24 



PNEUMATICS. 



accumulates in the cylinder above the 

 valve V, and its height increases until it 

 reaches the spout S, where it is dis- 

 charged. 



To find the force necessary to raise 

 the piston, we are to consider that the 

 water in the reservoir balances the wa- 

 ter in the cylinder from the bottom B to 

 the level L. The piston, therefore, has 

 only to lift the column from L, to the 

 level of the water in the cylinder. After 

 a few strokes, this level rises to S, and 

 continues permanently at. that level af- 

 tervvards. If, then, the number of feet 

 in S L be called h, and half the diame- 

 ter of the section of the piston, expressed 

 in parts of a foot, be called r, the num- 

 ber of cubic feet of water w r hich presses 

 on the piston, will be expressed by 

 h x r x r x 3.14. This, multiplied by 

 62^, will express the pressure on the 

 piston in pounds ; and if to this the 

 weight of the piston and rod, together 

 with the effects of friction, be added, 

 the whole force necessary to lift the 

 piston will be obtained. 



The quantity of water discharged is 

 found in the same manner as for the 

 suction-pump. 



III. The Forcing-Pump. 



(45.) A cylinder ABC (Jig. 25.) is 

 placed with its lower 

 end C in the reservoir. 

 It has a fixed valve at 

 V opening upward, and 

 a solid piston without 

 a valve playing air- 

 tight in the upper bar- 

 rel A B. It is connected 

 with another ban-el 

 D E by a valve V 

 opening upwards and 

 outwards. The tube 

 D E is brought to 

 whatever height it may 

 be necessary to elevate 

 the water. 



Let us suppose that 

 the solid piston P is in 

 contact with the valve 

 V, and that the water 

 in the lower barrel is 

 at the same level C 

 with the water in the 

 reservoir. Upon rais- ^! 

 ing the piston the air : -~>r -~:ri^--- 

 in B C will be rarefied, and the water 

 will ascend in B C exactly as in the 

 suction pump. Upon again depressing 

 the piston, the air in P V will be com- 

 pressed, and it will force open the valve 



V, and escape through it. The process, 

 therefore, until water is raised through 

 V into the upper barrel, is precisely the 

 same as for the suction-pump, the valve 

 V' taking the place of the piston-valve 

 in that machine. 



Now, let us suppose that water has 

 been elevated through V, and that the 

 space P V is filled with it. Uoon de- 

 pressing the piston, this water not being 

 permitted to return through V, is forced 

 through V, and ascends in the tube 

 D E. By continuing the process, w 7 ater 

 will accumulate in the tube D E, until it 

 acquires the necessary elevation and is 

 discharged. 



The force requisite to elevate the pis- 

 ton in this pump until the water reaches 

 it, is computed in exactly the same man- 

 ner as for the suction-pump, and, exclu- 

 sive of the weight of the piston and its 

 rods and the etfects of friction, it is equal 

 to the weight of a column of water 

 whose base is the section of the piston, 

 and whose height is the distance of the 

 level of the water in the barrel A C 

 above the level in the reservoir. It is 

 evident also from what has been said on 

 the suction -pump, that the valve V 

 should be less than thirty-four feet 

 above the level of the water in the re- 

 servoir. If the P express in pounds av. 

 the weight of the piston and its rods, r 

 be half the diameter of a section of the 

 piston expressed in parts of a foot, and 

 h be the number of feet in A C, the 

 force in pounds necessary to lift the 

 piston will be 



'Let us now examine the force neces- 

 sary to depress the piston. Let the level 

 of the w r ater in E D be M. The atmos- 

 pheric pressure on M will be balanced 

 by the same pressure on the piston by 

 the power of transmitting pressure pe- 

 culiar to fluids. This force may, there- 

 fore, be neglected; also thePV will 

 balance the partND of the column MD, 

 which is equal to it in height, and that 

 whether their sections be equal or not. 

 (See Hydrostatics.) Hence it appears, 

 that the pressure exerted by the water 

 in P V on the lower surface of the pis- 

 ton is equal to the weight of a column 

 of water whose base is equal to the sec- 

 tion of the piston, and whose height is 

 M N. This, therefore, is the force to be 

 overcome in the descent of the pistons 

 and the weight P of the piston and it, 

 rods assist in overcoming it. Let h 1 be 

 the number of feet in M N, and the me- 

 chanical force necessary to be applied 



