7*3 



STEAM AND STEAM-ENGINE. 



STEAM AND STEAM-ENGINE. 



794 



motion is uniform. Eliminating r' between () and (0), we. get for 

 the final general equation 



[ 



(H) 



The resistance expressed by K in this formula is the Mai pressure 

 on each unit of surface of the opposite side of the piston, and is 

 composed of three parts. First, of the load, or work to be moved or 

 done, which we will denote by r. Secondly, of the resistance arising 

 from the friction of the engine, which may be expressed by f+Sr; 

 f being the friction when there is no load, and Sr the increment due 

 to the additional friction for each unit of the load r. And, lastly, of 

 the pressure on the opposite surface of the piston, which will be the 

 atmospheric pressure in non-condensing engines, or that of the uncon- 

 densed steam and residue of air in condensing ones; this we shall 

 call j>. All these, r,f+Sr, and f, refer only to each unit of surface of 

 the piston, or 



B - (1 + 8) r + p + f, 



by substituting this value for B in (H), and putting t for 



l l+c 



we obtain 



_ s ft _ 



*'=< n + q[(l+S)r+p+f] 



Now the quantity 



-, it will be seen (C) is the total space occu- 



, 



pied by the steam (in contact with the water), under the pressure K : 

 hence to deduce the velocity r, the volume of steam porresponding to 

 the volume of water s, supposed to be converted into steam under a 

 pressure equal to R, must be calculated ; and this volume being divided 

 by a, the area of the piston must be multiplied by k. 



The equation thus deduced shows the relation between all the 

 quantities, known or sought, that enter into the mechanical theory of 

 the engine in its most general form : it should be observed how- 

 ever that to preserve homogeneity, the dimensions a, I, V, should 

 be expressed in the same unit as the volume s of the water 

 evaporated ; and the pressures p, r, and p referred to the same unit 

 as s. 



When this formula is used for computation, it must be understood 

 that the quantity s expresses the tfective evaporation ; that is, the 

 volume of water which really passes to the cylinder in the form of 

 steam, and which acts on the piston, and does not allow for any loss 

 by leakage or from any peculiarity in the structure of the engine. 



I f the engine be a condensing one, acting expansively, /' must be 



made equal the length at which the steam is cut off ; if expansion be 



nployed, i must be made equal to I, or to the whole length of 



the stroke, in which case the quantity Ic becomes - ,and the expres- 

 sion for the velocity becomes 



_ 



~ a ' n+qn ' l + c' 



The part p of the quantity B must be made equal the pressure of 

 the uncondensed steam, Ac. If the engine be a non-condensing one, 

 then p will be equal the atmospheric pressure. 



Since from (K) we obtain 



it might be supposed that when r = 0, the resistance would be infinite, 

 a paradox which would appear to vitiate the correctness of the formula. 

 But it must be borne in mind that when r= 0,8 = 0; for sis the 

 quantity of steam which passes through the cylinder in each unit of 

 time : and since no quantity of steam, however small, can pass with- 

 out moving the piston, as long as s has any real value, v will have one 

 too : when therefore r = 0, 8 = also ; and then 







or=Q, and not= oo; 



that is, the formula becomes indeterminate, but not the less direct, as 

 will appear by considering the other quantities it involves, and the 

 consequences of putting = 0. 



By supposing the velocity zero, it is, in the first place, evident that 

 no iteam can pose to the cylinder, as has been stated ; consequently 

 there can be no expansion, that is, I -I'. Again, the velocity being 

 zero, the piston at rest becomes equivalent to the fixed sides of the 

 boiler, and the pressure it sustains is equal to that in the boiler. 



The working of an engine may be considered under three condi- 

 tions : first, when it U working with a given pressure of steam, and 

 with any, whatever, load or velocity. Secondly, when it is working 

 with a given pressure, and with that load or velocity compatible with 

 tin- production of a maximum of useful or net force with that 

 ire : this may be termed the relative maximum of utfful effect. 

