A culvert is a relatively simple structure, typically a pipe or box, that projects through an earthen embankment to allow flow to be conveyed from an area upstream of a roadway to the downstream end of a roadway. Culverts consist of an inlet, an outlet, and a culvert barrel. Common culvert shapes include circular pipes, rectangular boxes, arches, and ellipses.
Although the culvert structure itself is simple, culvert hydraulics is quite complex. The culvert may flow full or partially full, the outlet may be submerged, and the flow regime may be subcritical or supercritical. These are hydraulic factors that must be considered when preparing a culvert design. A culvert analysis must also evaluate whether the culvert entrance or exit will be submerged during the design event to determine inlet and outlet control. This will influence the hydraulic analysis because a unique set of computations is required depending on the controlling flow conditions. Hydraulic modeling programs such as HEC-RAS will perform calculations for both inlet and outlet control conditions and select the most conservative result, which is the result that yields the highest headwater elevation for the design flow rate.
Inlet Control
Inlet control applies when the culvert barrel can convey more flow than the entrance of the culvert allows. Thus, a control point exists near the culvert entrance/inlet.
Under inlet control, which is also referred to as headwater control, the flow being conveyed through the culvert and the associated headwater depth depend on the structure’s entrance. The flow capacity of the culvert depends on the available opening area, the shape of the culvert opening, and the inlet configuration. This is because, under inlet control, the culvert barrel is capable of conveying more flow than the entrance can pass. For this reason, under inlet control conditions, culvert capacity can be increased by making the culvert entrance a rounded, flared, or beveled shape. On the other hand, adjusting the culvert’s slope or tailwater elevation will have a minor effect on the culvert’s flow capacity.
Inlet Control Computations
The following equations are published in the Federal Highway Administration (FHWA) Highway Design Series No. 5 (HDS-5). It should be noted that the entrance to a culvert is considered submerged when the headwater depth is about 20% greater than the vertical height of the culvert entrance (Linsley et al., 1992).
Unsubmerged Inlet
Form 1 is considered the most complete solution. However, the coefficients for various culvert shapes have been developed for the Form 2 equation.
Submerged Inlet
Inlet Control Data Required for HEC-RAS Modeling
The HEC-RAS information required specifically for inlet control analysis is inlet geometry. This includes the culvert shape, cross-sectional area, and height of the culvert. When a specific culvert shape is selected in HEC-RAS, the program automatically selects the appropriate set of FHWA charts and scale numbers for that shape. The modeler may accept these numbers or choose to select different values from a dropdown list.
Outlet Control
Outlet control applies when the culvert entrance is capable of conveying more flow than the barrel can pass. Thus, the headwater elevation for a particular flow rate is a function of the downstream conditions.
When a culvert is under outlet control, which is also called tailwater control or exit control, the headwater elevation for a given flow rate is a function of the downstream condition (tailwater elevation). Flow is either subcritical or under pressure through the structure. Increasing the culvert’s capacity is achieved by reducing entrance losses or by specifying a culvert material with a lower Manning’s roughness coefficient.
Outlet Control Computations
For outlet control calculations, the focus is on losses throughout the culvert. These losses include entrance losses, exit losses, and friction losses. In some cases, the modeler may also consider bend losses, losses at junctions, and grate losses.
Friction Losses
The following equation is published in HDS-5 and is based on Manning’s equation.
Entrance Losses
Exit Losses
The following equation estimates losses for a sudden expansion such as an endwall.
Outlet Control Data Required for HEC-RAS Modeling
As previously discussed, outlet control analyses involve calculation losses through the culvert. For HEC-RAS to perform an outlet control analysis, the user must specify the Manning’s roughness coefficient (n) of the culvert material and the culvert entrance loss coefficient. HEC-RAS provides a table within the program that can help the user determine the appropriate entrance loss coefficient. Simply, click the check mark button or refer to the HEC-RAS User’s Manual.
An exit loss coefficient is also required. The default value of the exit loss coefficient in HEC-RAS is 1.0, but the user can adjust this value. I recommend keeping the default exit loss coefficient unless you have reliable information that says another value would be more appropriate.
In HEC-RAS, the user does not need to specify a tailwater elevation because it is calculated as part of the water surface profile computations.
Comparison of Inlet and Outlet Control
The following table summarizes the differences between inlet and outlet control at culverts.
| Inlet Control | Outlet Control |
| The design flow rate is a function of the culvert inlet geometry. A rounded, flared, or beveled entrance can significantly increase flow capacity. Adjustments to the slope, lining/roughness, or tailwater elevation have a minor effect on the design flow rate. | The design flow rate is a function of culvert losses. These losses are the sum of the entrance loss, exit loss, and friction loss through the culvert barrel. |
| Inlet capacity < barrel capacity | Inlet capacity > barrel capacity |
| Culvert barrel never flows full through its entire length | The culvert barrel can flow full |
| The culvert acts as an orifice (submerged entrance conditions) or a weir (unsubmerged entrance conditions) | The culvert acts as a pressure conduit |
| The culvert slope is steep | The culvert slope is mild |
| Because the control section of a culvert under inlet control is at the upstream end, barrel flows are supercritical. Normal depth < critical depth Culvert slope > critical slope | Flow is subcritical or under pressure. Flow is typically subcritical within the culvert barrel but exits close to critical depth. Normal depth > critical depth Culvert slope < critical slope |
| The water surface elevation at the culvert outlet does not influence the headwater elevation. The entrance capacity is determined primarily by the available opening area, the shape of the culvert opening, and the inlet configuration. | The water surface elevation at the culvert outlet does influence the headwater elevation |
Culvert Analysis Terminology
This section serves as a glossary of terms used in the above blog post.
Critical depth – depth at the point of minimum energy. Depths greater than critical depth indicate subcritical flow, and depths shallower than critical depth indicate supercritical flow.
Culvert entrance – the opening of the culvert at the upstream end.
Culvert exit – the opening of the culvert at the downstream end.
Culvert shape – the configuration or cross-sectional shape of the culvert shape. The most common culvert shapes are a circle and a rectangular box.
Entrance loss – the difference in the energy grade line elevation between the section just upstream of the culvert mouth and the section just inside the culvert mouth.
Exit loss – the difference in the energy grade line elevation between the section just inside the culvert exit and the section just outside the culvert exit.
Friction loss – the loss of energy throughout the culvert barrel, between the section just inside the upstream end of the culvert and the section just inside the downstream end of the culvert.
Headwater elevation – the elevation of the energy grade line at the culvert entrance. The headwater elevation is equal to the water surface elevation at the culvert entrance if you assume that the velocity head is negligible.
Subcritical flow – occurs when the Froude number is less than one (Fr < 1). Typically associated with flow that has a low velocity and higher depth. Often described as calm or tranquil.
Supercritical flow – occurs when the Froude number is greater than one (Fr > 1). Typically associated with flows that have a high velocity and low depth. Often described as rapid. Occurs most often in man-made channels and street gutters.
Tailwater elevation – the elevation of the water surface at the exit of the culvert.