212 



MACHINEEY IX CONNECTION WITH WATEK. 



four times as great in four seconds, and so on. But the 

 distance fallen through increases as the square of the time ; 

 that is, it is four times as great in two seconds, nine times 

 as great in three seconds, sixteen times as great in four 

 seconds, etc. Thus we see that, in order to produce a 

 twofold velocity, a fourfold height is necessary, etc. So 

 also in the escape of water under a head : to double the 

 velocity of the stream, the head must be four times as 

 high ; to triple it, the head must be nine times as high, etc. 



DISCHARGE OF WATER THROUGH ORIFICES AND PIPES. 



Fig. 235. 



Fig. 236. 



Fig. 237. 



The discharge of "wuter from a vessel is greatly influ- 

 enced by the nature of the orifice through which it flows. 



If, for example, a 

 vessel or cistern 

 have a thin bottom 

 of tin, with a 

 smooth, circular 

 hole, we might natu- 

 rally suppose that 

 the discharge would 

 be as easy as it 

 could be made, and 

 that water would 

 pass as rapidly 

 through it as 

 through any orifice 

 of an equal size. But this is not the fact. 

 As the particles approach this orifice, their 

 motion throws them across, and they 

 partly obstruct the opening ; it will be 

 seen that they converge toward a point 

 just under the orifice, where the stream will be consider- 

 ably contracted (Fig. 235). If a short tube be inserted 

 into the hole (the head being the same), this crossing of 



