HEIGHT WHICH WATER RISES IN ONE STROKE. 271 



Therefore in the suction pump the tension of the 

 rod is equal to the weight of the column of water 

 wliose base is the area of the piston and whose height 

 is the height of the water in the pump above the level 

 of the well. 



If A be on a level with the spout, all the water lifted 

 will be discharged, and as the piston descends, the tension 

 of the rod will be 



145. Height Through which the Water Rises in 

 One Piston Stroke Let P and Q (Fig. 73) be the sur- 

 faces of the water at the beginning and end of an upward 

 stroke of the piston from 13 to A, and let h as usual be the 

 height of the water barometer. The air which occupied the 

 space BP at the beginning of the stroke occupies at the end 

 of it the space AQ ; and the pressures are respectively 



gp(h-PG), gp(h-QG). 

 Hence (Art. 48) 



li PC : h QC : : vol. AQ : vol. BP. 



If R and r are the radii of the cylinders AB and BC, we 

 have 



vol. AQ = Tr^AB + irr* (BC - QC), 



vol. BP = nr 2 (BC PC), 



^-^PC _ JffAB -f r 2 (BC QG) 

 IT^- QC ~ r*~(BC - PC)"" 



which determines QC for any given value of PC. 



COR. If the stroke of the piston be less than AB, as for 

 instance AH, then HC must be less than h. Also, a limit 

 exists with regard to H, which may be shown as follows : 



If P be the surface of the water when the piston M is at 

 A, then, as the piston descends, the valve V will close, but 

 thy valve V will not be opened until the pressure of the air 



