PIPE FLOW 261 



AUT. 73. FLOW IN LONG PIPES. 



A consideration of the preceding example will show that in a long pipe 

 the losses at bends, at entrance and exit, and at changes of section, are 

 usually so small in comparison with the friction losses as to be negligible, 

 so that for a long pipe connecting two reservoirs, the whole resistance 

 may be taken to be given by 



ifi+^fiM + '!<* + !<*+ | (eethead 



2 g m 2 g ( mi m 2 m 3 



vi, v 2 , etc., being the velocities, and wi 1} w 2 , etc., the hydraulic mean 

 depths, in the lengths h, / 2 , etc., of the pipe. 



In short pipes the losses due to velocity changes become of greater 

 importance as the length of pipe diminishes, and for pipes of lengths less 

 than 100 diamsters will, in general, be important. 



ART. 74. TIME OF DISCHARGE THROUGH AN UNIFORM PIPE LINE. 



If two reservoirs of area AI and A 2 are connected by a single pipe of 

 diameter d and length I, and if v be the velocity in the pipe when h is 

 the difference in surface level in the two reservoirs, we have 



where K = coefficient of loss at entrance and exit. 

 If the pipe is long this may be written 



v 2 ( 4 f I I 

 h = - >L L without sensible error. 



In this case v = ^ . . , feet per second. 

 Also -- relative velocity of surfaces AI and 



4 AI A* 



/a _dh_ AH *_*? f _i , 



dt V 4JT' 4 ' l^ + ^ 

 The time ( 2 ti = t) necessary to reduce the difference in level from 

 HI to 7/2 is then got by integrating this expression between the given 

 limits 



^ o v 4 



( i r 

 'tart^i 



