186 MOTION OF WATER IN PIPES. 



to be .004, while for a surface resembling medium sand- 

 paper, it is .009, the units being pounds, feet, and seconds.* 



103. Motion of Water in Pipes. When water is 

 conveyed to any considerable distance in pipes, the friction 

 of the internal surface causes a great resistance to the flow. 

 By the theoretical rule, the velocity of discharge v would be 

 due to the vertical depth h through which the water falls 

 (Art 76) ; but owing to friction, theoretical results are of 

 very little practical value. Besides, the friction is often 

 quite uncertain, the central parts of the stream move more 

 quickly than the parts in immediate contact with the pipe,, 

 and, though the circumstances are different, the velocity 

 over the internal surface is liable to changes, as in the case 

 of solid surfaces. The value of f therefore has to be ob- 

 tained by special experiments, and the results of such 

 experiments do not always agree with each other. It is 

 found, however, that/ lies between the limits .005 and .01, 

 depending partly on the condition of the internal surface, 

 and partly on the diameter and velocity; its value being 

 greater in small pipes than in large ones, and greater at 

 low velocities than at high ones. The mean of these limits, 

 or .0075, is sometimes taken for/, when there is no special 

 cause for increased resistance. 



Let v = the velocity of discharge in feet per second, 

 (I = the diameter of the pipe in feet, I = the length of the 

 pipe in feet, h = the head or fall of water in feet, and W 

 = the weight of water in pounds discharged per second. 

 Let /' be the resistance of friction due to a unit of diam- 

 eter, length, and velocity ; then the resistance in a pipe I 

 feet long and d feet diameter with a unit of velocity will be. 

 from (1) of Art. 102, /'W; but the quantity of water deliv- 



* For large surfaces, especially of considerable length, the friction IB very much 

 diminished. For instance, these valnes of/ were obtained by experimenting on a 

 surface 4 feet long, moving to foot per second : but when the length was 20 feet and 

 upwards, these values of/ were diminished to .0035 and .005 respectively. 



