| | Volume of | Mechanical
Total pressure| | the Steam | Effect of
in Pounds | Corresponding| compared to | a Cubic Inch
per Square | Temperature. | the Volume | of Water
Inch. | | of the | evaporated
| | Water that | in Pounds
| | has | raised One
| | produced it.| Foot.
——————————————+——————————————+—————————————+—————————————
1 | 102·9 | 20868 | 1739
2 | 126·1 | 10874 | 1812
3 | 141·0 | 7437 | 1859
4 | 152·3 | 5685 | 1895
5 | 161·4 | 4617 | 1924
6 | 169·2 | 3897 | 1948
7 | 175·9 | 3376 | 1969
8 | 182·0 | 2983 | 1989
9 | 187·4 | 2674 | 2006
10 | 192·4 | 2426 | 2022
11 | 197·0 | 2221 | 2036
12 | 201·3 | 2050 | 2050
13 | 205·3 | 1904 | 2063
14 | 209·1 | 1778 | 2074
15 | 212·8 | 1669 | 2086
16 | 216·3 | 1573 | 2097
17 | 219·6 | 1488 | 2107
18 | 222·7 | 1411 | 2117
19 | 225·6 | 1343 | 2126
20 | 228·5 | 1281 | 2135
21 | 231·2 | 1225 | 2144
22 | 233·8 | 1174 | 2152
23 | 236·3 | 1127 | 2160
24 | 238·7 | 1084 | 2168
25 | 241·0 | 1044 | 2175
26 | 243·3 | 1007 | 2182
27 | 245·5 | 973 | 2189
28 | 247·6 | 941 | 2196
29 | 249·6 | 911 | 2202
30 | 251·6 | 883 | 2209
31 | 253·6 | 857 | 2215
32 | 255·5 | 833 | 2221
33 | 257·3 | 810 | 2226
34 | 259·1 | 788 | 2232
35 | 260·9 | 767 | 2238
36 | 262·6 | 748 | 2243
37 | 264·3 | 729 | 2248
38 | 265·9 | 712 | 2253
39 | 267·5 | 695 | 2259
40 | 269·1 | 679 | 2264
41 | 270·6 | 664 | 2268
42 | 272·1 | 649 | 2273
43 | 273·6 | 635 | 2278
44 | 275·0 | 622 | 2282
45 | 276·4 | 610 | 2287
46 | 277·8 | 598 | 2291
47 | 279·2 | 586 | 2296
48 | 280·5 | 575 | 2300
49 | 281·9 | 564 | 2304
50 | 283·2 | 554 | 2308
51 | 284·4 | 544 | 2312
52 | 285·7 | 534 | 2316
53 | 286·9 | 525 | 2320
54 | 288·1 | 516 | 2324
55 | 289·3 | 508 | 2327
56 | 290·5 | 500 | 2331
57 | 291·7 | 492 | 2335
58 | 292·9 | 484 | 2339
59 | 294·2 | 477 | 2343
60 | 295·6 | 470 | 2347
61 | 296·9 | 463 | 2351
62 | 298·1 | 456 | 2355
63 | 299·2 | 449 | 2359
64 | 300·3 | 443 | 2362
65 | 301·3 | 437 | 2365
66 | 302·4 | 431 | 2369
67 | 303·4 | 425 | 2372
68 | 304·4 | 419 | 2375
69 | 305·4 | 414 | 2378
70 | 306·4 | 408 | 2382
71 | 307·4 | 403 | 2385
72 | 308·4 | 398 | 2388
73 | 309·3 | 393 | 2391
74 | 310·3 | 388 | 2394
75 | 311·2 | 383 | 2397
76 | 312·2 | 379 | 2400
77 | 313·1 | 374 | 2403
78 | 314·0 | 370 | 2405
79 | 314·9 | 366 | 2408
80 | 315·8 | 362 | 2411
81 | 316·7 | 358 | 2414
82 | 317·6 | 354 | 2417
83 | 318·4 | 350 | 2419
84 | 319·3 | 346 | 2422
85 | 320·1 | 342 | 2425
86 | 321·0 | 339 | 2427
87 | 321·8 | 335 | 2430
88 | 322·6 | 332 | 2432
89 | 323·5 | 328 | 2435
90 | 324·3 | 325 | 2438
91 | 325·1 | 322 | 2440
92 | 325·9 | 319 | 2443
93 | 326·7 | 316 | 2445
94 | 327·5 | 313 | 2448
95 | 328·2 | 310 | 2450
96 | 329·0 | 307 | 2453
97 | 329·8 | 304 | 2455
98 | 330·5 | 301 | 2457
99 | 331·3 | 298 | 2460
100 | 332·0 | 295 | 2462
110 | 339·2 | 271 | 2486
120 | 345·8 | 251 | 2507
130 | 352·1 | 233 | 2527
140 | 357·9 | 218 | 2545
150 | 363·4 | 205 | 2561
160 | 368·7 | 193 | 2577
170 | 373·6 | 183 | 2593
180 | 378·4 | 174 | 2608
190 | 382·9 | 166 | 2622
200 | 387·3 | 158 | 2636
210 | 391·5 | 151 | 2650
220 | 395·5 | 145 | 2663
230 | 399·4 | 140 | 2675
240 | 403·1 | 134 | 2687
——————————————+——————————————+—————————————+—————————————
[Pg511] In the absence of any direct method of determining the
general relation between the pressure and volume of common steam,
empirical formulæ expressing it have been proposed by different
mathematicians.
