.

Suppose an engine is supplied with steam at 120 pounds

absolute pressure, and the exhaust is at atmospheric pressure.

What is the thermal efficiency ?

The absolute temperature corresponding to 120 pounds pres-

sure is 341.05 -f 461 = 802.05, and the absolute temperature of

the exhaust is 212 -f 461 = 673.

Then E = 802 f " 6T8 = .16, or 16 per cent.

802.05

In actual engines this efficiency cannot be realized, because

the difference between the heat received and the heat rejected is

not all converted into useful work. Part of it is lost by radiation,

conduction, condensation, leakage and -imperfect action of the

valves. The cylinder walls of the theoretical engine are supposed

to be made of a nonconducting material, while in the actual

engine the walls are of metal, which admits of a ready interchange

of heat between cylinder and steam. This action of the walls

cannot be overcome, and is so important that a failure to consider

its influence will lead to serious errors in computations, and no

design can be made intelligently if based on the theory of the

engine with nonconducting walls. The theoretical engine carries

on its expansion without the loss of any heat, while in the actual

engine a large amount of heat is lost by radiation. There is also

a considerable loss of pressure between the boiler and engine, due

to resistance of flow through pipes and passages. In a slow-speed

engine with large and direct ports and valves this trouble may be

147

96 THE STEAM ENGINE.

minimized. The imperfect action of valve gears may also be

lessened with due care, but the action of the cylinder walls still

remains to be overcome.

In the theoretical card, admission is at constant boiler pres-

sure, cut-off is sharp and expansion complete, that is, expansion

continues until the temperature falls to that of the condenser and

the exhaust is at condenser pressure. The piston also sweeps the

full length of the cylinder.

In the actual engine there is a considerable loss of pressure

between boiler and engine, and the wire-drawing of the ports

and valves tends to cause a sloping steam line. Condensation

at the beginning of the stroke causes the real expansion line to

fall below the theoretical, while re-evaporation causes it to rise

above the theoretical toward the end of expansion. In the actual

Fig. 4.

engine, release takes place before the end of the stroke, expan-

sion is not complete, that is, the pressure at release is above

that of the condenser, and the resistance of exhaust ports causes

the back pressure to be above the actual condenser pressure.

Moreover, the piston does not sweep the full length of the

cylinder, and the clearance space must be filled with steam, which

does little or no work. The theoretical and actual cards are

shown in Fig. 4.

EFFICIENCY OF THE ACTUAL ENGINE.

We have seen that the efficiency of the theoretical engine is

purely a thermal consideration ; the efficiency of the actual engine,

148

THE STEAM ENGINE. 97

however, is a mechanical matter. The measure of the activity of

work is the horse-power which corresponds to the development

of 33,000 foot-pounds per minute. As 778 foot-pounds are equiv-

alent to one B. T. U., 33,000 foot-pounds, or one horse-power, is

equivalent to 33,000 -4- 778 = 42.42 B. T. U. Now if a certain

engine uses 84.84 B. T. U. per horse-power per minute, it is evi-

dent that its efficiency would only be |- or 50 per cent, because

42.42 -f- 84.84 = | . Hence* we may say that the efficiency of

the actual engine is equal to _ _. This

B. T. U. per H. P. per minute

efficiency is always much less than that of the perfect engine.

Let us now discuss the effects of some of the losses.

In the first place, the metal, being a good conductor of heat,

becGmes heated by the steam within and transmits this heat by

conduction and radiation to the air or external bodies. With the

cylinder well lagged much less heat is lost by radiation. If the

lagging were perfect and the temperature of the cylinder remained

the same as the temperature of the steam throughout the stroke,

there would be no loss by radiation, but we should still lose heat

by conduct' on to the different parts of the engine.

During expansion, the temperature and pressure of the steam

decrease as the volume increases, and the temperature at exhaust,

is much less than tho temperature at admission. In the perfect

engine the working substance after exhaust is compressed to the

temperature at admission, but in the actual engine much of this

steam is lost and the compression of a part of it is incomplete, so

that its temperature is less than the temperature at admission.

