(1 + ζ0) d/4ζ
of the pipe. Putting 1 + ζ0 = 1.505 and ζ = 0.01, the length of pipe equivalent to the mouthpiece is 37.6d nearly. This may be added to the actual length of the pipe to allow for mouthpiece resistance in approximate calculations.
§ 75. Coefficient of Friction for Pipes discharging Water.—From the average of a large number of experiments, the value of ζ for ordinary iron pipes is
ζ = 0.007567.
(7)
But practical experience shows that no single value can be taken applicable to very different cases. The earlier hydraulicians occupied themselves chiefly with the dependence of ζ on the velocity. Having regard to the difference of the law of resistance at very low and at ordinary velocities, they assumed that ζ might be expressed in the form
ζ = a + β/v.
The following are the best numerical values obtained for ζ so expressed:—
| α | β | |
| R. de Prony (from 51 experiments) | 0.006836 | 0.001116 |
| J. F. d’Aubuisson de Voisins | 0.00673 | 0.001211 |
| J. A. Eytelwein | 0.005493 | 0.00143 |
Weisbach proposed the formula