The late Professor Navier proposed the following:—Let S express
the volume of steam into which an unit of volume of water is
converted under the pressure P, this pressure being expressed in
kilogrammes per square mètre. Then the relation between S and P
will be
S = a/(b + mP),
where a = 1000, b = 0·09, and m = 0·0000484.
This formula, however, does not agree with experiment at pressures
less than an atmosphere. M. de Pambour, therefore, proposes the
following changes in the values of its co-efficients:—Let P
express the pressure in pounds per square foot; and let
a = 10000 b = 0·4227 m = 0·00258,
and the formula will be accurate for all pressures. For pressures
above two atmospheres the following values give more accuracy to
the calculation:—
a = 10000 b = 1·421 m = 0·0023.
In these investigations I shall adopt the following modified
formula. The symbols S and P retaining their signification, we
shall have
S = a/(b + P) (10.)
where
a = 3875969 b = 164.
These values of a and b will be sufficiently accurate for practical
purposes for all pressures, and may be used in reference to
low-pressure engines of every form, as well as for high-pressure
engines which work expansively.
When the pressure is not less than 30 pounds per square inch, the
following values of a and b will be more accurate:—
a = 4347826 b = 618.
_On the Expansive Action of Steam._
The investigation of the effect of the expansion of steam which
has been given in the text, is intended to convey to those who are
not conversant with the principles and language of analysis, some
notion of the nature of that mechanical effect to which the
advantages attending the expansive principle are due. We shall
now, however, explain these effects more accurately. [Pg512]
The dynamical effect produced by any mechanical agent is expressed
by the product of the resistance overcome and the space through
which that resistance is moved.
Let
P = the pressure of steam expressed in pounds per square foot.
S = the number of cubic feet of steam of that pressure
produced by the evaporation of a cubic foot of water.
E = the mechanical effect produced by the evaporation of a
cubic foot of water expressed in pounds raised one foot.
Then we shall have E = PS; and if W be a volume of water
evaporated under the pressure P, the mechanical effect produced by
it will be WPS.
By (10.) we have
SP = a − bS.
Hence, for the mechanical effect of a cubic foot of water
evaporated under the pressure P we have
E = a − bS. (11.)
Let a cubic foot of water be evaporated under the pressure P′, and
let it produce a volume of steam S′ of that pressure. Let this
steam afterwards be allowed to expand to the increased volume S
and the diminished pressure P; and let it be required to determine
the mechanical effect produced during the expansion of the steam
from the volume S′ to the volume S.
Let
E′ = the mechanical effect produced by the evaporation of
the water under the pressure P′ without expansion.
E″ = the mechanical effect produced during the expansion
of the steam.
E = the mechanical effect which would be produced by
the evaporation under the pressure P without expansion.
_E_ = the total mechanical effect produced by the evaporation
under the pressure P′ and subsequent expansion.
Thus we have
_E_ = E′ + E″.
Let s be any volume of the steam during the process of expansion,
p the corresponding pressure, and e″ the mechanical effect
produced by the expansion of the steam. We have then by (10.)
p = (a/s) − b;
∵ de″ = (ads/s) − bds.
