What This Solves
Calculates the downstream water surface elevation (tailwater depth) at a culvert or pipe outlet based on the receiving channel geometry and flow conditions.
Best Used When
- You need tailwater depth as input to culvert outlet control or outlet protection calculations
- You are analyzing the downstream channel to determine whether a culvert outlet is submerged
- You want to generate a tailwater rating curve for multiple flow rates in the downstream channel
Do NOT Use When
- You need the full culvert hydraulic analysis including headwater and outlet velocity — Use Culvert Outlet Control Calculator
- You need to size outlet protection based on the calculated tailwater and velocity — Use Outlet Protection Calculator
Key Assumptions
- Normal depth in the downstream channel is used as the tailwater elevation
- The downstream channel has a uniform slope, roughness, and cross-section near the outlet
- No backwater effects from downstream structures or confluences affect the tailwater
- The channel is stable and not actively aggrading or degrading
Input Quality Notes
Field survey of the downstream channel cross-section is strongly recommended. If backwater from a downstream structure or confluence is possible, tailwater should be determined from a water surface profile analysis.
Estimate the tailwater depth and elevation at a culvert or storm-drain outlet for a chosen design discharge and downstream channel, then check the flow regime, outlet submergence and backwater using Manning’s equation and critical-flow principles from FHWA HDS-5 and Chow.
Manning's n Values for Channels
| Channel Type | n |
|---|---|
| Concrete lined | 0.013 |
| Riprap lined | 0.035 |
| Grass lined | 0.030 |
| Natural - clean | 0.030 |
| Natural - weeds | 0.050 |
| Natural - brush | 0.070 |
| Floodplain - pasture | 0.035 |
| Floodplain - brush | 0.070 |
Source: Chow (1959), Table 5-6
Tailwater Control Types
| Control Type | Description |
|---|---|
| Normal Depth | Uniform flow in downstream channel |
| Critical Depth | Control section at or near outlet |
| Known WSE | Surveyed or calculated elevation |
| Downstream Pool | Pond, lake, or detention basin |
| Tidal | Coastal tidal influence |
Source: FHWA HDS-5, Chapter 4
Ready to Calculate
Enter channel parameters and click Calculate to analyze tailwater conditions.
For educational purposes only. Not a substitute for professional engineering judgment.
How tailwater analysis works
Tailwater is the water-surface depth in the receiving channel above the outlet invert. The calculator works it out for the selected tailwater control and then derives the velocity, Froude number, submergence and backwater status. Three relationships do the heavy lifting.
1. Normal depth (uniform flow) — Manning’s equation:
Q = (k / n) · A · R2/3 · S1/2
solved iteratively for the depth yn that carries the design discharge, where k = 1.486 in US customary units (ft, cfs) and k = 1.0 in SI (m, m³/s). The hydraulic radius R = A / P uses the flow area A and wetted perimeter P for the chosen channel shape.
2. Critical depth — critical-flow condition:
Q² / g = A³ / T
solved iteratively for yc, where T is the water-surface top width and g is gravitational acceleration (32.2 ft/s² or 9.81 m/s²). Critical depth is used directly when a control section sits at the outlet.
3. Velocity, Froude number and tailwater elevation:
V = Q / A · Fr = V / √(g · Dh) · TWelev = Invert + TWdepth
with hydraulic depth Dh = A / T. The flow is classified as subcritical (Fr < 0.95), critical (0.95 ≤ Fr ≤ 1.05) or supercritical (Fr > 1.05). The outlet is treated as submerged when the tailwater depth exceeds about 75% of the outlet height, and backwater is reported when TW > yn.
Channel geometry formulas used
The flow area A, wetted perimeter P and top width T at a depth y depend on the channel shape. The calculator uses the standard open-channel relations below, with bottom width b and side slope z (horizontal : vertical, so z:1). Natural channels are approximated as trapezoidal with z = 2.
| Channel shape | Flow area A | Wetted perimeter P | Top width T |
|---|---|---|---|
| Rectangular | b·y | b + 2y | b |
| Trapezoidal | (b + z·y)·y | b + 2y√(1 + z²) | b + 2z·y |
| Triangular | z·y² | 2y√(1 + z²) | 2z·y |
| Circular (partial) | (r²/2)(θ − sinθ) | r·θ | 2√(r² − (r−y)²) |
| Natural (approx.) | (b + 2y)·y | b + 2y√5 | b + 4y |
For circular pipes, r is the radius and θ = 2·arccos((r − y)/r) is the subtended angle in radians. Hydraulic radius R = A/P and hydraulic depth Dh = A/T. Source: Chow (1959), Open-Channel Hydraulics.
