which gives the length of the equivalent uniform main which would have the same total loss of head for any given discharge.
| Fig. 87. |
§ 83. Other Losses of Head in Pipes.—Most of the losses of head in pipes, other than that due to surface friction against the pipe, are due to abrupt changes in the velocity of the stream producing eddies. The kinetic energy of these is deducted from the general energy of translation, and practically wasted.
Sudden Enlargement of Section.—Suppose a pipe enlarges in section from an area ω0 to an area ω1 (fig. 87); then
v1/v0 = ω0/ω1;
or, if the section is circular,
v1/v0 = (d0/d1)2.
The head lost at the abrupt change of velocity has already been shown to be the head due to the relative velocity of the two parts of the stream. Hence head lost
ɧe = (v0 − v1)2/2g = (ω1/ω0 − 1)2 v12/2g = {(d1/d0)2 − 1}2 v12/2g
or