Hagerman & Company, Inc. Technology Bulletin

Using Manning’s Equation to Design Pipes in Civil 3D

by Jeffrey W. Old, P. E.
AEC Solutions Engineer

Introduction

Out of the box, AutoCAD Civil 3D 2008 seemingly does not have the ability to design pipes based on a flow value, usually expressed in cubic feet per second. To make matters worse, any experienced civil designer will tell you that capability does exist in Civil 3D’s waning predecessor, Land Desktop. They may tell you about the good old days when you could establish a flow and a slope on a pipe and the software would size the pipe for you. That completeness does not exist in Civil 3D (yet?!?) but, using mathematical expressions for Manning’s equation, we can make our lives much simpler by labeling pipes in plan or profile with its flow capacity to see what our design can do.

Notes on Manning’s Equation

Long considered the engineering default for figuring gravity flow in a pipe, Manning’s Equation is a simple expression using four components of a pipe. The four components are cross-sectional area of flow expressed in square feet, slope expressed in feet of fall over feet of run, hydraulic radius expressed in feet and calculated as flow cross-sectional area divided by the wetted perimeter, and a roughness coefficient known as Manning’s “n” value which has no units.

The basic equation in English units is as follows:

Q = (1.49/n) * Area * (hydraulic radius)^(2/3) * (slope)^(1/2), where Q is flow in cubic feet per second.

By assuming that a pipe’s theoretical maximum capacity occurs when flowing 100% full, hydraulic radius for a circular pipe can be reduced to a simple term:

Hydraulic radius = area / perimeter

Hydraulic radius = pi*r^2 / 2*pi*r

Hydraulic radius = r / 2, where r is radius in feet.

Taking into account that simplification, Manning’s equation for circular pipe flowing full can be reduced to a function of pipe radius, slope and roughness:

Q = (1.49/n) * pi * r^2 * (r/2)^(2/3) * (slope)^(1/2).

Notes on Mathematical Expressions in Civil 3D

Object Label Styles in Civil 3D can be composed using the basic components of the objects they are designed to label. For example, a Label Style for a parcel line can be set up to display the bearing and distance of that line, two of its basic components. Similarly, Pipe Label Styles can be set up to display its basic components, such as slope or diameter, in plan or profile view. Taking this a step further, Tables can be constructed with fields populated by the basic components of a series of parcel lines or pipes.

With Label Styles comes the ability to create and name mathematical expressions based on the components of the objects they are labeling. For example, an expression can be created for spot shot elevations on a surface which subtracts a given value from the actual surface elevation. The expression might be called SUBGRADE and the composition might look something like this: {Surface Elevation}-2 where Surface Elevation is a component, or named property, of the surface.

Once created, that Expression can now be used as a component for Label Styles and Table Styles. Simply create a Surface Label Style for Spot Elevations employing the expression called SUBGRADE.

Writing the Expression for Flow

From the Settings tab, I can now create a custom expression for flow in a full circular pipe. The expression looks like this:

1.49*pi*((({Start Crown Elevation}-{Start Invert Elevation})/2)^2)*(1/0.013)*((({Start Crown Elevation}-{Start Invert Elevation})/4)^(0.6667))*(SQRT({Pipe Slope}))

This expression might look a little odd considering that I have substituted the term ((Start Crown Elevation – Start Invert Elevation)/2) for Pipe Radius. You will have to trust me on this one as simply using Pipe Radius, which is a named component of the pipe, does not work for some reason. Similarly, I have been unsuccessful in trying to use the component {Inner Pipe Diameter}.

Also, this expression assumes a Manning’s “n” value of 0.013 which is the old tried and true standard for concrete pipe. Pipes do, in fact, have a named component for Manning’s “n” value which you can set. Unfortunately, adding that component to your expressions will yield a bad result so keep them on the shelf with Pipe Radius and Inner Pipe Diameter.

The next step is to create a Pipe Label Style for Plan and Profile which shows off this value for flow. Here is an example of what this label with all the pertinent hydraulic facts might look like:

This is a style that may be useful for design purposes only and then, when it comes time to produce your construction plans, give that label a style more suitable for production drawings.

Now, as pipes are created and labeled, the label style DESIGN FLOW will show the pipe’s flow capacity.

This is especially effective in profile view where the invert grips of each pipe can be tweaked until the desired pipe capacity is reached. You may have to interrupt each iteration of invert raising or lowering with a regen, but it is still quite effective.

Use in Pipe Tables

Creating pipe and structure tables is a new capability of AutoCAD Civil 3D 2008. Now with the added expression for flow, it becomes easy to add the capacity of a pipe to a table. If flow velocity is something you need to add to a table, simply create an expression for velocity (which is the same as Flow but omit the (pi)*r^2 term remembering that Q=VA) and add that to a table style.

Conclusion

The next time someone tells you that designing pipes in Civil 3D cannot be done hydraulically, just tell them they haven’t explored the full capability of mathematical expressions. Making a couple of assumptions, it is easy to see that any user with a simple understanding of Manning’s equation can create an expression for flow capacity and compare that value to the expected flow calculated by the design storm. This comparison can then be used to help set the diameter and slope of a pipe.