10.4 Culverts, Weirs, Orifices, and Control Sections

Control Sections Set the Flow Problem

The WRE open-channel specification explicitly includes stormwater collection and drainage, culverts, hydraulic grade lines, and energy dissipation. Most of these reduce to one question: what controls the relationship between water level and discharge? A control may be a culvert inlet, a culvert outlet, a weir crest, an orifice plate, a critical-depth section, a gate, a drop structure, or a downstream tailwater condition. Name the control first and the rest of the problem usually collapses to a short equation.

Common Control Equations

Weir and orifice coefficients depend on geometry, crest shape, approach conditions, contraction, and the unit system. Use the coefficient and equation form given in the problem or available in the NCEES handbook; never mix a coefficient calibrated for one unit system or weir type into another without confirming it. A typical orifice C_d is about 0.6-0.62; a 90-degree V-notch weir uses Q = 2.5 H^(2.5) in US units.

Culvert Control Workflow

A culvert is a short hydraulic structure, not just a pipe under a road; inlet shape, barrel slope, roughness, length, tailwater, the allowable headwater, and outlet velocity all matter.

1. Identify barrel size, length, slope, material, entrance type, and the allowable headwater (HW) elevation.
2. Check inlet control: steep barrel, free outlet, shallow tailwater, or entrance-limited flow.
3. Check outlet control: long barrel, mild slope, submerged outlet, high tailwater, or loss-dominated barrel.
4. Compute required headwater for both controls when data allow.
5. Use the higher required headwater as the governing condition.
6. Check outlet velocity and downstream channel protection.

Inlet control means the entrance admits less flow than the barrel could carry; the barrel flows partly full and a beveled entrance, headwall, or larger inlet increases capacity. Outlet control means the full barrel and downstream water surface govern; a larger diameter, smoother barrel, or lower tailwater helps. Standard practice (FHWA HDS-5 method) computes both and the governing condition is whichever demands the higher headwater.

Tailwater, Submergence, and Energy Dissipation

Tailwater can convert a free discharge into a submerged one. A submerged weir no longer follows the free-overflow Q = CLH^(3/2) law unless a submergence correction (e.g., the Villemonte equation) is applied. A submerged culvert outlet reduces capacity and raises upstream headwater. In stormwater systems a downstream pipe, pond, channel, or floodplain stage can control the hydraulic grade line far upstream, so always check the receiving boundary.

High outlet velocity is a sitework problem as much as a hydraulics problem. A culvert or drop structure may pass the design flow yet still fail the project if outlet scour threatens a roadway embankment, adjacent property, or the receiving channel. Energy dissipators include riprap aprons, plunge pools, stilling basins, baffle blocks, drop structures, and impact basins, each sized for the outlet velocity and shear.

Weir and Orifice Exam Habits

• Measure head from the correct datum: the crest for weirs, the opening/energy difference for orifices.
• Use the effective length L, reduced for end contractions (about 0.1H per contracted end on a Francis-style rectangular weir), not always the full physical width.
• Confirm whether flow is free or submerged before choosing an equation.
• Keep units consistent with the coefficient (US C about 3.33 assumes feet and cfs).
• For multi-opening structures, compute per opening or sum effective area and length carefully.

A strong answer states the control first. Once the control is identified the equation is usually short; if the control is wrong, the arithmetic can be flawless and still produce the wrong hydraulic result.

Worked Mini-Example: Inlet vs Outlet Control

A 36-inch (3.0 ft) diameter concrete culvert, 100 ft long on a 0.5 percent slope, must pass 50 cfs with the headwater limited to 5 ft above the inlet invert. Under inlet control you compare the required headwater-to-diameter ratio from the entrance nomograph; a square-edged inlet on a steep, freely discharging barrel is typically inlet-controlled and the headwater is set by the entrance geometry alone, independent of barrel length.

Under outlet control you write an energy balance from headwater to tailwater through the barrel: HW = TW + entrance loss + friction loss + exit loss + velocity-head terms, where friction uses the barrel n and length. You compute the required headwater both ways and the governing condition is whichever gives the larger headwater. If outlet control requires 5.4 ft but inlet control requires only 4.2 ft, the culvert is outlet-controlled at 5.4 ft, which exceeds the 5 ft limit, so you would upsize the barrel or improve the inlet. Picking the smaller of the two headwaters is the classic error.

Stormwater Application Notes

In stormwater design the culvert or storm-sewer system is rarely isolated. The downstream pond stage, receiving stream flood elevation, or a downstream constriction can submerge the outlet and raise the entire upstream hydraulic grade line, flooding inlets that would otherwise drain. Always trace the hydraulic grade line from the controlling downstream boundary upstream, not the reverse.

For detention-basin outlet structures, a riser commonly combines a low-flow orifice (square-root-of-head behavior, for frequent small storms) with a weir crest or grate at the top (H^(3/2) behavior, for large storms), so the stage-discharge curve switches equation form as the head rises. Knowing which equation governs at a given pond stage is a frequent exam discrimination.