7.3 Culvert Hydraulics - Inlet/Outlet Control
Flow through a culvert and the resulting headwater elevations are influenced by many factors. Although a full range of flows passes through a culvert, the culvert design is normally based on a selected flood peak discharge, such as the 25-year storm event. Calculations must determine whether the culvert is under inlet or outlet control during the design event. Computations are made for both inlet and outlet control conditions and the most conservative answer is selected (that is, the result that yields the highest headwater elevation for a given discharge, or the lowest flow rate for a given headwater elevation). If the higher energy grade line is produced by inlet control, HEC-RAS performs an additional analysis to ensure that the flow is supercritical throughout the culvert barrel's length. If a hydraulic jump occurs within the barrel, the culvert is assumed to flow full, with the headwater elevation computed under outlet control conditions. HEC-RAS, along with other programs such as Haestad Methods' CulvertMaster and PondPack, perform both inlet and outlet control computations and choose the appropriate controlling scenario, unless the modeler specifies that the program use only inlet or outlet control.
Inlet Control
When a culvert functions under inlet control (also called headwater control or entrance control), the flow through the culvert and the associated headwater depth upstream of the structure are primarily functions of the culvert entrance. The headwater depth must increase to force increasing discharges through the culvert entrance. The entrance capacity is determined primarily by the available opening area, the shape of the opening, and the inlet configuration of the entrance. Under inlet control, the culvert never flows full through its entire length. The discharge passing into the culvert occurs as weir flow (for unsubmerged entrance conditions) or orifice flow (for submerged entrance conditions). The entrance to a culvert is considered submerged when the headwater depth (HW) is about 20 percent greater than the vertical height (D) of the culvert entrance (Linsley et al., 1992). Generally, since the control section of a culvert operating under inlet control is at the upstream end of the culvert, barrel flows are supercritical and outlet velocities are determined using forewater computations for gradually varied flow profiles. Thus, inlet control is associated with culvert barrels that have a steep slope.
Flow Conditions under Inlet Control.
Under inlet control, the culvert barrel is capable of passing more discharge than the culvert entrance can allow. Therefore, improvements in culvert performance for inlet control situations concentrate on streamlining the entrance shape. A rounded, flared, or beveled entrance can significantly increase flow capacity, whereas adjustments to culvert slope, lining, or tailwater elevation have a minor effect, if any. The flow passes through critical depth near the culvert entrance and is usually supercritical throughout the culvert barrel. Depending on downstream conditions, a low-grade hydraulic jump may occur at the culvert exit. If needed, a water surface profile through the culvert can be obtained by either the direct step or standard step method, starting at critical depth near the entrance. Figure 7.4 displays the four culvert flow conditions that can occur under inlet control conditions. The possible solutions depend on whether the inlet and outlet are submerged or unsubmerged. Of the four possible types, profiles A and C are the most common.
Figure 7.4 The four culvert flow conditions that may occur under inlet control conditions.
With condition A, both the inlet and outlet are open to the atmosphere (unsubmerged). The culvert entrance acts as a weir, with flow passing through critical depth near the entrance. Figure 7.5 further illustrates this condition in a multiple-barrel culvert. The drawdown into the culvert indicates critical depth is probably occurring near the mouth of the culvert. The wave riding up each intermediate wall separating the barrels is indicative of supercritical flow. Condition A is addressed through the normal culvert analysis procedures within HEC-RAS.
Figure 7.5 A multiple-barrel culvert operating under condition A.
For condition B, the downstream tailwater elevation is sufficiently high to cause a hydraulic jump within the culvert barrel. Because the entrance is open to the atmosphere, the hydraulic jump location is relatively stable and the control remains at the entrance (flow passes through critical depth at the culvert mouth). This condition rarely occurs, but can be addressed with HEC-RAS using a mixed flow analysis (discussed in Chapter 8).
For condition C, the inlet is submerged and the outlet is unsubmerged. The mouth of the culvert acts as an orifice, with flow passing through critical depth near the culvert entrance. Condition C is the most common inlet control situation encountered for design flow in culverts and is addressed with HEC-RAS culvert analysis procedures.
Condition D rarely occurs. Since both the entrance and exit are submerged, a hydraulic jump forms within the culvert. If no source of air is available, the jump entrains and evacuates the air in the culvert, with the hydraulic jump moving upstream as the air is removed. The culvert eventually flows full, with the culvert condition switching from inlet to outlet control. For condition D, the storm drain inlet in the highway median is the source of air. The air introduced into the culvert stabilizes the location of the hydraulic jump and prevents it from moving upstream, maintaining inlet control at the entrance. This condition cannot be addressed automatically with HEC-RAS; however, the modeler could specify that the program only use inlet control for this culvert, to prevent the program from selecting outlet control if the computed energy grade line elevation at section 3 is higher than that for inlet control.
