190 HYDRODYNAMICS. 



falling body. Thus, for example, if the head he six- 

 teen feet, the speed would be thirty-two feet (as shown 

 under Gravitation), from which, deducting the fric- 

 tion, the real velocity would be about twenty-two feet 

 per second. 



It has been already shown that the velocity of a fall- 

 ing body increases at the same rate as the increase in 

 the time of falling ; for instance, the speed is twice as 

 great in two seconds as in one ; three times as great in 

 three seconds ; 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, &c. Thus we 

 see that, in order to produce a two-fold velocity, a four- 

 fold height is necessary, &c. 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, &c. 



DISCHARGE OF AVATER THROUGH ORIFICES AND PIPES. 



The discharge of water from a vessel is greatly in- 

 fluenced 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 

 naturally suppose that the discharge would be as easy 

 as it could be made, and that water would pass as rap- 

 idly 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 



