2002
December 4, 2002.  Water flowing from a tank
November 2, 2002.  Natural Gas Flow
September 21, 2002.  Pressurized Non-Circular Ducts/Conduits
August 23, 2002.  New Calculation - Bypass Loop
July 15, 2002.  Flow in Bypass Loop
June 10, 2002.  New Calculation - Small Bore Orifice for Gas Flow
May 29, 2002.  Open channel flow measurement - what device to use
May 7, 2002.  Backwater Calculator now on-line
April 16, 2002.  Gradually Varied Flow Calculations
March 27, 2002.  Gradually Varied Flow and Rapidly Varied Flow
March 4, 2002.  New small diameter orifice calculation. Modeling closed piping loops
February 12, 2002.  Small Diameter Orifice Flowmeter
January 15, 2002.  New Calculation - Inverted Siphon (Depressed Sewer)

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Water flowing from a tank

One of our users inquired about how to increase the discharge from a tank by pressurizing the head space above the water in the tank. He was using the Discharge from a Tank calculation ( http://www.LMNOeng.com/TankDischarge.htm ).

Since the calculation assumes the top of the tank is open to the atmosphere, how do you account for the additional tank pressure? Let's look at the free discharging orifice (as opposed to the submerged orifice). H is the distance shown in the figure on the calculation page. The equation to use is H=h1+h1. Let h1 be the depth of water above the orifice. Let h2=P/S where P is the head pressure (gage pressure; not absolute pressure) in the tank and S is the weight density of the water in the tank (also known as specific weight). If P=0, then H=h1 as expected for a tank open to the atmosphere.

Let's look at an example. If h1=3 ft. and P=5 psig (pounds per square inch, gage pressure), then h2 = (5 lb/in2)(144 in2/ft2)/(62.3 lb/ft3)=11.6 ft. 62.3 is S for water at 70 F. If your water has a different temperature, use S for your temperature (but it won't be very different). Therefore, H=3 + 11.6 = 14.6 ft. You can also use the calculation backwards: Enter the discharge that you need and the calculation will compute H. Then, determine P based on your h1.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com   LMNO@LMNOeng.com

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com .

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Natural Gas Flow

Recently, LMNO Engineering has been consulting for the natural gas industry. The LMNO Engineering website currently doesn't have any calculations specifically for natural gas. We have calculations using the Darcy-Weisbach method which can analyze gases so long as gas compressibility is minimal for the pipe run.

Crane TP-410 provides several equations specifically developed for natural gas flow. They are the Spitzglass, Weymouth, and Panhandle formulas. All three formulas are empirical. The Spitzglass formula is valid for low pressure gas having less than 1 psig pressure (69 mbar gage). Weymouth is valid for high pressure gas, and the Panhandle is valid for 6 to 24 inch (15 to 60 cm) gas lines with Reynolds numbers between 5 million and 14 million.

We receive quite a few e-mail questions about natural gas and are considering developing calculations using the Spitzglass, Weymouth, and Panhandle equations. I am interested in any feedback you might have about whether these calculations would be helpful to you.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com   LMNO@LMNOeng.com

Reference:
Crane Co. Flow of fluids through valves, fittings, and pipe. Technical Paper 410 (TP 410). 1988.

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid mechanics calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, OH 45701 USA (740) 592-1890
LMNO@LMNOeng.com

Pressurized Non-Circular Ducts/Conduits

Recently, we have been receiving a lot of inquiries asking how to model non-circular pressurized conduits. Our free calculation titled "Non-Circular to Circular Pipe Conversions" at http://www.LMNOeng.com/PipeDuct.htm will help. The calculation allows one to use the circular pipe design calculations ("Design of Circular Water Pipes" and "Design of Circular Liquid and Gas Pipes") for non-circular cross-sections.

If you have a rectangular or annular cross-section, the non-circular calculation will convert your geometry to an equivalent diameter (called hydraulic diameter) which can then be used in the circular design calculations to predict velocity. However, to calculate the flowrate, take the velocity from the design calculation page and copy it to the non-circular calculation page so that the velocity is multiplied by the actual duct area. This will give the correct flowrate. The flowrate output in the circular design calculation is computed as VA where A=(pi/4)D2, which is incorrect for a non-circular cross-section. Even though the D is the hydraulic diameter, (pi/4)D2 is not equal to the area computed from the actual duct geometry. Type some sample numbers in the non-circular calculation to prove it to yourself, then compare the calculation's area to (pi/4)D2 using your calculator.

