170 OF THE POWER OF STEAM, [SECT. iv. 



351. For well water the same mode of calculation gives about ^ for 

 the relation between the capacity of the air pump and the cylinder. The usual 

 proportion in Boulton and Watt's practice is i ; and as I have made no 

 allowance for leakage nor imperfect action of valves, this proportion appears to be 

 nearly correct for the case considered. l 



352. There is one thing very evident in this operation : it is that an air 

 pump half the size would be as effective as the present construction, if we could 

 condense in the pump itself; and I see no difficulty in doing so, and propose to 

 show its application to a simple atmospheric engine. (See art. 400.) The ad- 

 vantage, however, will be better understood if we show the power an air pump 

 requires to work it. 



POWER REQUIRED FOR WORKING AN AlR PuMP OF A STEAM ENGINE. 



353. Let v = the velocity in feet per second ; p' = the force of the steam or 

 vapour in Ibs. per circular inch ; r = the friction of the piston and piston rod, 

 and resistance of the valves ; a = the diameter of the pump in inches ; and 



a = the area of the valves. 



n 



The head capable of producing the velocity n v through the valves, (see art. 

 136.) is n v = 6-5 Jh ; and, 



42 



In a mixture of air and steam, at the mean force in such a pump, 2100 feet 

 in height is equivalent to a pressure of 1 Ib. per circular inch ; hence, 



n 1 v* n a 



2100 x 42 88200 



the pressure in Ibs. 



Put / = the length of the stroke ; and the resistance to the descent of the piston 

 will be, 



*'/ /tt^ X 



88200 \ * 88200/ 



The resistance to the ascent of the piston will be found by considering that the 

 air and vapour is compressed till its elastic force becomes of such an excess above 

 the atmospheric pressure, that it escapes through the valve at the velocity cor- 

 responding to the motion of the piston. The friction of the piston and weight of 

 the water is to be added ; and the force of the vapour in its expanded state may 



1 In some instances air pumps for double engines have been made about two-thirds of the 

 diameter of the steam cylinder, and half the stroke : such pumps are undoubtedly too large. 