Outlet Control
Outlet control occurs when the culvert barrel is not capable of conveying as much flow as the inlet opening will accept. When a culvert functions under outlet control (also called tailwater control or exit control), the headwater elevation for a given discharge is a function of the downstream condition (the tailwater elevation). For the design discharge, the headwater elevation is usually found by computing the losses through the culvert and adding them to the downstream tailwater energy grade elevation. These losses are the sum of the entrance loss, the exit loss, and the friction loss through the culvert barrel. Using outlet control for the design discharge often assumes the culvert flows full over all or most of its length, with the structure acting as a pressure conduit.
Culvert Flow Conditions for Outlet Control.
Under outlet control, the headwater depths are found by adding the water surface elevation at the culvert exit to the losses through the culvert. Flow is either subcritical or under pressure through the structure. Increasing the culvert's performance is usually achieved by further streamlining the inlet geometry (reducing the entrance loss coefficient) and/or by using a culvert material with a lower value of Manning's n.
Under open channel conditions for outlet control, flow is subcritical within the culvert but often exits the culvert at or near critical depth, if the tailwater elevation is less than that of critical depth. Downstream protection against scour should be considered as part of the culvert design. Figure 7.6 shows riprap protection at the sides and invert of a culvert.
Figure 7.6 Riprap protection at a culvert entrance. Note the significant vegetation in the channel that may dislodge the rocks and increase the water surface elevation by causing a higher n value.
For open channel flow through a culvert, a direct step backwater computation can be performed between the exit and entrance of the culvert to compute the headwater elevation. Figure 7.7 displays the five possible flow conditions for a culvert under outlet control. The most common types are D for design flow conditions and E for lower flows. The five types are based on whether the entrance and exit are submerged or unsubmerged.
Figure 7.7 The five flow conditions that may occur for outlet control.
Condition A occurs only when the downstream channel and overbank capacities are less than the culvert capacity, thus submerging the culvert exit due to the high tailwater elevation. Condition A is often caused by a pond or lake immediately downstream of the culvert or a smaller downstream culvert causing upstream ponding. This condition is addressed through use of the HEC-RAS culvert analysis procedures.
Condition B is normally transient and occurs infrequently at the discharge for which the culvert was designed. Tests have found that a culvert will not generally flow full unless the headwater depth exceeds the vertical height of the culvert by about 20 percent. This submergence level is not achieved under condition B, resulting in an unsubmerged condition at the culvert entrance. This is not handled in HEC-RAS culvert routines; when the computed depth equals the culvert height, the culvert is assumed to flow full for its full length.
Condition C is often assumed to simplify the computations when a culvert analysis is done by hand; however, a large head is needed at the culvert entrance to cause a culvert to flow full all the way through to the exit. Although this situation is not often encountered in the field, the advantage of assuming full-flow conditions through the culvert is that the tailwater elevation may be conveniently located at the top of the culvert exit. This condition is handled by the HEC-RAS culvert routines if normal depth in the culvert (for the discharge being analyzed) exceeds the vertical culvert height at the culvert exit.
Condition D is the most typical situation for a culvert's design discharge. The culvert flows full for a significant portion of its length, but the water surface eventually breaks free of the culvert top at some point within the culvert barrel. Figure 7.8 shows a culvert under high submergence with the outlet flowing less than full. The water surface elevation at the culvert exit could range from nearly the full depth of the culvert to critical depth. In the absence of a computed tailwater elevation, FHWA research recommends that culvert computations use a tailwater depth equal to the average of the culvert vertical height (D) and critical depth (for the design flow). Since HEC-RAS computes a water surface elevation at the culvert exit, this tailwater elevation is used by the program to handle Condition D for a culvert under outlet control.
Condition E is handled as open channel flow and a direct step computation is used to compute an elevation at the upstream end of the culvert, beginning at the tailwater elevation or the elevation of critical depth, whichever is higher. HEC-RAS uses vertical changes in depth of 0.05-0.1 ft (0.015-0.03 m) to compute a water surface profile for open channel flow through a culvert.
Comparison between Inlet and Outlet Control.
Table 7.1 summarizes the differences between inlet and outlet control. The following sections on inlet and outlet analysis further expand on these differences.
FHWA
Figure 7.8 Headwater (a) and tailwater (b) for a highly submerged culvert operating in condition D.
Analysis Summary.
A culvert analysis must evaluate the culvert entrance and exit conditions for submergence, determine inlet or outlet control, and perform a unique set of computations depending on the controlling flow conditions. HEC-RAS can perform these analyses to accurately determine headwater and tailwater elevations. If the design discharge is required for a set of known headwater and tailwater conditions, a program such as Haestad Methods' CulvertMaster would be more suitable. HEC-RAS does not compute discharge.
Determining the proper flow condition at a culvert requires specific analysis procedures to arrive at the correct solution. Figure 7.9 displays the flowchart for computing culvert flow conditions as followed by HEC-RAS. The following section illustrates the computation methods used by the program.
Figure 7.9 Flow chart for culvert computations in HEC-RAS.