Conversely, if you use "Design of Circular Water Pipes" to determine a pipe diameter based on a required velocity, the non-circular calculation can be used to convert the diameter to a height and width of a rectangular duct or an inner and outer diameter for an annular cross-section. For the same reasons as in the previous paragraph, the circular pipe design calculations cannot be used to compute hydraulic diameter based on flowrate, since A=(pi/4)D2 is used.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com  LMNO@LMNOeng.com

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

New Calculation - Bypass Loop
http://www.LMNOeng.com/Pipes/bypass.htm

Our bypass calculation is now complete. My last newsletter provided an example of how to use it for design. The calculation has three options: 1) It will size a pump in the bypass loop to draw fluid from the main pipe into the loop, 2) It will size a pump in the main pipe that forces fluid into the bypass loop, or 3) It will determine the length of a contraction in the main pipe so that fluid is forced into the loop.

The calculation has a demonstration mode for mercury flowing through wooden pipes. It's not a very useful fluid or pipe material for most people but shows the functionality of the calculation for free. Other fluids and pipe materials are selectable from the drop-down menus, but require paid registration to enable the Calculate button. As with our other calculations, you can select from a wide variety of units using the drop-down menus.

We hope the calculation is useful to you. Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com  LMNO@LMNOeng.com

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com .

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

Flow in Bypass Loop

Let's say you have an 8 inch (20 cm) diameter water pipe flowing at 300 gpm (US gpm or 19 liter/s). For some reason you need to bypass 0.5 gpm (0.03 liter/s) of the water through a 0.5 inch (1.3 cm) diameter loop that is 5 ft. (1.5 m) long. How do you get the water to flow from the 8 inch diameter main pipe into the bypass loop at the desired rate of 0.5 gpm?

There are different ways to achieve the 0.5 gpm in the bypass loop. You could install an orifice, valve or other type of flow restriction in the main pipe between the bypass take-off and return. The flow restriction will increase the loss (pressure difference) across the restriction encouraging water to flow through the bypass loop. Another option would be to install a pump in the bypass loop which would draw water from the main pipe into the bypass loop. As another alternative, if you already have a pump in the main line - and the location of the bypass loop is adaptable - then the bypass take-off could be at the discharge side of the pump and the bypass return could be to the inlet side of the pump.

As a note of caution: Most methods used to achieve a desired flowrate through the bypass loop will cause a reduction of flow in the main pipe.

We are currently developing a calculation that will help you determine the best way to achieve a desired flowrate through a bypass loop. The calculation will be valid for both liquids and gases. It will enable you to investigate sizing a restriction in the main pipe, sizing a pump in the bypass loop, or locating the bypass loop across a pump in the main pipe.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com  LMNO@LMNOeng.com

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

New Calculation - Small Bore Orifice for Gas Flow
http://www.LMNOeng.com/Flow/SmallOrificeGas.htm

You asked for it! We wrote it! A calculation for gas flow through a small bore orifice. The calculation will compute flowrate, differential pressure, or bore diameter for gas flow through an orifice installed in a pipe having a diameter between 0.64 cm and 5 cm.

Our calculation is based on the equations and methodology described in ASME MFC-14M-2001. You may select flange taps or corner taps. The method is valid for pipe Reynolds numbers greater than 1000 and diameter ratios between 0.1 and 0.8 for corner taps (0.15 and 0.7 for flange taps).

As with all of our calculations, a variety of units are selectable from drop-down menus. Fluid properties are built-in for air, methane, nitrogen, oxygen, carbon dioxide, and other gases. Alternatively, you may enter properties for gases not listed.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com  LMNO@LMNOeng.com

Reference:
American Society of Mechanical Engineers (ASME). 2001. Measurement of fluid flow using small bore precision orifice meters. ASME MFC-14M-2001.

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

Open channel flow measurement - what device to use

Maybe you need to determine the discharge (flowrate) in an open channel. How should you do it? There are many methods depending on your situation.

If the water is discharging freely out of a horizontal culvert, you can measure the culvert diameter and either the depth or the top width of the water. Then use the end depth method http://www.LMNOeng.com/Waterfall/CulvertDischarge.htm to determine the discharge.

Or, if the discharge out of the culvert is not too high, you can hold a bucket under the water and measure the time required to fill the bucket. Then, compute the discharge by dividing the bucket volume by the fill time.

If you need to determine the discharge in a channel, a weir or flume could be installed. A weir will cause the water to back up behind the weir. Then, the water depth upstream of the weir is directly related to the discharge. See http://www.LMNOeng.com/Weirs/vweir.htm. Alternatively, a flume could be installed. The water won't back up nearly as much behind a flume, but they are more expensive to make. The water depth at the throat of the flume is related to the discharge. See http://www.LMNOeng.com/Flumes/flumes.htm.

A cheaper way to determine discharge in an open channel is simply to drop a cork into the channel and record the time required for it to travel a certain distance. The stream velocity is computed from distance divided by time. Then, if you can determine the stream's cross-sectional area, the discharge equals velocity times area. This method may not be very accurate since it is often difficult to determine the area of a stream, and the stream area is often not constant. Further, the velocity measured is the velocity of the water surface which tends to be higher than the stream's average velocity.