Suppose an engine is running with admission at 100 pounds

absolute and exhaust at 18 pounds absolute. Then from steam

tables we find the temperature at admission to be 327.6, and at

exhaust 222.4. The metal walls of the cylinder, being good con-

ductors and radiators of heat, are cooled by the low temperature

of exhaust, so that the entering steam comes through ports and into

a cylinder that is more than 100 cooler than the steam. This

means that heat must flow from steam to metal until botli are of

the same temperature. Th?s causes the steam to give up part of

its latent heat, and as saturated t team cannot lose any of its heat

without condensation, we find the cylinder walls covered with a

149

THE STEAM ENGINE.

film of moisture known as initial condensation. This conden-

sation in simple unjacketed engines working under fair conditions

may easily be 25 per cent or more of the entering steam. The

moisture in the cylinder has of course the same temperature as

the steam ; it has simply lost its heat of vaporization.

Although metal is a good conductor of heat it cannot give

up nor absorb heat instantly ; consequently during expansion

the temperature of the steam falls more rapidly than that of the

cylinder. This allows heat to flow from the cylinder walls to

the moisture on them. As fast as the steam expands so that the

pressure in the cylinder becomes less, this condensation will begin

to evaporate. As the pressure falls it requires less and less heat

to form steam, and therefore more and more of this moisture will

be evaporated. At release the pressure drops suddenly, and more

heat at once flows from the cylinder walls, and re-evaporation con-

tinues throughout the exhaust. Probably all of the water remain-

ing in the cylinder at release is now re-evaporated, blows out into

the air or the condenser, and is lost so far as useful work is

concerned.

The steam that is first condensed in the cylinder does no

work ; its heat is used to warm up the cylinder, and later, when

it is re-evaporated, it works only during a part of the expansion

and at a reduced efficiency, because it is re-evaporated at a pres-

sure and consequently at a temperature very much lower than

that of admission. If the cut-off is short, perhaps 20 per cent of

the steam condensed may be re-evaporated during expansion ; if the

cut-off is long, 10 per cent may be re-evaporated, the rest remaining

in the cylinder at release still in the form of moisture. Thus

some of the entering steam passes through the cylinder as

moisture, until after cut-off, and still more passes clear through

without doing any work at all.

Suppose an engine is using 30 pounds of steam per horse-

power per hour and admission is at 100 pounds absolute. The

latent heat of vaporization at this pressure is 884 B. T. U. per

pound. If the condensation amounts to 331 p er cent, then 10

pounds are condensed and we lose 10 times 884, equals 8,840

B. T. U. per hour, or 147.3 per minute ; and since 42.42 B. T. U.

represents 1 horse-power, we shall lose by condensation 147.3

150

THE STEAM ENGINE.

divided by 42.42, equals 3* horse-power (nearly). If the cut-off is

shortened, the condensation increases and may amount to 50 per

cent at very short cut-off. Of course we use very much less

steam at short cut-off than with long cut-off, and doubtless in

many cases 50 per cent of the steam at short cut-off is not as

great an absolute quantity as 30 per cent at long cutoff. Never-

theless, in all cases it is the percentages that go to make up the

efficiency.

In addition to the actual loss from condensation in the cylinder

there is still another loss due to the re-evaporation. Suppose, as

before, that 10 pounds of steam are condensed in the cylinder,

and that 20 per cent of this is re-evaporated during expansion.

This will leave 8 pounds to be re-evaporated during exhaust.

Suppose the exhaust is at 3 pounds above atmospheric pressure,

or 18 pounds absolute (about). Then the heat of vaporization is

958.5 B. T. U. per pound of steam, and it will require 8 times

958.5, which equals 7668.0 B. T. U., to evaporate the 8 pounds.

All of this heat is taken from the cylinder, leaving the engine

much cooler than it would be were it not for this re-evaporatioiv

This gives some idea of the great amount of heat passing away at

exhaust, which is known as the exhaust waste.

In all cylinders it is necessary to have a little space between

the cylinder cover and the piston when at the end of the stroke.

