7*1 



STEAM AND STEAM-KN 



STEAM AND STEAM KN<;lNi:. 



Itt 



A* long u a oontinued force of any kind produce* a continued 

 motion with a constant velocity in any body, the force must be in 

 equilibrium with the resistance it hat to overcome ; for if the force 

 were greater than the resistance, it would produce an accelerating 

 motion, which i contrary to the supposition : and if the resistance 

 became greater than the force, the velocity would retard till the equi- 

 librium were produced : aa long, therefore, as a iteam-engine is moving 

 with a constant Telocity, the preattrt on tlir pittm must be equal to the 

 resistance to be overcome, consisting of the net work to be done, 

 together with the friction of the various parts, the resistance of the 

 unoondennd steam, of the air on the opposite side of the piston, and 

 of other sources of resistance, which all concur to produce the gross 

 resistance to be overcome. Putting \' for the pressure of the steam 

 on each unit of surface of the piston, and u for the resistance for the 

 same unit, or for the quotient obtained by dividing the total resistance 

 by the number of units of surface, wo bare 



(A) 



as the firat equation of condition ; but since the velocity of the motion 

 must be taken into consideration, when the poircr or force of the 

 engine is to bo determined, we must consider the velocity with whieh 

 this pressure is applied, or, in other words, the rate at which the 

 steam U applied to the cylinder; and it is obvious that when the 

 engine is melring with a constant velocity, the supply to the piston 

 must be exactly that produced in the same time by the evaporation 

 going on in the boiler. If, therefore, 8 expresses the volume of water 

 evaporated in a unit of time and transmitted to the cylinder, and m 

 the ratio of the volume of tteam, formed under the pressure p in the 

 boiler, to the volume of voter which produced it, ros would express 

 the volume of steam generated in each unit of time under the pressure 

 p : by panning into the cylinder this steam assumes the pressure r', and, 

 neglecting the further change produced by the variation in the tem- 

 perature of steam in changing from pressure p to pressure r', the 

 volume of that quantity of steam would be inversely as the pressures 

 by Itariotte's law; consequently the volume ms, when transferred to 



p 

 the cylinder, would become m s -, ; and putting for the velocity of 



the piston and a for its area, or will be the volume of steam expended 

 in each unit of time ; hence we get 



p 

 or = ms p ...... (B) 



eliminating p' between equations (A) and (B), we obtain 



ms ! 



n 



B = - 

 M 



arR 



8 = - 

 mp 



for the velocity, retUlance, and evaporation, when the other quantities 

 are known ; it must be observed, however, that the element neglected 

 in these general deductions, namely, the change produced by the 

 variation in temperature, has an important influence on the result, and 

 must therefore now be taken into account. 



is the general expression for the steam during its action in the engine, 

 It being the volume, and p the pressure, and n and 7 constants, 

 determined by experiments, for different kinds of engines.* 



It can be shown tht the density and relative volume of a vapour, whether 

 or not in conUct with the liquid, may be deduced, if iu pressure and tempera- 

 ture sre known ; and that when in contact with the liquid, the temperature 

 Trie directly with the pressure. In deducing formulae for the steam-engine, 

 it it nece-nary to be able to determine an expression for the relative volume of 

 tic steam in conUct with the water, or the volume of the steam at the maximum 

 of density and pressure at any-proposed temperature. Now thi cannot be done 

 from the existing formula] for analytical reasons, and it become* necessary to 

 adopt some empirical formula, for determining this relative volume of steam at 

 its maximum of density, In terms of its pressure only ; this formula must be 

 tested by iu conformity with experiment. The late M. JJavicr proposed for thi 

 pnrpoM, 



__ 1000 

 ** = O'OO + 0-0000484 .p 



In which ^ U the ratio of the volume of steam to an equal weight of water, and 

 > the preuure ; but thi formula, though true within certain limits of pressure, 

 i not consistent with experiments at pre*ures lower than the atmospheric, and 



e following i. propounded by M. do Pambour, as more correct and comi-rc- 

 henlrc : 



10000 



** ~ 0-1217 



1MM 

 *" = 1-411 + O-dozTp for "en-condensing engines ; 



; being the pressure in pounds on Hie square foot. These formula) in ircncr.il 

 terms, therefore are expressed by 



1 

 * = * 



Let a certain volume of voter, s, be converted into steam of the 

 pressure p, and let M represent the volume of fttam produced, then 



if u' and i' stand for the volume and pressure of steam from the "" 

 volume of water 8, under other conditions, then 



and therefore the ratio of the volumes of steam produced under these 

 different conditions from the same volume of water will be 



M' ,. 



(D) 



that is, the volume* will not be inversely as the pressures simply, 

 :i<-,-,,i-,liii.u t.i M i:i..tte'8 law; but inversely as the pressures augmented 

 by a constant. 



From the above equation we get 



P = 



u'/n 



(E) 



Let r = pressure of the steam in the boiler. 



p' = pressure of the steam in the cylinder ; p'< p generally. 



w = pressure at any instant when acting expansively in the 

 engine. 



I = length of the stroke. 



[ = the length of that part of stroke performed before the com- 

 munication between the boiler and cylinder is cut off. 



A = the length of that portion of the stroke performed when the 

 pressure is become . 



o = area of piston. 



c = clearage, or space in the cylinder at each end left between 

 the piston and the ends of the cylinder, including the 

 part of the steam-pipe between the slide-valve and the 

 cylinder, which space is necessarily filled with steam at 

 each stroke. 



When the piston has performed \ of its course under the I'.\JHMV 

 force of the steam, let d . \ be the differential of this length, then the 

 corresponding force or effect will be trad. \: and at the same instant 

 the space a(t + e) occupied by the steam before the expansion will 

 become a (\ + c). Hence from (E) 



!' + ,- 



and 



- + r' 



'j ^~ c - ~ ,,,l.\. 



Integrating between the limits /' and I, we obtain 



for the value of the total effect produced by ejqmnsi'iu from the 

 moment when the communication with the boiler is cut off, to the end 

 of the stroke. By adding to this therefore the effect v'al', procured 

 previously, we get 



+ P' 



log _ 



(F) 



If in this expression, l' = l, which is equivalent to supposing the 

 gine to be working without expansion, we get r' = B, as it ought 



engine 

 to be. 



s 

 Hemming the equation ^ ., which expresses the volume of steam 



at the pressure p' furnished by the boiler in the unit of time, and 

 a(f + e) being the volume of this steam cxpcixl, -.1 at . arli str-k. ; 

 then if there are K strokes in that time, the expenditure of steam 

 will bo 



and if r he put for the velocity of the piston, we have r = K/, nr 



v 

 K= j : ; hence, by substitution, the expenditure will be 



8 



rq(f-t-c) 

 I 



a I- 'I V' 



ting the expenditure to the volume furnished by the bniler, 

 which, as has been above stated, must be tin; condition when the 



