ON THE THEOUY OF HVDUAULICS. 285 



We may understand the action of the forces immediately concerned in this 

 experiment, by attending to the mutual effects of the water and of the at- 

 mosphere. The water entering the orifice must immediately acquire a velo- 

 city etjual to that of the whole water in the pipe, otherwise there would be 

 a vacuum in the upper part of the \npc, which the pressure of the atmo- 

 sphere will not permit ; and this pressure, considered as a hydrostatic force, 

 is equal to that which would be derived in any other way from a column of 

 the same height with the pipe, since the weight of the water in the pipe is 

 wholly employed in diminishing the counterprcssure of the atmosphere below, 

 not only in. the beginning, when it is at rest, but also while it is in motion ; 

 for that motion being uniform throughout its descent, the power of gravi- 

 tation is expended in producing pressure only; so that the pressure of the 

 atmosphere on the water in the funnel becomes completely analogous to the 

 pressure of a reservoir of water, of the same height with the pipe. The cir- 

 cumstance, which causes the appearance of paradox in this experiment, exists 

 also in the simplest case of the discharge of water; for it may be shown, that 

 the portion of accelerating force actually employed in generating the velocity 

 with which a stream is discharged through a small orifice, is twice as great 

 as the pressure of the fluid on a part of the vessel equal in extent to the ori- 

 fice; and in the same manner the quantity of force exerted by the atmosphere 

 on the water in the funnel, as well as that with which the descending fluid 

 impels the air below, is equal to twice the weight of the quantity existing 

 at any time in the pipe. 



There is, however, a limit, which the mean velocity in such a pipe can 

 never exceed, and which is derived from the magnitude of the pressure of the 

 atmosphere. For the water cannot enter the pipe with a greater velocity 

 than that with which it would enter an exhausted pipe, and which is produced 

 by the whole pressure of the atmosphere ; and this pressure being equivalent to 

 that of a column of water 34 feet high, the velocity derived from it is about 

 47 feet in a second: so that if the vertical pipe were more than 34 feet long, 

 there would be a vacuum in a part of it near the funnel. 



Wherever a pipe of considerable length descends from a funnel, if tlie sup- 

 ply of the fluid be scanty, and especially if it approach the orifice obliquely, 

 the pressure of the atmosphere, and the centrifugal force of the particles 



