WORK OF STEAM IN THE EXPANSIVE ENGINE. 269 



138. Work of Steam in the Expansive Engine. 



Let K be the area of the piston in square feet, h j the length 

 of the stroke, including the clearance,* h the point of the 

 cylinder at which the steam is cut off, Q the number of 

 cubic feet of water evaporated per minute, P and P l the 

 pressures of the steam at the beginning and end of the 

 stroke respectively, N the number of strokes performed by 

 the piston per minute, F the volume of steam from a cubic 

 foot of water at P pressure, and F = / (P), as before. 

 Then, for the volume of steam discharged per minute at P 

 pressure, we have 



(1) 



Similarly, Qf(Pi) = 



and /(P t ) = f(P). (2) 



The work performed upon the piston before the steam is 

 cut off is NKP (h c) ; adding this to (2) of Art. 136, we 

 have 



UQ= Q pdf(P) + NKP(h - c) 

 /p, 



= Q [ffidfW + h -=^ Pf(P}] (3) 



[from (1)], 



which is the total work performed by the steam per 

 minute. 



COR. Let L be the useful load in Ibs. upon each square 

 foot of the piston, F the friction in Ibs. per square foot of 

 the piston, arising from the motion of the unloaded piston, 

 /the coefficient of friction arising from the useful load, and 



* The clearance is the space in the cylinder lying beneath the piston, at the low- 

 est point of its stroke. 



