OK THE THEORY OF HYDRAULICS. 279 



' - Tlus velocity may be found, as we have already seen, by multiplying the square 

 root of the height of the reservoir, expressed in feet, by 8, or more correctly, by 

 8^; thus, if the height be 4 feet, the velocity will be sixteen feet in a second ; 

 if the height be 9 feet, the velocity will be 24, the squares of 2 and 3 being 

 4 and 9; and if the height were 14 feet, the velocity would be 30 feet in a 

 second, and a circular orifice an inch in diameter would discharge exactlv an 

 ale gallon in a second. In the same manner, the pressure of the atmosphere 

 being equal to that which would be producetl by a column of air of uniform 

 density 28000 feet high, tlie air would rush into a vacuum with a velocity 

 of more than 1300 feet in a second. 



The velocity is also equal, whatever may be the direction of the stream ; 

 for since the pressure of fluids acts equally in all directions, at equal depths, 

 the cause being the same, the effect must also be the same. And if the mo- 

 tion be occasioned by a pressure derived from a force of any other kind, the 

 effect may be found by calculating the height of a column of the fluid, which 

 would be capable of producing an equal pressure. When also the force 

 arises from the difference of two pressures, the velocity may be determined 

 in a similar manner. Thus, the pressure of a column of water, 1 foot in heio-ht, 

 would force the air through a small orifice, with a velocity of 230 feet in a 

 second, corresponding to the height of 830 feet ; a column of mercury 1 inch 

 high, would produce the same effect as a reservoir of water more than 

 thirteen times as high, and the force of the air confined in a closed bottle 

 under the receiver of the air pump, will cause a jet to rise to the same height 

 as a column of mercury which measures the difference of the elasticities of the 

 air in the bottle and in the receiver. 



But these calculations are only confirmed by experiment in cases when 

 the ajutage through which the fluid runs is particularly constructed ; that 

 is, when it is formed by a short tube, of which the sides are so curved that 

 the particles of the fluid may glide along them for some distance, and escape in 

 a direction parallel to the axis of the stream, A short cylindrical pipe is found 

 to answer this purpose in some measure; but the end may be more completely 

 obtained by a tube nearly conical, but with its sides a little convex inwards, 

 so as to imitate the shape which a stream or vein of water spontaneously as- 

 sumes when it runs through an orifice in a thin plate : for in such cases the 



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