COEFFICIENT OF FRICTION FOR PIPES. 191 



pipe from the reservoir be placed sufficiently far below the water sur- 

 face of the reservoir to allow the water to flow from the reservoir into 

 the pipe, as fast as it afterwards flows along or through the length of 

 the pipe to the end of discharge. For there must be at least sufficient 

 head to overcome the resistance at the entrance to the pipe, and to 

 allow the water in the reservoir to flow out of an opening freely into 

 the air with that velocity which previous calculation shows it will 

 have in the pipe. The remainder of the head, which is employed in 

 overcoming the resistance of friction, and perhaps other resistances 

 which will be considered hereafter, may be obtained by having the 

 pipe incline downwards. 



Since the friction in pipes of the same diameter increases as their 

 lengths, when the water first enters the pipe it is opposed by but little 

 friction, and has great velocity ; but this velocity gradually diminishes 

 as the advancing water meets the friction along increased lengths of 

 the pipe, and finally becomes least when the water fills the whole 

 length and begins to flow from the end of discharge. The velocity 

 then becomes uniform along the pipe, and will continue to be so, if the 

 velocity head and head due to the resistance at the entrance to the 

 pipe are together sufficient to allow the water of the reservoir to enter 

 the pipe with this same velocity. 



105. Coefficient of Friction for Pipes Discharg- 

 ing Water. From the average of a great many experi- 

 ments, the value of /for ordinary pipes Is 



/ = 0.030268. (1) 



But practical experience shows that no single value can 

 be taken applicable to very different cases. The coefficient 

 of friction, like the coefficient of efflux, is not perfectly con- 

 stant. It is greater for low velocities than for high ones, 

 L e., the resistance of friction of the water in pipes does not 

 increase exactly as the square of the velocity. Prony and 

 Eytelwein assumed that the loss of head by the resistance 

 of friction increases with the first power of the velocity and 

 with its square ; and hence they established for this loss of 

 head the formula 



A, = (, + ,) , (2) 