Hence by integrating we obtain
e″ = a log. s − bs + C;
[Pg513] which, taken between the limits s = S′ and s = S, becomes
E″ = a log. S/S′ − b(S − S′). (12.)
But by (11.) we have
E′ = a − bS′,
E = a − bS;
∵ E′ − E = b(S − S′);
∵ E″ = a log. S/S′ − E′ + E;
∵ _E_ = E″ + E′ = a log. S/S′ + E. (13.)
Or,
_E_ = a (1 + log. S/S′) − bS. (14.)
Hence it appears that the mechanical effect of a cubic foot of
water evaporated under the pressure P may be increased by the
quantity a log. S/S′, if it be first evaporated under the greater
pressure P′, and subsequently expanded to the lesser pressure P.
The logarithms in these formulæ are hyperbolic.
To apply these principles to the actual case of a double acting
steam engine,
Let
L = the stroke of the piston in feet.
A = the area of the piston in square feet.
n = the number of strokes of the piston per minute.
∵ 2n AL = the number of cubic feet of space through which
the piston moves per minute.
Let cLA = the clearage, or the space between the steam valve
and the piston at each end of the stroke.
∵ The volume of steam admitted through the steam valve
at each stroke of the engine will be 2n AL(1 + c).
Let
V = the mean speed of the piston in feet per minute,
∵ 2nL = V.
The volume of steam admitted to the cylinder per minute will
therefore be VA (1 + c), the part of it employed in working the
piston being VA.
Let
W = the water in cubic feet admitted per minute in the form
of steam through the steam valve.
S = the number of cubic feet of steam produced by a cubic
foot of water.
[Pg514] Hence we shall have
WS = VA (1 + c);
∵ S = (VA(1 + c))/W. (15.)
Since by (10.) we have
P = a/S − b;
∵ P = [Wa/(VA(1 + c))] − b. (16.)
By which the pressure of steam in the cylinder will be known, when
the effective evaporation, the diameter of the cylinder, and speed
of the piston, are given.
If it be required to express the mechanical effect produced per
minute by the action of steam on the piston, it is only necessary
to multiply the pressure on the surface of the piston by the space
per minute through which the piston moves. This will give
VAP = W(a/(1 + c)) − VAb; (17.)
which expresses the whole mechanical effect per minute in pounds
raised one foot.
If the steam be worked expansively, let it be cut off after the
piston has moved through a part of the stroke expressed by e.
The volume of steam of the undiminished pressure P′ admitted per
minute through the valve would then be
VA (e + c);
and the ratio of this volume to that of the water producing it
being expressed by S′, we should have
S′ = (VA(e + c))/W.
The final volume into which this steam is subsequently expanded
being VA(1 + c), its ratio to that of the water will be
S = (VA (1 + c))/W.
The pressure P′, till the steam is cut off, will be
P′ = [Wa / (VA(e + c))] − b. (18.)
The mechanical effect E′ produced per minute by the steam of full
pressure will be
E′ = P′AVe = [Wae / (e + c)] − AVbe;
and the effect E″ per minute produced by the expansion of the
steam will by (12.) be [Pg515]
E″ = Wa log.[(1 + c) / (e + c)] − bVA(1 − e).
Hence the total effect per minute will be
_E_ = Wa [(e/(e + c)) + log.([1 + c]/[e + c])] − bVA. (19.)
If the engine work without expansion, e = 1;
∵ _E′_ = ( Wa/(1 + c)) − bVA, (20.)
as before; and the effect per minute gained by expansion will
therefore be
_E_ − _E′_ =
Wa [(e/(e + c)) − (1/(1 + c)) + log.([1 + c]/[e + c])]; (21.)
which therefore represents the quantity of power gained by the
expansive action, with a given evaporating power.
In these formulæ the total effect of the steam is considered
without reference to the nature of the resistances which it has to
overcome.
These resistances may be enumerated as follows:—
1. The resistance produced by the load which the engine is
required to move.
2. The resistance produced by the vapour which remains
uncondensed if the engine be a condensing engine, or of the
atmospheric pressure if the engine do not condense the steam.
3. The resistance of the engine and its machinery, consisting
of the friction of the various moving parts, the resistances
of the feed pump, the cold water pump, &c. A part of these
resistances are of the same amount, whether the engine be
loaded or not, and part are increased, in some proportion
depending on the load.