I hope I have provided some helpful ideas for measuring discharge in open channels. Thank you for your interest in the LMNO Engineering newsletter,
Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com  LMNO@LMNOeng.com

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

Backwater Calculator now on-line
http://www.LMNOeng.com/Channels/gvf.htm

Please take a look at our newest calculation http://www.LMNOeng.com/Channels/gvf.htm. It has a nice demonstration mode, so you can see many graphs showing water depth upstream or downstream of a barrier. It will also plot velocity, Froude number, and top width versus distance in the demonstration mode. In addition to the graph, numbers for depth, velocity, Froude number, etc. are output at any distance specified by the user.

Using the default numbers in the calculation, press "Calculate" to see a graph of water surface and channel invert elevations. The graph shows that the water surface eventually parallels the channel invert. This happens because, as you go further and further upstream of the dam, the water seeks the normal depth. Normal depth is also known as the uniform flow depth. Invert is the channel bottom.

The calculation is very helpful for determining whether an existing channel will overflow during a flood, or for designing a channel to contain floodwaters. As usual, the calculation allows many different units.

Since this is our third newsletter in a row on gradually varied flow, I will write about a different topic next time. If you have any ideas for newsletter topics, please let me know.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com    LMNO@LMNOeng.com

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

My last newsletter discussed gradually varied flow (GVF) and rapidly varied flow (RVF). As a quick review, GVF and RVF are terms used to classify open channel flows - such as flow in rivers, canals, and culverts. RVF occurs over short distances such as when water flows over a weir or dam, drops off the end of a pipe, or encounters an hydraulic jump. GVF occurs over long distances such as the water approaching a weir, dam, or drop-off; or following a sluice gate.

Since we will soon have a GVF calculation on our website, I am discussing GVF calculations today. A GVF calculation first requires computation of the normal and critical depths (Yn and Yc). If the discharge, channel slope, channel material, and channel dimensions (except water depth) are known, then Yn can be computed using Manning's equation. Yn is also known as the uniform flow depth. It is the depth that water seeks in a long channel. Yc is computed by setting the Froude number to 1.0 and solving for depth. Please see http://www.LMNOeng.com/Channels/trapezoid.htm for normal and critical depth equations and computations. If Yn is greater than, equal to, or less than Yc, then the channel has a mild slope, critical slope, or steep slope, respectively.

To perform a GVF calculation, you need to know the water depth at some location in your channel (call this Ys, for start depth). For example, maybe you know the water depth behind a dam at a certain discharge - such as 10 m at 30 cms (cubic meters per second). Or, maybe you know the water depth under a sluice gate at a certain discharge. If the channel slope is mild and Ys is greater than Yc, then the channel has downstream control and the GVF calculation proceeds upstream. If the slope is steep and Ys is less than Yc, then the channel has upstream control and the GVF calculation proceeds downstream. The GVF computation then provides the water depth profile in the channel upstream or downstream of Ys, depending on whether or not there is downstream or upstream control.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

Gradually Varied Flow (GVF) and Rapidly Varied Flow (RVF)

GVF and RVF are terms used to classify open channel flows - such as flow in rivers, canals, and culverts. RVF occurs over short distances such as when water flows over a weir or dam, drops off the end of a pipe, or encounters an hydraulic jump. GVF occurs over long distances such as the water approaching a weir, dam, or drop-off; or following a sluice gate.

In long prismatic (constant cross-section geometry) channels, the water will attempt to reach the "normal depth". Normal depth is the water depth determined using Manning's equation (or Chezy's equation). How the water depth changes with distance as it approaches its normal depth is called a GVF profile. A GVF profile is a computation of water depth versus distance along the channel length. A GVF computation typically involves starting at a known depth (e.g. at a dam) and making successive computations upstream using the continuity equation and energy slope in Manning's equation (rather than using the channel bottom slope). It is a numerical computation and for best accuracy you want to use the smallest distance increments possible. If you have had a course in open channel flow, you might recall the different GVF profile types - such as M1, M2, M3, S1, S2, S3, etc. I'll leave discussion of these to another newsletter!

RVF computations require the continuity equation and the energy equation (like Bernoulli equation but with losses) and/or momentum equation. To analyze an hydraulic jump, continuity and momentum are required. To analyze flow over a dam/weir, continuity and energy are used. Often, empirical methods are used to analyze flow over weirs.

I discussed gradually and rapidly varied flows in this newsletter because we will soon complete a GVF computation for trapezoidal channels.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

1) New small diameter orifice calculation
2) Modeling closed piping loops

Usually I don't try to have two different topics in the same newsletter, but I wanted to let you know that the small diameter orifice calculation for liquids that I mentioned in my last newsletter is now on our site at http://www.LMNOeng.com/Flow/SmallOrificeLiq.htm.

