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When calculating headwater of a culvert does the size upstream basin within the roadside ditch come into play? As an example, if you have 5cfs of flow into 12" culvert and you calculate that the headwater would be 1ft above the crown of pipe. Would this 1ft calculation differ if you have a 10% ditch slope coming into the culvert vs a 0.5% ditch slope? With the 10% it would seem like the upstream basin would be almost non existent and the inflow to the culvert would inundate this area to a depth greater then the 1ft above crown.

the top of the upstream basin is the headwater elevation unless there is a design constraint imposed to provide additional freeboard above an ##-year storm. The headwater is formed because the max culvert flow capacity is reduced by the lack of having a headwater present.... if less is leaving than coming in, headwater forms and the culvert operates more efficiently. the ditch slope has nothing to do with the math of the culvert to my knowledge except for whatever increases in CFS that the culvert itself has to accomodate.... except that a low-slope ditch headwater might have a lot of storage associated with it that might let the culvert detain a little too.

If I understand your question correctly, the only time that the "basin" upstream would affect the headwater elevation is if there enough storage to attenuate the flow. This in essence reduces the peak discharge which will in-turn reduce your headwater elevation. The "Head" required to overcome the losses within a culvert is just that. In a subcritical regime the control is downstream and in a supercritical regime upstream (or face of culvert ie: inlet control).

The other way the headwater can be reduced is to apply the approach velocity or a portion of it.

I hope this helps with you original question.

without a significantly large inlet transition structure, you really cannot count on the approach velocity. For small culverts such as this 12 inch pipe, an improved inlet would be a waste of money and would not reduce the headwater. Your headwater will always be equal to or less than your energy grade line.

Technically the approach velocity will have a reducing affect on the computed EGL at the upstream end of your culvert. In the real world, the approach velocity is almost always neglected in favor of conservatism. The computed EGL loss is based on V^2/2g. To take into account the approach velocity, V would be the difference in the two velocities thereby reducing the EGL loss.

Terry Stringer
Better Hydraulics & Hydrology Software
http://www.HydrologyStudio.com

I'll get Terry back for his prior complement. His answer here is correct. Basically, "yeah there's a small effect but it's not worth fooling with."

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East - http://www.campbellcivil.com

I would say that technically, if you had a 10% approach slope transitioning to a .5% slope, there would be a hydraulic jump at the inlet and you would lose essentially all of your velocity head. there would be perhaps zero reducing effect. It certainly would not be conservative to assume that you had any velocity head to work with.

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