The computations involved in the design of a siphon are illustrated in the following example, in which it is desired to construct a siphon to pass under the railway cut shown in Fig. 40. The first step is to determine the limiting diameter and slope of the smallest pipe in the siphon. One-sixth of the capacity of the 6–foot approach sewer or 19 cubic feet per second will be assumed as the minimum flow. The diameter of the pipe necessary to carry 19 cubic feet per second at a velocity of 2 feet per second is 42 inches. The hydraulic gradient should have a slope of 0.0005 if the material used has a roughness coefficient of .015. This is the minimum permissible slope of the siphon. The selection of a steeper slope will necessitate the laying of the sewer at a greater depth, and will permit the use of smaller pipes for the siphon. The selection of the exact slope must then be based on judgment with the minimum limitation above placed. The slope will be arbitrarily selected as 0.001, the same as that of the approach sewer. The diameter of the dry weather pipe will therefore be 36 inches, with a capacity of 18 second-feet, which is approximately the assumed dry weather flow. The velocity of flow will be 2.5 feet per second. The length of flow along the siphon is 150 feet.
Fig. 40.—Diagram for the Design of an Inverted Siphon.
The next step should be the determination of the elevation at the lower end of the 36–inch pipe. This is done by multiplying the assumed grade by the equivalent length of straight pipe, and subtracting the product from the elevation at the upper end. The length of straight pipe which will give the same loss of head as the siphon is called the equivalent pipe. It is determined as follows:
First, determine the head loss at entrance. This will vary between nothing and one velocity head, dependent on the arrangement at the entrance.[[41]] The length of straight pipe which will give this same loss can be computed from the expression l = h
S, using for S the assumed slope of the hydraulic gradient.
Second, determine the head loss due to the bends, This is determined from the expression
h = fl
d V2
2g
in which h = the head loss in the bend; l = the length of the bend; d = the diameter of the pipe; v = the average velocity of flow; g = the acceleration due to gravity; 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]]
| R d | 24 | 16 | 10 | 6 | 4 | 2.4 |
| f | 0.036 | 0.037 | 0.047 | 0.060 | 0.062 | 0.072 |