 An 1 thirdly, when the pressure having been determined to furnish 



the force most consonant with the action of steam in any specific 

 engine, the load is regulated so as to be that most advantageous for 

 that pressure : this last constitutes the absolute maximum of uteful 

 effect for that machine. 



The three fundamental problems for solution in the calculation of 

 steam-engines consist in determining the velocity, the load, and the 

 rate of evaporation in the boiler, since the useful effect, or net avail- 

 able power, is a function of these three quantities ; and this net avail- 

 able power may be expressed in six different ways : 



First, by the number of pounds raised to a unit of height in a unit 

 of time. 



Secondly, by what is termed the " horse-power " of the engine. 



Thirdly, by the weight raised by the consumption of lib. of fuel. 



Fourthly, by the weight raised by the evaporation of a cubic foot of 

 water. 



Fifthly, by the number of pounds of fuel, or of cubic feet of water, 

 for each horse-power. 



Sixthly, by the number of horses-power which is furnished by each 

 pound of fuel, or by each foot of water. 



For the various formulae by which all these problems may be nume- 

 rically solved for different kinds of engines, and for the investigations 

 by which those formulae are deduced, we must refer to more compre- 

 hensive works ; contenting ourselves here with deducing the general 

 equations for the other unknown quantities of evaporation, useful 

 effect, and horse-power, as we have done for velocity. 



From (K) we obtain 



as the expression for the evaporation of which an engine must be cap- 

 able to overcome a given resistance r, with a proposed velocity v, 

 s being the quantity of water which is to be converted into steam and 

 transmitted to the cylinder in each unit of time. 



The useful or net force of the engine generated in the same unit of 

 time is obviously arc ; since v, the velocity, is in fact the space moved 

 through by the piston in that time ; by multiplying therefore both 

 sides of (L) by v we obtain 



si at' r n ~| 



Useful force = arv= ,. , . r -r \ + p + f \ . . (N.) or bv 

 (1-f-o)^ 1-fo Li/ ^ J \ i/ J 



multiplying both sides of (K) by at; we obtain an expression for the 

 same quantity in terms of the load 



Srl . . (N.) 



Useful force = an' = 



It will be noticed that for any proposed engine this force does not 

 depend on the pressure of the steam in the boiler, p not entering into 

 these expressions ; but on the evaporation s effected in the boiler in 

 each unit of time. 



What is termed a " horse-power " is estimated as 33,000 Ibs. raised 

 one foot in a minute [HORSE POWER] : by dividing therefore the equa- 

 tions last obtained by 33,000, we get 



Useful force in horse-power = UsefulJVrce 



33000 



and if during the unit of time N Ibs. of coals are used in the 

 furnace, 



T-r.i. f -., ,. f i Useful force 



* Useful force from 1 Ib. of fuel= 



N 



We must now return to our general description of the engine and of 

 its modifications. 



In 1781 an engineer named Hornblower proposed using the expan- 

 sive principle by means of a double cylinder, but was prevented from 

 carrying out his plan by the comprehensive and jealously guarded 

 patents of Watt and his partners. In 1804, however, Woolf brought 

 this principle of the double-cylinder engine into use. The annexed 

 figure (/</. 11) will explain the mode of its action with an improved 

 slide-valve. 



The steam enters through the passage p above the piston in the 

 smaller cylinder A, at a considerable pressure : while the piston is des- 

 cending under its infiuence, the steam from beneath passes through 

 the tube r above the piston in the large cylinder B, which is impelled 

 downwards by its expansion, the steam which was previously under 

 this piston having passed to the condenser by the passage t. When 

 the stroke is completed, the slide is moved downwards by its rod o. 

 The small plugs or pistons v and w pass below the openings r and 

 t, and the slide below the orifices p and q, and the action is 

 reversed. 



But though possessing considerable advantages, the double-cylinder 

 engine has not become common, unless in the case of large pumping 

 engines, probably owing to the complication of its structure, and the 

 increased effects of radiation from so large a surface, more than com- 

 pensating its merits; and the expansive principle, equally applicable to 

 a single cylinder, is now principally employed in engines of the com- 

 mon construction. 



To reduce the compass and weight of the engine sufficiently to 