In vertical engines the space is greater at the bottom than at the

top. The volume of this space, together with the volume of the

steam ports, is called the clearance. It varies from 1 to 20 per

cent, depending upon the type and speed of the engine ; the higher

the speed, the greater the clearance. This clearance space must

be filled with steam before the piston receives full pressure, but

this steam does no work except in expanding, and the volume of

the clearance offers additional surface for condensation.

Another important loss is that due to friction. We know that

it takes considerable power to move an unloaded engine; if fitted

with a pLun, unbalanced slide valve, the power necessary to move

the valve alone is considerable. The piston is made steam tight

by packing rings, and leakage around the piston rod is prevented

by stuffing boxes. All these devices cause friction as well as wear

at the joints. The amount of power wasted in friction varies

151

100 THE STEAM ENGINE.

greatly, depending upon the kind of valves, general workman-

ship, state of repair and lubrication.

MULTIPLE EXPANSION.

Two engines may be used together on the same shaft, partly

expanding the steam in one of the cylinders, and then passing it

over to the other to finish the expansion. One advantage from

this arrangement is that the parts can be made lighter. The high-

pressure cylinder can be of much less diameter than would be

possible if the entire expansion were to take place in one cylinder.

This, of course, makes the pressure exerted on the piston rod

much less, and the piston rod and connecting rod can thus be

made much lighter. The low-pressure cylinder must be larger

than it otherwise would be, but its parts need not be much heavier,

because the pressure per square inch is always low.

This arrangement gives not only the advantage of lighter

parts, but a decided increase of economy over the single cylinder

type. If attention is given to the matter, a loss of economy would

be expected, because the steam is exposed to a much larger surface

through which to lose heat, but the gain comes from another

source, and is sufficient to entirely counterbalance the effect of

a larger cylinder surface.

When very high pressure steam and a great ratio of expan-

sion is used, the difference between the temperature of the enter-

ing and that of the exhaust steam is great. For instance, suppose

steam at 160 pounds (gage) pressure enters the cylinder and the

exhaust pressure is 2 pounds (gage), the difference in temperature

is, from steam tables,

370.5 218.1= 152.4

This difference becomes nearly 230 if the steam is con-

densed to about three pounds absolute pressure. The cylinder and

ports of the engine are cooled to the low temperature of the

exhaust steam, and, as we have seen, a considerable quantity

of the entering steam is condensed to give up heat enough to

raise the temperature of the cylinder to that of the entering

steam. As the ratio of expansion increases, the difference in

temperature increases, and consequently the amount of steam

thus condensed also increases. To keep this initial condensation

152

THE STEAM ENGINE. 101

as small as possible we must limit the temperature, that is, we

must not have as great a difference between admission and

exhaust. To do this we must divide the expansion between two

or more cylinders.

It will be remembered that the great trouble Watt found with

Newcomen's engine was its great amount of condensation, and he

stated as the law which all engines should try to approach, " that

the cylinder should be kept as hot as the steam which enters it."

This is to avoid condensation when steam first comes in. If,

instead of expanding the steam in one cylinder, we expand it

partly in one and then finish the expansion in another, we shall

have passed it out of the first cylinder before its temperature falls

a great deal, and consequently the cylinder walls will be hotter

than they would be if we had expanded it entirely in one cylinder.

This would then reduce the amount of steam condensed. The

importance of this may not be evident at first, but it makes a

great difference in the economy of the engine. If there is less

condensation, there will be less moisture to re-evaporate, and con-

sequently less exhaust waste ; hence we shall save in two ways at

the same time.

In a compound engine we admit the steam first to the smaller

or high-pressure cylinder, and exhaust it to the larger or low-

pressure.

Suppose steam at 160 pounds (gage) pressure is admitted

to a cylinder, and the ratio of expansion is such that the steam

is exhausted at about 60 pounds (g a g e ) pressure; then the dif-

ference of temperature is

370.5 307 = 63.5.

If, now, the steam when exhausted from the first cylinder

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