1S30.] 



THE CIVIL r.iNraNEER AND AlU'HlTiXT.S JOURNAL. 



140 



GENERAL THEORY OF THE STEAM ENGINE. 



By Akistides A. Mou^•AY, Esq. 



No. Vi. 



On the Action of the Steam in the Cylinder of a Stcnn Engine, 



(Continued. ) 



We sliiiU first consider the most simple ciise, namely, that of a low 

 pressure condensing engine without expansion, and with the ordinary 

 slide valve, as the action of this valve is more simple than any other 

 for calculation. 



On the subject of the slides we have to observe, that, although their 

 motion is gradual and as slow as it can he, yet there is no loss of eflfect 

 arising from this circumstance. We should not have thought it ne- 

 cessary to mention this fact here, as \ve stated it cursorily in our last 

 paper, but we have since seen a paragraph in Tredgold's Treatise on 

 the .Steam Engine, where he asserts the contrary. This paragraph is 

 at page 201, and runs thus: 



" When valves, cocks, or sliders are to be moved to admit steam to 

 a steam-engine, the motion should be as quick as circumstances will 

 permit, so that the passages may be wdiolly opened or wholly closed 

 at the proper time with the least delay : for it may be easily shown 

 that a considerable loss of effect arises from valves opening or shutting 

 witli a slow motion." 



Now the slide, when it has no travel, takes one half of tlie duration 

 of the stroke to open, and the other half to shut the ports ; and, as the 

 eccentric is placed a quarter of a revolution in advance of the crank, 

 the ports are full open when the piston is at the middle of the stroke, 

 and comjiletely closed at each end. If, however, we can show that 

 the aperture of the steam port is always proportional to the velocity 

 of the piston, it will be proved that the steam will follow the piston 

 with the same pressure from the beginning to the end of the stroke. 

 This will, howev(T, only apply to the steam port as regards the disad- 

 vantage of the slow motion of the slide ; for the more rapidly the 

 waste steam can be made to pass into the condenser, the greater effect 

 will obviously be obtained from the steam.* At the beginning of the 

 stroke of the piston, then, the slide is in the middle of its stroke ; the 

 piston has no velocity, and the steam-port is completely sluit, but just 

 readv to open, and its aperture increases in the ratio of the distance 

 travelled by the slide from its present position in the middle of its 

 stroke. Now that distance is equal to e sin a, when the shaft has de- 

 scribed the angle a, e being the eccentricity or distance of the centre 

 of the eccentric from that of the shaft. In the same time the piston 

 will have acquired tlie velocity r sin a, if v is its velocity in tlie middle 

 of the stroke. These two cjuantities evidently increase always in the 

 same ratio, therefore the orilice of the steam-port is always sufficiently 

 large to admit steam of the same elasticity as at the middle of the 

 stroke of the piston, supposing no w'aste space to require tilling with 

 steam at the beginning of c.ch stroke, and this is elfected before the 

 piston has described a sensible portion of its stroke, the steam having 

 a much greater tendency to How into nearly a vacuum than into steam 

 of very little less than its own pressure. 



In order to allow for the filling of the waste space with steam, we 

 will suppose the slide, instead of having no lead, to have just so much 

 as will allow that space to be filled with steam of the same elasticity 

 as that in the steam-pipe, by the time the steam has arrived at the 

 end of the cylinder, and is ready to begin its stroke, the aperture of 

 the port being at the same time enlarged so much, that in the middle 

 of the stroke of the |iiston it should be suflicient to allow the steam to 

 follow the piston with the required elasticity. 13ut, since this neces- 

 sary lead of the slide and enlargement of the port are, as will be here- 

 after proved, excessively small, we shall omit to take them into con- 

 sideration, merely assuming the effect for the sake of which these 

 alterations were supposed, namely, that the waste space is already 

 filled with steam of the same elastic force as that in the steam-pipe 

 at the moment the piston commences its stroke. 



