VELOCn'T OP WATEK. 211 



CHAPTER IL 



HYDRAULICS. 

 VELOCITY OF FALLING WATER. 



Liquids in motion are subject to the same laws as solids 

 in motion. Falling water increases in velocity at the 

 same rate that the motion of falling solids is accelerated, 

 as ah-eady explained under the head of Gravitation. Thus 

 a perpendicular stream of water descends one foot in a 

 quarter of a second, four feet in half a second, nine 

 feet in three-fourths of a second, and sixteen feet in one 

 second. Like falling solids, the velocity at the end of 

 the first quarter will be eight feet per second ; at the end 

 of the second quarter, sixteen feet ; at the end of the third 

 quarter, twenty-four feet ; and at the end of the fourth 

 quarter, thirty-two feet per second. 



Now, if there be an orifice made in the side of a vessel 

 of water, the %vater will spout out with the same swiftness 

 as if it fell perpendicularly from an equal height, were it 

 not retarded a little by friction. For example, if the 

 head of water is one foot above the orifice, the velocity 

 would be at the rate of eight feet per second, but for fric- 

 tion, which reduces it to about five and a half feet. The 

 velocity for any other height of head may be easily found 

 by deducting the same proportionate rate from the veloc- 

 ity of a falling body. Thus, for example, if the head be 

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

 under Gravitation)^ from which, deducting the friction, 

 the real velocity would be about twenty-two feet per 

 second. 



It has been already shown that the velocity of a falling 

 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 ; 