When the engine is maintained in a state of uniform motion, the
sum of all these resistances must always be equal to the whole
effect produced by the steam on the piston. The power expended on
the first alone is the _useful effect_.
Let R = the pressure per square foot of the piston surface, which
balances the resistances produced by the load.
mR = the pressure per square foot, which balances that part of the
friction of the engine which is proportional to the load.
r = the pressure per square foot, which balances the sum of all
those resistances that are not proportional to the load.
The total resistance, therefore, being R + mR + r, which, when the
mean motion of the piston is uniform, must be equal to the mean
pressure on the piston. The total mechanical effect [Pg516] must
therefore be equal to the total resistance multiplied by the space
through which that resistance is driven. Hence we shall have
[R(1 + m) + r]VA = Wa[(e/(e + c)) + log.([1 + c]/[e + c])] − VAb;
∵ RVA(1 + m) = Wa[(e/(e + c)) + log.([1 + c]/[e + c])] − VA(b + r).
For brevity, let
e′ = a[(e/(e + c)) + log.([1 + c]/[e + c])];
∵ RVA(1 + m) = We′ − VA(b + r). (22.)
By solving this for VA, we obtain
VA = We′/(R(1 + m) + b + r);
∵ RVA = We′R/(R(1 + m) + b + r). (23.)
This quantity RVA, being the product of the resistance RA, of the
load reduced to the surface of the piston, multiplied by the space
through which the piston is moved, will be equal to the load
itself multiplied by the space through which it is moved. This
being, in fact, the useful effect of the engine, let it be
expressed by U, and we shall have
U = We′R/(R(1 + m) + b + r). (24.)
Or by (22.),
U(1 + m) = We′ − VA(b + r). (25.)
The value of the useful effect obtained from these formulæ will be
expressed in pounds, raised one foot per minute, W being the
effective evaporation in cubic feet per minute, A the area of the
piston in square feet, and V the space per minute through which it
is moved, in feet.
Since a resistance amounting to 33,000 pounds moved through one
foot per minute is called one-horse power, it is evident that the
horse power H of the engine is nothing more than the useful effect
per minute referred to a larger unit of weight or resistance; that
is to 33,000 pounds instead of one pound. Hence we shall have
H = U/33000. (26.)
Since the useful effect expressed in (24.) and (25.) is that due
to a number of cubic feet of water, expressed by W, we shall
obtain the effect due to one cubic foot of water, by dividing U by
W. If, therefore, U′ be the effect produced by the effective
evaporation of a cubic foot of water, we shall have [Pg517]
U′ = U/W. (27.)
If the quantity of fuel consumed per minute be expressed by F, the
effect produced by the unit of fuel, called the DUTY of the
engine, will, for like reason, be
D = U/F. (28.)
If the fuel be expressed in hundredweights of coal, then D will
express the number of pounds' weight raised one foot by a
hundredweight of coal.
By solving (24.) and (25.) for W, we obtain
W = [U(R(1 + m) + b + r)]/Re′, (29.)
W = (1/e′)[U(1 + m) + VA(b + r)]. (30.)
By eliminating U, by (26.), we shall have
W = [33000 H(R(1 + m) + b + r)]/Re′, (31.)
W = (1/e′)[33000 H(1 + m) + VA(b + r)]. (32.)
The evaporation necessary per horse power per minute will be found
by putting H = 1 in these formulæ.[41]
It will be observed that the quantities A and V, the area of the
cylinder and the speed of the piston, enter all these formulæ as
factors of the same product. Other things, therefore, being the
same, the speed of the piston will be always inversely as the area
of the cylinder. In fact, VA is the volume of steam per minute
employed in working the piston, and if the piston be increased or
diminished in magnitude, its speed must be inversely [Pg518]
varied by the necessity of being still moved through the same
number of cubic feet by the same volume of steam.
It has been already stated in the text, that no satisfactory
experiments have yet been made, by which the numerical value of
the quantity r can be exactly known. In engines of different
magnitudes and powers, this resistance bears very different
proportions to the whole power of the machine. In general,
however, the larger and more powerful the engine, the less that
proportion will be.