Suppose now the piston in the middle of the stroke, in which case 

 the steam port will be full o|ien, and let the elastic force of the steam 

 in the steam passages = P, that of the steam in the cylinder = ;;, the 

 ratio of the area of the piston to that of the steam port = in, and V=: 

 the mean velocity of the piston in feet per minute. Let it be required 

 to determine// when all the other quantities are known. 



In order to solve this problem, we have to fiiiil, Jirst, the velocity of 



•'■ In condensing engines, working with low pressm-e steam, the resi tanec 

 of the wa^to steam is iisnally considered as equal to tlie prcssMrc in tlip con- 

 denser; we shall show in a future paper that where tl'-O slide valve is used 

 with no lead, the pressure of the waste stciim on the piston is much greater 

 tlian ia the condeusti during d, cousiderahle portigu gf the stroke. 



the steam through the port necessary to enable it, when expanded to 

 the elastic force p, wliich it assumes in the cylinder, to follow the 



piston with the velocity— — which the piston has attained in the 



middle of the stroke ; secondlij, the height of a column of steam of the 

 elasticity P, which would give it that velocity, and lMtli/,the pressure 

 of that column, which will be equal to the loss of pressure wdiieh the 

 steam suffers in entering the cylinder. 



In the first place, the velocity of the steam through the port, if it 



retained its density, would be --- — ; but, since we suppose a loss of 



pressure, we must also assume a diminution of density ; and, if we call 



ii' anil r, the relative volume of the steam in the steam passages and 



in the cylinder respectively, the velocity through the port will be 



f' nt IT V 



— ;r . The height due to this velocity is, 



h = 



1)'^ m- T- V- 

 28,800 g I'- ' 



and this is the height of the column of which the pressure is to be 

 determined. This would evidently be knoviai if we knew the height 

 of the colunm whose weight is equivalent to the total elastic force P, 

 which we shall therefore now endeavour to ascertain. 



Letjj and v be the elastic force and relative volume of steam at the 

 temperatiu'e /, and ]/ and o' those of steam at the temperature t' ; 

 also let H be the height of a column of the former, whose weight is 

 equivalent to its pressure ]>, and IF the height of a column of the lat- 

 ter whose weight is equivalent to its pressure y. It is evident that 

 wc must have 



»_ P^ 

 H~ Pv' 



But we have also 



w 



V (f + 4-1&) 



Vt' 



!)' (t -f 448) ■ 



which value being substituted in the preceding equation, it becomes 



H'_T' 



H "" T' 



When t = 210, H is the height of the column of atmospherie steairt 

 equivalent to its clastic force, and H' that of the column of steam at 

 any other temperature /' equivalent to its clastic force y. Assuming 

 the density of water to be 1700 times that of atmosidieric steam, and 

 the pressure of the atmosphere to be equal to the weight of a cohinin 

 of water 34 feet high, the value of H will be 5rbU0 feel, and we shall 

 have 



H' = ^'fiT', 

 liGO ' 



or, reducing the eoellicient and dropping the accents, ' 



H = S7'.37570 T., 



Since the value of P is supposed to be known, we can find that of T 

 by referring to a table, so that we may consider H as already deter- 

 mined, and therefore make use of it in the determination of the loss of 

 pressure P — p, wdiich the steam surtijis in entering the cylinder. 



As the two colunnis H and h have the same density, their pressures 

 are evidently proportional to their altitudes, therefore 



P—p _ h 

 P ~ H' 



whence 



P-i^ = - 



V^P 



2SS0O g !i2 H' 



or, substituting for the constants 7r' and g their \aiucs, and for II it's 

 value S7:J757(J T, as found above, 



-1>- 



•U00000121aG 



t'T 



.^P. 



(a) 



We may be allowed to presume that the difference between v' and 

 V in all cases which occur in practice is so trifling that the ratio — 



n (,2 



may, without any sensiMi' error, be reganled as equal to unity, whicif 

 will reduce the preceding equation to the following simpler one, 



m' V- 

 P — ^; ^ -00000012150 -^- P. (6.) 



X 



