_f_ = a factor dependent on the radius (_R_) of the bend and _d_.
The relation between _f_, _R_, and _d_, for 90° bends is shown as follows:[42]
After the head loss has been determined, the equivalent length of straight pipe is determined as above.
Third. The equivalent length of pipe will be the sum of the actual length of pipe and the equivalent lengths as found above.
In the problem in hand the head lost at the entrance will be assumed as one-third of a velocity head, or 0.0324 foot. With the assumed slope of 0.001 this is equivalent to 32 feet of pipe. The radius of the bend is about 20 feet and the length for a 45° central angle is about 16 feet. The head loss for this angle will probably be a little more than one-half that for a 90° angle. The expression will therefore be taken as about 0.2(_V_^2)⁄(2_g_) and for two bends is equivalent to about 40 feet of pipe. The equivalent length of pipe is therefore 150 + 32 + 40 = 222 feet. The elevation at the lower end should therefore be: the elevation at the upper end, 92.07 − 222 × .001 = 91.85.
The diameters of the remaining pipes in the siphon are determined so that the sewage in the approach sewer is backed up as little as is consistent with good judgment before each pipe comes into action. This is done satisfactorily by a method of cut and try. Let it be assumed that the siphon will be composed of three pipes: the dry weather pipe taking 18 second-feet, the second pipe taking 28 second-feet, and the third pipe taking the remaining 70 second-feet. The diameters of the two larger pipes on the assumed slope of 0.001 will therefore be 42 inches and 60 inches respectively. Other combinations might be used which would be equally satisfactory. There are many methods by which the sewage can be diverted into the different channels of the siphon. For example, the openings into the different pipes may be placed at the same elevation, and the sewage allowed to enter them in turn through automatically or hand-controlled gates, or in another method of control the openings may be placed at such elevations that when the capacity of one pipe has been exceeded the sewage will flow into the next largest pipe as shown in Fig. 40. The outlets from the different pipes are ordinarily placed at the same elevation, thus leaving each pipe standing full of sewage. Stop planks should be provided at the outlet in order that the pipes may be pumped out for cleaning. The objection to this arrangement is that the larger pipes may operate at a velocity less than 2 feet per second, and they will be standing full of sewage which might become septic. However, as they will take nothing but the storm flow near the top of the sewer no difficulty should be encountered from sedimentation in them, and all are large enough for a man to enter for inspection or cleaning.