That part of this resistance which arises from the reaction of the
uncondensed vapour on the piston is very variable, owing to the
more or less perfect action of the condensing apparatus, the
velocity of the piston, and the magnitude and form of the steam
passages. M. de Pambour states, that, by experiments made with
indicators, the mean amount of this resistance in the cylinder is
2-1/2 lbs. per square inch more than in the condenser, and that
the pressure in the latter being usually 1-1/2 lb. per square
inch, the mean amount of the pressure of the condensed vapour in
the cylinder is about 4 lbs. per square inch. Engineers, however,
generally consider this estimate to be above the truth in
well-constructed engines, when in good working order.
In condensing low pressure engines of forty horse power and
upwards, working with an average load, it is generally considered
that the resistance produced by the friction of the machine and
the force necessary to work the pumps may be taken at about 2 lbs.
per square inch of piston surface.
Thus the whole resistance represented by r in the preceding
formulæ, as applied to the larger class of low pressure engines,
may be considered as being under 6 lbs. per square inch, or 864
lbs. per square foot, of the piston. It is necessary, however, to
repeat, that this estimate must be regarded as a very rough
approximation; and as representing the mean value of a quantity
subject to great variation, not only in one engine compared with
another, but even in the same engine compared with itself at
different times and in different states.
In the same class of engines, the magnitude of the clearage is
generally about a twentieth part of the capacity of the cylinder,
so that c = 0·05.
That part of the resistance which is proportional to the load, and
on which the value of m in the preceding formulæ depends, is still
more variable, and depends so much on the form, magnitude, and the
arrangement of its parts, that no general rule can be given for
its value. It must, in fact, be determined in every particular
case.
In the practical application of the preceding formulæ in
condensing engines we shall have [Pg519]
a = 3875969 b = 164 c= 0·05;
e′ = 3875969([e/(e + 0·05)] + log.[1·05/(e + 0·05)]).
In engines which work without condensation, and therefore with
high pressure steam, we shall have
a = 4347826 b = 618 c = 0·05
e′ = 4347826([e/(e + 0·05)] + log.[1·05/(e + 0·05)])
To facilitate computation, the values of e′ corresponding to all
values of e, from e = ·10 to e = ·90, are given in the following
table:—
———————————————————————————————————————————————————————————————
|Condensing|Non-condensing|| |Condensing|Non-condensing
| Engines | Engines || | Engines | Engines
e | e′. | e′. || e | e′. | e′.
————+——————————+——————————————++————+——————————+———————————————
·10 | 10126265 | 11359029 ||·51 | 5966367 | 6692708
·11 | 9956867 | 11169008 ||·52 | 5903837 | 6622565
·12 | 9793136 | 10985344 ||·53 | 5842288 | 6553525
·13 | 9634926 | 10807875 ||·54 | 5781693 | 6485552
·14 | 9482029 | 10636364 ||·55 | 5722024 | 6418619
·15 | 9334219 | 10470560 ||·56 | 5663251 | 6352693
·16 | 9191251 | 10310186 ||·57 | 5605353 | 6287745
·17 | 9052888 | 10154978 ||·58 | 5548297 | 6223742
·18 | 8918896 | 10004675 ||·59 | 5492064 | 6160662
·19 | 8789043 | 9859014 ||·60 | 5436628 | 6098478
·20 | 8663120 | 9717760 ||·61 | 5381969 | 6037166
·21 | 8540918 | 9580682 ||·62 | 5328065 | 5976699
