10.4 Culverts, Weirs, Orifices, and Control Sections
Key Takeaways
- A control section fixes a relationship between head and discharge, so identify the controlling location before applying a capacity equation.
- Culvert hydraulics depend on inlet control, outlet control, headwater, tailwater, barrel roughness, slope, entrance shape, and outlet losses.
- Weirs are free-surface overflow controls where discharge varies approximately with H^(3/2) for common sharp-crested and broad-crested forms.
- Orifices are submerged openings where discharge depends on opening area and the square root of driving head.
- Outlet velocity and tailwater conditions determine whether energy dissipation, erosion protection, or backwater checks are needed.
Control Sections Set the Flow Problem
The WRE open-channel specification explicitly includes stormwater collection and drainage, culverts, hydraulic grade lines, and energy dissipation. Many of these items reduce to one question: what controls the relationship between water level and discharge? A control section may be a culvert inlet, culvert outlet, weir crest, orifice plate, critical-depth section, gate, drop structure, or downstream tailwater condition.
Common Control Equations
| Control | Typical form | What head means |
|---|---|---|
| Sharp-crested rectangular weir | Q = C L H^(3/2) | Head above crest, measured upstream away from drawdown |
| Broad-crested weir | Q = C L H^(3/2) | Upstream energy head above broad crest |
| Triangular weir | Q = C H^(5/2) | Head above vertex |
| Orifice | Q = C_d A (2gH)^(1/2) | Head difference across opening centerline |
| Culvert inlet control | Inlet geometry and headwater dominate | Headwater above inlet control section |
| Culvert outlet control | Barrel, tailwater, and losses dominate | Energy difference through the barrel |
Weir and orifice coefficients depend on geometry, crest shape, approach conditions, contraction, and units. On the exam, use the coefficient and equation form provided or available in the reference. Do not mix a coefficient calibrated for one unit system or weir type into another without confirmation.
Culvert Control Workflow
A culvert is not just a pipe under a road. It is a short hydraulic structure where inlet shape, barrel slope, roughness, length, tailwater, headwater limit, and outlet velocity all matter. The workflow is:
- Identify barrel size, length, slope, material, entrance type, and allowable headwater.
- Check whether inlet control is likely: steep barrel, free outlet, shallow tailwater, or entrance-limited flow.
- Check whether outlet control is likely: long barrel, mild slope, submerged outlet, high tailwater, or loss-dominated barrel.
- Compute or compare required headwater for both controls when data are available.
- Use the higher required headwater as the governing condition.
- Check outlet velocity and downstream channel protection.
Inlet control means the entrance admits less flow than the barrel could convey. Improving the inlet, such as using a beveled entrance or headwall, can increase capacity. Outlet control means the entire barrel and downstream water surface influence flow. Increasing barrel diameter, reducing roughness, or lowering tailwater can help.
Tailwater, Submergence, and Energy Dissipation
Tailwater can convert a free discharge into a submerged condition. A submerged weir no longer behaves like a free overflow weir unless a submergence correction applies. A submerged outlet can reduce culvert capacity and raise upstream headwater. In stormwater systems, a downstream pipe, pond, channel, or floodplain stage can control the hydraulic grade line upstream.
High outlet velocity is a sitework issue as much as a hydraulics issue. A culvert or drop structure may pass the design flow but still fail the project if outlet scour threatens a roadway embankment, adjacent property, or receiving channel. Energy dissipators include riprap aprons, plunge pools, stilling basins, baffles, drop structures, and outlet protection sized for velocity and shear.
Weir and Orifice Exam Habits
- Measure head from the correct datum: crest for weirs, opening centerline or energy difference for orifices.
- Use the effective length, not necessarily the full physical wall length, when end contractions apply.
- Confirm whether the flow is free or submerged.
- Keep units consistent with the coefficient.
- For multi-opening structures, compute per opening or use total effective area and length carefully.
A strong answer states the control first. Once the control is known, the equation is usually short. If the control is wrong, the arithmetic can be perfect and still produce the wrong hydraulic result.
A rectangular sharp-crested weir has an effective length of 4.0 ft. Using Q = 3.33LH^(3/2), what is the approximate discharge when the head above the crest is 0.60 ft?
An 18-inch diameter orifice discharges under 6.0 ft of head with C_d = 0.62. What is the approximate flow rate?