h = (4[zeta]/d)[{(1 + [zeta]0)d/4[zeta]} + L] v²/2g; (6)
from which it is clear that the head expended at the mouthpiece is
equivalent to that of a length
(1 + [zeta]0)d/4[zeta]
of the pipe. Putting 1 + [zeta]0 = 1.505 and [zeta] = 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 [zeta] for
ordinary iron pipes is
[zeta] = 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 [zeta] on the velocity.
Having regard to the difference of the law of resistance at very low
and at ordinary velocities, they assumed that [zeta] might be
expressed in the form
[zeta] = a + [beta]/v.
The following are the best numerical values obtained for [zeta] so
expressed:--
+----------------------------------+----------+----------+
| | [alpha] | [beta] |
+----------------------------------+----------+----------+
| 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 |
+----------------------------------+----------+----------+