·22 | 8422242 | 9447559 ||·63 | 5274896 | 5917057
·23 | 8306916 | 9318193 ||·64 | 5222444 | 5858219
·24 | 8194770 | 9192396 ||·65 | 5170684 | 5800159
·25 | 8085644 | 9069984 ||·66 | 5119605 | 5742860
·26 | 7979392 | 8950796 ||·67 | 5069186 | 5686304
·27 | 7875870 | 8834674 ||·68 | 5019410 | 5630469
·28 | 7774952 | 8721468 ||·69 | 4970263 | 5575340
·29 | 7676514 | 8611048 ||·70 | 4921727 | 5520894
·30 | 7580447 | 8503284 ||·71 | 4873790 | 5467121
·31 | 7486640 | 8398056 ||·72 | 4826434 | 5414000
·32 | 7394990 | 8295250 ||·73 | 4779648 | 5361519
·33 | 7305407 | 8194760 ||·74 | 4733417 | 5309659
·34 | 7217807 | 8096496 ||·75 | 4687728 | 5258408
·35 | 7132097 | 8000352 ||·76 | 4642569 | 5207751
·36 | 7048206 | 7906249 ||·77 | 4597928 | 5157676
·37 | 6966058 | 7814100 ||·78 | 4553794 | 5108170
·38 | 6885585 | 7723832 ||·79 | 4510155 | 5059218
·39 | 6806720 | 7635365 ||·80 | 4466999 | 5010808
·40 | 6729408 | 7548642 ||·81 | 4424317 | 4962931
·41 | 6653578 | 7463580 ||·82 | 4382096 | 4915569
·42 | 6579187 | 7380132 ||·83 | 4340332 | 4868720
·43 | 6506174 | 7298230 ||·84 | 4299010 | 4822368
·44 | 6434491 | 7217822 ||·85 | 4258120 | 4776500
·45 | 6364099 | 7138858 ||·86 | 4217658 | 4731113
·46 | 6294944 | 7061285 ||·87 | 4177613 | 4686192
·47 | 6226989 | 6985058 ||·88 | 4137974 | 4641728
·48 | 6160190 | 6910126 ||·89 | 4098737 | 4597713
·49 | 6094510 | 6836450 ||·90 | 4059893 | 4554140
·50 | 6029916 | 6763992 || | |
————+——————————+——————————————++————+——————————+———————————————
[Pg520] In engines which work without expansion we have
e′ = a/(1 + c).
For condensing engines without expansion, we shall then have
e′ = 3875969/1·05 = 3691399; (33.)
and for non-condensing engines,
e′ = 4347826/1·05 = 4140787. (34.)
As the diameters of the cylinders of engines are generally
expressed in inches, the corresponding areas of the pistons
expressed in square feet are given in the following table, so that
the values of A may be readily found:—
——————————————————————————————————————————————————————————————————————
Diam. | Area. | Diam. | Area. | Diam. | Area. | Diam. | Area.
———————+—————————+———————+—————————+———————+—————————+———————+————————
Inches.| Sq.feet.|Inches.| Sq.feet.|Inches.| Sq.feet.|Inches.| Sq.feet.
10 | 0·545 | 48 | 12·566 | 86 | 40·339 | 124 | 83·863
11 | 0·660 | 49 | 13·095 | 87 | 41·283 | 125 | 85·221
12 | 0·785 | 50 | 13·635 | 88 | 42·237 | 126 | 86·590
13 | 0·922 | 51 | 14·186 | 89 | 43·202 | 127 | 87·970
14 | 1·069 | 52 | 14·748 | 90 | 44·179 | 128 | 89·361
15 | 1·227 | 53 | 15·321 | 91 | 45·166 | 129 | 90·763
16 | 1·396 | 54 | 15·904 | 92 | 46·164 | 130 | 92·175
17 | 1·576 | 55 | 16·499 | 93 | 47·173 | 131 | 93·599
18 | 1·767 | 56 | 17·104 | 94 | 48·193 | 132 | 95·033
19 | 1·969 | 57 | 17·721 | 95 | 49·224 | 133 | 96·479
20 | 2·182 | 58 | 18·348 | 96 | 50·265 | 134 | 97·935
21 | 2·405 | 59 | 18·986 | 97 | 51·318 | 135 | 99·402
22 | 2·640 | 60 | 19·635 | 98 | 52·382 | 136 | 100·880
23 | 2·885 | 61 | 20·295 | 99 | 53·456 | 137 | 102·369
24 | 3·142 | 62 | 20·966 | 100 | 54·542 | 138 | 103·869
25 | 3·409 | 63 | 21·648 | 101 | 55·638 | 139 | 105·380
26 | 3·687 | 64 | 22·340 | 102 | 56·745 | 140 | 106·901
27 | 3·976 | 65 | 23·044 | 103 | 57·863 | 141 | 108·434
28 | 4·276 | 66 | 23·758 | 104 | 58·992 | 142 | 109·977
29 | 4·587 | 67 | 24·484 | 105 | 60·132 | 143 | 111·532
30 | 4·909 | 68 | 25·220 | 106 | 61·283 | 144 | 113·097
31 | 5·241 | 69 | 25·967 | 107 | 62·445 | 145 | 114·674