Choosing the tailwater control
Channel-controlled outlets
Use normal depth when the outlet discharges into a long, prismatic channel of known slope and roughness — the tailwater settles to the uniform-flow depth. Use critical depth when a free overfall, steepening or control section sits at or just below the outlet on a steep (supercritical) reach.
Water-body controlled outlets
Use a known water-surface elevation when the downstream level is surveyed or computed (e.g. a backwater study or a larger receiving stream), or a downstream pool elevation when the outlet sits in a pond, lake or detention basin. Use tidal for coastal outlets — but a full tidal-cycle analysis is required, and the tool only uses the larger of normal/critical depth as a placeholder.
Source: FHWA HDS-5 (2012), Chapter 4.
Worked example
A culvert outlets into a trapezoidal channel: design discharge Q = 100 cfs, bottom width b = 10 ft, side slope z = 2 (2:1), longitudinal slope S = 0.005 ft/ft, Manning’s n = 0.030, outlet invert at elev. 100.00 ft, normal-depth control.
- Solve Manning’s equation iteratively → normal depth yn ≈ 1.8 ft, which becomes the tailwater depth.
- Tailwater elevation = invert + TW = 100.00 + 1.8 = 101.8 ft
- Flow area A = (b + z·y)·y = (10 + 2·1.8)·1.8 ≈ 24.5 ft²; velocity V = Q/A ≈ 4.1 ft/s
- Froude number is < 1, so the flow is subcritical — the downstream channel controls and backwater can propagate upstream.
Based on the calculator’s HDS-5 trapezoidal verification case. Iterative Manning’s solutions carry normal engineering tolerance; enter the values above to reproduce the result.
Frequently asked questions
What is tailwater depth and why does it matter for a culvert?
Tailwater (TW) is the depth of water in the downstream channel measured above the culvert outlet invert. It matters because it is one of the two things that can control how a culvert flows. When the tailwater is high enough to submerge the outlet, the culvert usually operates under outlet control and the tailwater elevation directly raises the headwater (and therefore the upstream flood level). Tailwater also sets the conditions an outlet energy dissipator or riprap apron must be designed for, so per FHWA HDS-5 it is computed for the design discharge as part of every culvert analysis.
How is tailwater depth calculated?
For a normal-depth control, the downstream channel depth is found by solving Manning’s equation Q = (k/n)·A·R^(2/3)·S^(1/2) iteratively for the depth y that conveys the design discharge (k = 1.486 in US customary units, 1.0 in SI). Critical depth is found separately from the critical-flow condition Q²/g = A³/T. The tailwater used then depends on the control: normal depth for a uniform downstream channel, critical depth at a control section, or a surveyed water-surface or pool elevation when a downstream pond, lake or larger water body sets the level.
When is a culvert outlet considered submerged?
This calculator flags the outlet as submerged once the tailwater depth exceeds about 75% of the outlet height (barrel rise or channel depth). At that point the tailwater, rather than the inlet geometry, tends to govern the hydraulics, so outlet-control headwater should be checked. A free (unsubmerged) outlet points you toward checking inlet control instead. The governing condition for design is always the larger of the inlet-control and outlet-control headwater.
What is the Froude number and the flow regime telling me?
The Froude number Fr = V / √(g·D_h), where D_h = A/T is the hydraulic depth, classifies the downstream flow. Fr < 1 is subcritical (tranquil, deep, slow) and a downstream tailwater can propagate upstream as backwater; Fr ≈ 1 is critical; Fr > 1 is supercritical (rapid, shallow, fast) and a hydraulic jump may form where it meets a higher tailwater. The regime tells you whether the downstream channel actually controls the tailwater and whether energy dissipation is needed at the outlet.
When does tailwater create backwater effects?
Backwater is present when the imposed tailwater depth is greater than the channel’s normal depth for the same discharge (TW > y_n). The water surface then sits above the uniform-flow profile, the velocity drops, and the elevated level can extend upstream through the culvert and raise the headwater. This is common where a downstream pond, tide or constriction holds the water up, and it is why the calculator compares the tailwater against normal depth.
Standards & related tools
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Last verified: February 2026