Up to five siphon pipes. For flow under an obstruction, such as a river.
Inverted Siphon calculation is mobile-device-friendly as of February 11, 2015
Register to enable "Calculate" button.
Units: cm=centimeter, cfs=cubic feet per second, ft=feet, gpm=US gallons per minute, gph=US gallons per hour, gpd=US gallons per day, m=meters, MGD=Millions of US gallons per day, s=second
Inverted siphons (also called depressed sewers) allow stormwater or wastewater sewers to pass under obstructions such as rivers. Our inverted siphon calculation allows up to five parallel siphons to go under the river. Unlike the main sewer pipe, the siphon pipes flow under pressure and must have flow velocities greater than 3 ft/s (0.9 m/s) to keep material suspended. Therefore, several siphons having smaller diameters than the main sewer may be required. The calculation computes siphon diameters (or siphon flows), velocities, inlet chamber wall heights, and siphon invert elevations.
Plan view of inlet chamber (3 siphons):
Section A-A (exploded scale):
For ease of fabrication, all siphon inverts can be located at the elevation of the lowest siphon invert.
Introduction to Inverted Siphons (Depressed Sewers)
Unlike the main sewer pipe, the siphon pipe(s) flow under pressure. Special care must be taken in inverted siphon design since losses are greater for pressurized flow, and the velocity in each siphon pipe must be at least 3 ft/s (0.9 m/s) for sewage or 4 ft/s (1.2 m/s) for storm water (Metcalf and Eddy, 1981). Therefore, even if there is only one main sewer pipe, several siphons may be required. If minor losses due to bends or elbows in the siphon are significant compared to the siphon length, include the equivalent length of the elbows. Increase the siphon length (Ls) so that Ls is the physical length of a siphon plus the equivalent length of minor losses due to elbows in siphon.
Equations and Methodology for Inverted Siphon (Depressed Sewer) Calculation
Compute the maximum flow in the main sewer pipe using Manning's equation for full pipe flow:
Compute the diameter of each siphon, Di, or the flow through each siphon, Qi, using Manning's equation for full pipe flow through each siphon:
Compute the wall heights, yj (relative to main invert), in the inlet box. The walls separate the siphons from each other. The wall heights are the same height as the water depths, yj, in the main pipe corresponding to the discharge through the siphons. Here, Qj=1 is the discharge through siphon 1, Qj=2 is the discharge through siphons 1 and 2, and so on. Manning's equation for a partially full main pipe is used, but is solved backwards (numerically) in order to compute yj. We allow up to five siphons (four walls).
Compute the siphon invert elevations in the inlet chamber. According to Metcalf and Eddy (1981), there is no loss in the inlet box for flow going from the main culvert to the first siphon since the flow travels in a straight path. However, for siphons 2 through n the flow must turn 90o to go over the chamber wall (a head loss of 1.5 velocity heads) and has an additional head loss of one velocity head as the flow enters siphon i. Therefore, for i=2 to n siphons and j=2 to n-1 walls:
where Ei is relative to the invert of the main pipe. Note that for the first siphon, Hi=0, and for the last siphon yj is replaced by Dm. Often, all siphon inverts are located at the same elevation (the elevation of the lowest siphon) for ease of construction.
Variables for Inverted Siphon (Depressed Sewer) Software
* Corrugated metal pipe n value can vary significantly with pipe diameter and type of corrugations (values can range from 0.012 to 0.033) - AISI (1980).
Error Messages and Validity for Inverted Siphon (Depressed Sewer) Calculation
"Need 1e-9<Main n<1e9", "Need 1e-9<Siphon n<1e9". The Mannings n values for the main culvert and siphons must be between these limits.
"Need 1e-9<D1<1e9 m", "Need 1e-9<D2<1e9 m", "Need 1e-9<D3<1e9 m", "Need 1e-9<D4<1e9 m", "Need 1e-9<D5<1e9 m". If siphon diameters are input, they must be between these limits.
"Need 1e-9<Q1<1e9 m3/s", "Need 1e-9<Q2<1e9 m3/s", "Need 1e-9<Q3<1e9 m3/s", "Need 1e-9<Q4<1e9 m3/s". If siphon flows are input, the flows must be between these limits.
Run-time errors. The following messages may be
generated after performing some calculations:
"Need siphon Q>0". If diameters are being computed, the flowrate through the last siphon is automatically computed such that the sum of the flow through all siphons is equal to the discharge through the main culvert. If the siphon flows input by the user exceed the discharge in the main culvert, then the flow in the last siphon will be negative, which will generate the error message. You should reduce the flows in the siphons so that there is positive flow in the last siphon. Or, you could reduce the number of culverts.
"Siphons under-designed". Shown only if siphon flows are being computed and Qs/Qm<0.95. You need to increase the siphon diameters. This message will not be generated if diameters are being computed - because diameters are computed so that the total flow through the siphons is exactly equal to the discharge through the main culvert.
"Siphons over-designed". Shown only if siphon flows are being computed and Qs/Qm>1.05. Since wall heights cannot be computed for flows grossly exceeding that of the main culvert, the calculation stops. You need to decrease the siphon diameters. This message will not be generated if diameters are being computed - because diameters are computed so that the total flow through the siphons is exactly equal to the discharge through the main culvert.
References and Bibliography for Inverted Siphons (Depressed Sewers)
a Barfuss, Steven and J. Paul Tullis. Friction factor test on high density polyethylene pipe. Hydraulics Report No. 208. Utah Water Research Laboratory, Utah State University. Logan, Utah. 1988.
c Barfuss, Steven and J. Paul Tullis. Friction factor test on high density polyethylene pipe. Hydraulics Report No. 208. Utah Water Research Laboratory, Utah State University. Logan, Utah. 1994.
e Bishop, R.R. and R.W. Jeppson. Hydraulic characteristics of PVC sewer pipe in sanitary sewers. Utah State University. Logan, Utah. September 1975.
Chow, V. T. 1959. Open-Channel Hydraulics. McGraw-Hill, Inc. (the classic text)
Hammer, M. J. and M. J. Hammer, Jr. 1996. Water and Wastewater Technology. Prentice Hall, 3ed.
Metcalf and Eddy, Inc. 1981. G. Tchobanoglous, editor. Wastewater Engineering: Collection and Pumping of Wastewater. McGraw-Hill, Inc. (Note that there are some errors in the invert elevations computed on p. 175.)
d Neale, L.C. and R.E. Price. Flow characteristics of PVC sewer pipe. Journal of the Sanitary Engineering Division, Div. Proc 90SA3, ASCE. pp. 109-129. 1964.
b Tullis, J. Paul, R.K. Watkins, and S. L. Barfuss. Innovative new drainage pipe. Proceedings of the International Conference on Pipeline Design and Installation, ASCE. March 25-27, 1990.
Viessman, W. and M. J. Hammer. 1998. Water Supply and Pollution Control. Addison-Wesley, 6ed.
© 2000-2015 LMNO Engineering, Research, and
Software, Ltd. All rights reserved.
LMNO Engineering home page (more calculations)