Using Manning’s Equation to Design
Pipes in Civil 3D
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.
CAD/CAM/CAE
Solutions
