Modeling an Elliptical or Arch Pipe
Starting with HydroCAD 9.0, arch and elliptical pipes are available on the culvert, reach, and pipe storage screens. Just enter the pipe dimensions and you're done! For earlier versions, you may be able to approximate the pipe, as discussed below.
What Dimensions Do I Need?
In addition to the width and height, you will need to know the top and bottom
radii for the specific pipe you plan to use. (For an elliptical pipe, the
top and bottom radii will be the same.) Although you may commonly
refer to these pipes by just their width (span) and height, the radii can vary
significantly depending on the pipe design, material, and manufacturer.
Please consult your pipe supplier or a pipe handbook for details on the specific
pipe you plan to use. In fact, the actual span and height may differ from
the nominal dimensions.
After you enter the width, height, and radii, HydroCAD will automatically calculate the corresponding corner radius. If the entry screen says "no corner solution" is generally means that the top and/or bottom radii are too small to allow a smooth (tangential) connection between the corner and the top/bottom of the pipe. In some cases, you may need to increase the manufacturer's radius very slightly in order to enable a corner solution. If you are having trouble getting started, try entering these sample values to see how the entry screen works:
Width=36" Height=22" Top Radius=19" Bottom Radius=51"
Common dimensions can be found in the following sources:
Corrugated Steel Pipe:
Pipe Arches, NCSPA web page
Modern Sewer Design, 3MB PDF by AISI, See tables 1-6 to 1-10Reinforced Concrete Pipe:
Modeling in Earlier Versions
With HydroCAD 8.5 and earlier, you will need to approximate the discharge for an arch or elliptical pipe using one of these alternatives:
- First, it is generally recommended that any culvert be modeled in HydroCAD as an outlet device on a pond. This is necessary in order to consider the storage characteristics of the catch basin or other inlet area, which in turn effects the culvert headwater.
- The most accurate way to model non-circular culverts is to obtain a stage-discharge curve from the manufacturer and enter this into HydroCAD as a special outlet device. The disadvantage of this approach is that the curve will be based on a specific culvert slope, length, entrance conditions, etc, making it impossible to vary these parameters without entering a new curve. In addition, curves may not be available for certain pipes.
- An easier option is to use a circular culvert that will behave in a manner similar to the actual shape. The problem with this "equivalent circular culvert" approach is that the accuracy may vary significantly with changing head.
- In many cases, an elliptical culvert or arch pipe is best modeled as a box culvert with the same overall dimensions as the actual culvert, but with an appropriate discharge multiplier. For an elliptical pipe, the multiplier would be about .8 (80%), while a flat-bottomed arch pipe might have a multiplier as high as .9 (90%).
The final option is relatively accurate because these shapes have a cross-sectional area that is a fixed fraction of a circumscribed rectangle. Although the ratio of the circumference does vary somewhat with the aspect ratio, the variation is only 79-83% for aspect ratios from 1:1 (circular) to a 2:1 ellipse. This small variation allows relatively good accuracy using one of the fixed multipliers mentioned above. The pipe manufacturer may be able to assist you with the best value for a specific pipe.
Although this technique is only an approximation, it should offer reasonable accuracy for many situations. As with all outlet modeling, we recommend that you examine the resulting stage-discharge curve and verify its accuracy.