192 HYDRODYNAMICS. 



In pipes which wholly surround the flowing stream, 

 the friction becomes still greater, and the difficulty is 

 only obviated by making the pipe of larger dimensions 

 than would otherwise be necessary, so as to allow a free 

 passage of a sufficient quantity of water through, the 

 centre of the tube, while a ring or hollow cyUnder of 

 water is nearly at rest all around it. The tables in 

 the Appendix exhibit this decreased velocity in tubes 

 of various sizes. 



SECTION III. 

 VELOCITY OF WATER IN DITCHES. 



It is often of great practical utility to know what 

 amount of water may be carried off in draining or sup- 

 plied in irrigation by channels of any given size and 

 descent. The following rule will apply to all cases, 

 from the plow-furrow to the mill-race, or even to the 

 large river, and may be used by any boy who under- 

 stands common arithmetic, and which is illustrated 

 and made plain by the example that follows the rule. 



To ascertain the mean [or average) velocity of wa- 

 ter in a straight channel of equal size throughout : 



Let/=the fall in two miles in inches; 



Let d—WxQ hydraulic mean depth; 



Let v = the velocity in inches per second; 

 then the rule is thus expressed, v — 0.^1\^fd, or, in 

 plain words, the velocity is equal to the hydraulic mean 

 depth multiplied by the fall, with the square root of 

 this product extracted, and then multiplied by 0.91. 



The " hydraulic mean depth'''' is found by dividing 

 the. cross-section of the channel by the perimeter or 