On a separate topic, today I received a phone call from someone inquiring about how to model a closed pipe loop containing a pump. I think there might be general interest in modeling closed loops, so I'm going to discuss it. Let's simplify the system and say we have a pump followed by 300 ft of 4 inch diameter pipe which goes up to a height of 50 ft, winds around awhile, then goes back down to the pump. He wanted to know the pump head required to deliver a certain flowrate.

This loop system can be modeled using http://www.LMNOeng.com/DarcyWeisbach.htm and setting the elevation difference (Z1-Z2) and the pressure difference (P1-P2) both to 0.0. Then, select Scenario A (pipe only) and "Q known, Solve for Pump Head". My friend on the phone was surprised that I told him to set the elevation and pressure differences to 0.0. However, setting them to 0.0 is correct since it is a closed loop: the pipe goes up after the pump but comes back down before going back into the pump, so all elevation changes cancel each other out. Likewise, the high pressure at the discharge side of the pump is lost as the fluid (water, gas, whatever) moves through the piping system, but is entirely gained back after going through the pump.

The losses in the system - due to pipe friction, valves, bends, contractions, expansions, etc. - combine to form the total dynamic head (pump head) that the pump must overcome.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

Small Diameter Orifice Flowmeter

Many website visitors have asked if we have a calculation for orifice flowmeters having pipe diameters less than 2 inch (5 cm). Our current orifice meter calculations are valid only for pipes having at least 2 inch diameters:
http://www.LMNOeng.com/orifice.htm (liquid flow, > 2 inch pipe diameter)
http://www.LMNOeng.com/Flow/OrificeGas.htm (gas flow, > 2 inch pipe diameter)

In the past for pipes having less than 2 inch diameters, we have suggested our Bernoulli calculation which uses a fixed value for the discharge coefficient and therefore is not as accurate as an orifice calculation based on a standard methodology such as ISO or ASME. The ISO and ASME standards are developed from the results of many experiments conducted at various locations over a period of many years or decades. The discharge coefficient correlations in the standards are often complex - being functions of diameters, Reynolds numbers, and empirical constants.

Due to your requests, we have been working on a small diameter orifice calculation for liquids, and it will be finished for our next newsletter. It will be based on ASME MFC-14M-2001, "Measurement of fluid flow using small bore precision orifice meters." We are also working on a small diameter orifice gas flow calculation which accounts for the expansibility of a gas as it accelerates through the orifice - based on the same ASME standard.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com

ISO is the International Organization of Standards
ASME is the American Society of Mechanical Engineers
Our Bernoulli calculation can be found at http://www.LMNOeng.com/Flow/bernoulli.htm

You received this free newsletter because you requested it at our website. If you no longer wish to receive it, send a message stating "Discontinue Newsletter" to LMNO@LMNOeng.com.

(c) 2002 LMNO Engineering, Research, and Software, Ltd.

LMNO Engineering, Research, and Software, Ltd.
The fluid flow calculations website: http://www.LMNOeng.com
7860 Angel Ridge Rd. Athens, Ohio 45701 USA +1(740) 592-1890
LMNO@LMNOeng.com

New Calculation - Inverted Siphon (Depressed Sewer)
http://www.LMNOeng.com/Channels/InvertedSiphon.htm

My last newsletter discussed the concept of the inverted siphon - it is used to allow sewers to pass under obstructions such as rivers, subways, other piping systems, etc. We have now completed our inverted siphon calculation.

The calculation will determine the diameters of up to 5 siphons. The calculation will also work in reverse - you enter the diameters, and the flowrates are computed.

In all cases, the user enters the diameter, slope, and roughness coefficient for the main sewer pipe. Our calculation computes the discharge through the main sewer under design conditions (flowing full) using the Manning equation. The user also enters the elevation difference between the inlet and outlet junction chambers. The junction chambers are where the main sewer pipe branches into the siphon pipes and where the siphon pipes then merge back into the main sewer pipe after passing the obstruction.

The user also enters the siphon length and Manning roughness coefficient for the siphon pipes since they may be of different material than the sewer main. The hydraulic grade line of the siphon is computed as the elevation drop divided by the siphon length. Unlike the sewer main, the siphon pipes are designed to flow under pressure.

The calculation then computes siphon diameters, inlet invert elevations, wall heights in the inlet chamber (to allow for splitting of the main sewer flow into the various siphons), and velocity through each siphon.

We hope the calculation is useful to those of you in the civil engineering public works discipline. We wrote it due to the large number of requests for this type of calculation. The calculation can be found at http://www.LMNOeng.com/Channels/InvertedSiphon.htm.

Ken Edwards, Ph.D., P.E. (Owner/Engineer/Programmer)
LMNO Engineering, Research, and Software, Ltd.
http://www.LMNOeng.com