DISCHARGE OF WATER THROUGH PIPES. 213 



particles will be partly prevented, and the liquid will flow 

 more rapidly. The greatest effect is produced when tlie 

 tube is twice as long as its diameter (fig. 236). If the 

 tube be enlarged at its upper and lower end, similar to the 

 form of the contracted stream of water in fig. 237, the 

 quantity discharged is greatly increased. 



When water flows down an inclined plane, the same law 

 applies as to the motion of a solid body rolling down a 

 plane. The velocity increases as the square of the distance, 

 and is the same as the velocity of a body falling freely 

 downward from a height equal to the perpendicular height 

 of the plane. Unless the stream, however, is very large, 

 its speed is quickly diminished by the friction of its chan- 

 nel,* until this friction becomes as great as the descending 

 force, after which the motion becomes uniform. Hence 

 the reason that large streams, with an equal degree of de- 

 scent, flow so much moVe rapidly than small ones, the 

 gravitating force being so much greater that friction has 

 a less retarding effect upon them. ^ 



In pipes which wholly surround the flowing stream, the 

 friction becomes still greater, and the difficulty is only ob- 

 viated 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 cylinder of water is nearly at 

 rest all around it. The tables in the Appendix exhibit 

 this decreased velocity in tubes of various sizes. 



Lead pipes, for conveying the water of springs under- 

 ground, should commonly be three-fourths of an inch in 

 diameter. Five-eighths will answer where the distance is 

 short and the descent considerable. But with a half- inch 

 pipe, the friction of the sides is so great, compared with 

 the small force of the current, that but little water will 

 flow throusfh it. 



Which increases as the square of the velocity. 