32 | 5·585 | 70 | 26·725 | 108 | 63·617 | 146 | 116·261
33 | 5·940 | 71 | 27·494 | 109 | 64·801 | 147 | 117·859
34 | 6·305 | 72 | 28·274 | 110 | 65·995 | 148 | 119·468
35 | 6·681 | 73 | 29·065 | 111 | 67·201 | 149 | 121·088
36 | 7·069 | 74 | 29·867 | 112 | 68·417 | 150 | 122·719
37 | 7·467 | 75 | 30·680 | 113 | 69·644 | 151 | 124·361
38 | 7·876 | 76 | 31·503 | 114 | 70·882 | 152 | 126·013
39 | 8·296 | 77 | 32·338 | 115 | 72·131 | 153 | 127·676
40 | 8·727 | 78 | 33·183 | 116 | 73·391 | 154 | 129·351
41 | 9·168 | 79 | 34·039 | 117 | 74·662 | 155 | 131·036
42 | 9·621 | 80 | 34·907 | 118 | 75·944 | 156 | 132·732
43 | 10·085 | 81 | 35·785 | 119 | 77·236 | 157 | 134·439
44 | 10·559 | 82 | 36·674 | 120 | 78·540 | 158 | 136·157
45 | 11·045 | 83 | 37·574 | 121 | 79·854 | 159 | 137·886
46 | 11·541 | 84 | 38·485 | 122 | 81·180 | 160 | 139·626
47 | 12·048 | 85 | 39·406 | 123 | 82·516 | 161 | 141·377
—————+—————————+———————+—————————+———————+—————————+———————+————————
[Pg521] The practical application of the preceding formulæ will be
shown by the following examples.
EXAMPLES.
1. _A 36-inch cylinder with 5-1/2 feet stroke is supplied by a
boiler evaporating effectively 60 cubic feet of water per hour,
and the piston makes 20 strokes per minute without expansion;--
what is the power of the engine and the pressure of steam
in the cylinder?_
Let it be assumed that r = 6 × 144 = 864 and m = 0·1. Since the
engine is a condensing engine, we have b = 164 and e′ = 3691399.
By the formulæ (25.) and (26.) we have
H = [We′ − VA(b + r)]/[33000(1 + m)];
and since by the data we have
W = 1 A = 7·069 V = 2nL = 40 × 5·5 = 220,
the formula, by these substitutions, becomes
H = (3691399 − 220 × 1028 × 7·069) / (33000 × 1·1);
∵ H = 57·6.
Since e = 1, the pressure P of steam in the cylinder, by (18.), is
P = (We′/VA) − b.
Therefore
P = (3691399/1555·18) − 164 = 2210;
which being the pressure in pounds per square foot, the pressure
per square inch will be 15-1/3 lbs.
2. _To find the effective evaporation necessary to produce a power
of 80 horses with the same engine. Also, find the pressure of
steam in the cylinder, the speed of the piston being the same._
By the formula (32.), with the above substitutions, we have
W = (33000 × 80 × 1·1 + 220 × 7069 × 1028)/3691399 = 1·22.
The evaporating power would therefore be only increased 22 per
cent., while the working power of the engine would be increased
nearly 40 per cent.
The pressure P in the cylinder will be given, by (18.), as before.
P = [(1·22 × 3691399)/1555·18] − 164 = 2732;
which is equivalent to 19 lbs. per square inch. [Pg522]
3. _What must be the diameter of a cylinder to work with a power
of a hundred horses, supplied by a boiler evaporating effectively
70 cubic feet of water per hour, the mean speed of the piston
being 240 feet per minute, and the steam being cut off at half
stroke? Also, what will be the full pressure of steam on the
piston?_
Taking, as in the former examples, m = 0·1, b = 164, and r = 864,
we shall have
H = 100 W = 7/6 V = 240,
and by the column for condensing engines, in table, p. 519, we
have e′ = 6029916, where e = 0·50. Making these substitutions in
We′ = 33000 H (1 + m) + VA (b + r),
we shall have
(7/6) × 6029916 = 3300000 × 1·1 + 240 × 1028 × A.
Whence we find
A = 13·8;
and by the table, p. 520, the corresponding diameter of the
cylinder will be 50-1/3 inches.
If P′ be the full pressure of the steam, we shall have, by (18.),