Culvert hydraulics

Culvert hydraulics

While culverts are simple in concept, consisting of a pipe, an entrance and an outlet, their hydraulics can be quite complicated. Many combinations of flows can occur, depending on the headwater and tailwater levels, whether flows inside the culvert are sub-critical or super-critical, and whether there is a transformation from one state to the other.

In the 1960s, the US Federal Highway Administration (Herr & Bossy, 1965) developed a design procedure that simplified possible flow situations into two cases - inlet and outlet control. This is based on the idea that the flowrate through a culvert, for a given set of headwater and tailwater levels, will be controlled by (a) an orifice effect at the entrance, (b) friction effects within the pipe, or (c) the tailwater level at the outlet.  

Inlet control occurs where the entrance capacity limits the flow capacity of the culvert. It is marked by part-full flows in the pipe, because this has a greater full-pipe capacity than the entrance. Two cases are shown below:


Because most culverts are relatively short and steep, inlet control is the most common situation encountered when flows occur through culverts. Herr and Bossy developed nomographs to determine inlet control capacities for circular and box culverts. Given the culvert dimensions and a particular flowrate, the height of the headwater above the invert of the culvert entrance can be calculated. These nomographs have been reproduced in many road authority and pipe manufacturer manuals.  Henderson (1966) and Boyd (1986) developed sets of equations to cover this situation, and these are applied in DRAINS. Different equations apply over different ranges of headwater level.

Outlet level occurs when pipe friction or the downstream tailwater level control the flow, limiting it to some level below the entrance flow capacity. A number of cases can occur, with full and part-full flows in the culvert, as shown below:


Outlet control analysis requires that a hydraulic grade line (HGL) be projected backwards from the outlet of the culvert, allowing for exit, friction and entrance losses, all of which are a function of velocity head V2/2g, where V is the pipe flow velocity. This requires a starting point. If the tailwater submerges the outlet, as in the first case shown above, the starting level is the tailwater level. If the tailwater is below the obvert of the culvert, the starting point is the higher of the tailwater level and a level half way between the obvert and the critical depth of the flow at the outlet, as shown in the third diagram above. For a particular set of culvert dimensions and flowrate, the upwards-projected line can determine the headwater level.

Herr and Bossy developed a trial and error design procedure whereby headwater levels were determined making inlet control  and outlet control assumptions.  The case that gave the higher headwater level was assumed to govern the situation.  

DRAINS and hydraulic programs apply more complex procedures, but the basis is the same. DRAINS applies relationships developed by Henderson and Boyd.

As well as culverts, inlet and outlet control assumptions apply in DRAINS to headwalls and to detention basin outlets.

The above procedures apply to simple culverts and are sufficient in most design and analysis applications. Special adjustments may be required for efficient culvert entrances that use hoods and other devices to make culverts 'prime' or run full at lower headwater depths than usual. These adjustments generally apply in the selection of the loss parameters.


References:
  1. Boyd, M. (1986) Head-Discharge Relations for Culverts, Monier Rocla Technical Journal, November
  2. Henderson, F.M. (1966) Open Channel Flow, Macmillan, New York
  3. Herr. L.A. and Bossy, H.G. (1965)  Hydraulic Charts for the Selection of Highway Culverts, Hydraulic Engineering Circular 5, US Federal Highway Administration, Washington DC
  4. Normann, J.M., Houghtalen, R.J. and Johnston, W.J. (2005) Hydraulic Design of Highway Culverts, Hydraulic Design Series HDS 5, 2nd Edition, Federal Highway Administration, Washington, DC