What This Solves
Calculates headwater elevation and outlet velocity for a culvert under outlet control conditions (when downstream water level affects upstream hydraulics).
Best Used When
- You need to determine the upstream water level for a culvert with known tailwater elevation
- You are checking whether a culvert operates under inlet or outlet control
- You need to calculate outlet velocity for erosion protection design
Do NOT Use When
- You need to design riprap or rock apron protection at the culvert outlet — Use Outlet Protection Calculator
- You are designing an energy dissipation structure (stilling basin or similar) at the outlet — Use Energy Dissipator Calculator
- You need to size riprap for channel protection downstream of the culvert — Use Riprap Sizing Calculator
Key Assumptions
- Outlet control conditions exist (tailwater or barrel friction controls the headwater)
- The culvert barrel has uniform cross-section and roughness along its length
- Standard entrance loss coefficients apply to the inlet geometry
- Flow is steady (not changing over time)
- The culvert is flowing full or partially full depending on tailwater depth
Input Quality Notes
Accurate tailwater elevation is critical for outlet control calculations. Use field measurements or routing calculations to estimate tailwater, not just normal depth in the downstream channel.
Analyze outlet control hydraulics for a highway or drainage culvert: enter the design discharge, barrel geometry, slope, roughness and tailwater to get the required headwater depth, outlet velocity, critical and normal depth, and an itemized head-loss breakdown using FHWA HDS-5 methodology.
Inlet Loss Coefficients (Ke)
| Inlet Type | Ke |
|---|---|
| Square edge with headwall | 0.50 |
| Groove end with headwall | 0.20 |
| Groove end projecting | 0.25 |
| Mitered to slope | 0.70 |
| Beveled edges | 0.25 |
| Side-tapered inlet | 0.20 |
| Slope-tapered inlet | 0.15 |
Source: FHWA HDS-5, Table 4-1
Manning's n Values for Culverts
| Material | n |
|---|---|
| Concrete | 0.012 |
| Corrugated Metal (annular) | 0.024 |
| HDPE (smooth) | 0.012 |
| PVC (smooth) | 0.010 |
| Corrugated Metal (helical) | 0.012-0.024 |
| Stone Masonry | 0.025-0.030 |
Source: FHWA HDS-5, Table 3-3
Ready to Calculate
Enter culvert parameters and click Calculate to analyze outlet control hydraulics.
For educational purposes only. Not a substitute for professional engineering judgment.
How outlet control is calculated
Under outlet control the barrel and tailwater govern flow, so the headwater is found from the energy equation. The calculator works backward from the outlet to the inlet, summing the head losses through the barrel:
HW = HGLout + HL + S·L − Invertin
where the total head loss is the sum of the entrance, friction and exit components:
HL = he + hf + ho
Each component is computed as follows:
- Entrance loss — he = Ke·(V²/2g), where Ke is the inlet loss coefficient (see table in the calculator) and V²/2g is the barrel velocity head.
- Friction loss — hf = Sf·L, with the friction slope from Manning's equation Sf = (n·V / (k·R2/3))² over barrel length L.
- Exit loss — ho = Ko·(V²/2g), with the exit loss coefficient Ko typically 1.0 for a sudden expansion into a larger channel.
The barrel full-flow capacity and normal depth come from Manning's equation Q = (k/n)·A·R2/3·S1/2, and critical depth is solved iteratively from the critical-flow condition Q²·T/(g·A³) = 1. The Manning conveyance factor k is 1.486 in US customary units and 1.0 in SI.
Variables
- Q — design discharge (cfs or cms)
- D / H — barrel diameter or rise (ft or m)
- L — culvert length (ft or m)
- S — barrel slope (ft/ft or m/m)
- n — Manning's roughness coefficient
- TW — tailwater depth above outlet invert
Outputs
- HW — headwater depth above inlet invert
- V — outlet velocity (Q/A at outlet)
- yc / yn — critical and normal depth
- he, hf, ho — head-loss components
- Qfull — full-flow barrel capacity
Outlet flow-type classification
The calculator classifies the outlet condition from the relationship between barrel capacity, normal depth, critical depth and tailwater. This sets the outlet depth used to compute exit velocity and the outlet hydraulic grade line.
| Flow type | Condition | Outlet depth used |
|---|---|---|
| Full | Capacity used ≥ 100%, or normal depth ≥ barrel height | Barrel height H (pressure / full bore) |
| Partially full | Tailwater > critical depth (outlet submerged below crown) | Greater of TW or the mean of yc and H |
| Free outlet | Tailwater ≤ critical depth (unsubmerged outlet) | Critical depth yc |
Logic per FHWA HDS-5, Chapter 4 (outlet control). The inlet loss coefficient (Ke) and Manning's n reference tables appear within the calculator above.
Worked example
A 48-inch (4.0 ft diameter) concrete circular culvert, 200 ft long at a 1% slope (S = 0.01 ft/ft), carrying Q = 100 cfs with a square-edged headwall inlet (Ke = 0.5) and 2.0 ft of tailwater:
- Manning's n = 0.012 (concrete)
- Full-flow area A = πD²/4 = π(4.0)²/4 = 12.57 sq ft
- Hydraulic radius R = A/P = 12.57 / (π·4.0) = 1.00 ft
- Headwater depth from the energy equation is approximately 5.2 ft above the inlet invert (HDS-5 Chapter 4 verification case).
This is the HDS-5 Chapter 4 reference case built into the calculator's verification suite. Enter the same inputs above to reproduce the full step-by-step breakdown.
Frequently asked questions
What is the difference between inlet control and outlet control?
A culvert operates under inlet control when the barrel can carry more flow than the entrance will admit — the headwater is governed by the inlet geometry (shape, edge condition, and headwater depth). It operates under outlet control when the barrel and the downstream (tailwater) conditions limit the flow — the headwater is governed by the energy equation: friction loss along the barrel plus entrance and exit losses. FHWA HDS-5 requires checking both and designing for whichever produces the higher required headwater. This calculator solves the outlet-control case; check inlet control separately.
How is headwater depth calculated under outlet control?
Outlet control headwater is found from the energy equation. The calculator computes the hydraulic grade line at the outlet (outlet invert plus the greater of tailwater or outlet depth), adds the total head loss through the barrel, and adds the elevation drop S·L back to the inlet: HW = HGL_out + H_L + S·L − Invert_in. The total head loss H_L is the sum of the entrance loss (Ke·V²/2g), the friction loss (Sf·L from Manning), and the exit loss (Ko·V²/2g). Higher discharge, longer barrels, rougher pipe, and higher tailwater all raise the required headwater.
Why does outlet velocity matter for culvert design?
The outlet velocity (V = Q/A at the outlet) determines the erosion potential at the discharge end. High exit velocities scour the downstream channel and can undermine the culvert and embankment. When the computed outlet velocity exceeds the permissible velocity of the receiving channel, outlet protection — a riprap apron, energy dissipator, or stilling basin — is required. The calculator reports outlet velocity so you can compare it against the allowable velocity for the downstream soil or lining.
What tailwater depth should I use?
Tailwater is the water-surface depth above the outlet invert in the downstream channel at the design discharge. It should be estimated from the downstream channel hydraulics (for example a normal-depth backwater calculation) for the same return-period flow used for the culvert. When tailwater submerges the outlet it raises the outlet hydraulic grade line and increases the required headwater; when tailwater is below critical depth the outlet runs free. Using a realistic tailwater is essential because outlet-control headwater is sensitive to it.
Standards & related tools
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Last verified: February 2026