Culvert Flow Calculator

Example data table

Formula used

1) Inlet control (orifice approximation)

The inlet estimate treats the opening as an orifice driven by headwater depth: Q_inlet = C_d · A · √(2 g HW)

A is full-flow area of the opening, and C_d captures entrance contraction and approach effects.

2) Outlet control (loss-based full-flow)

The loss-based option uses a simplified energy balance: H = (V² / (2 g)) · (K_e + K_exit + f L / D_h)

with Q = A · V. Available head is H = HW − TW + (S · L) using the inlet invert as datum.

The friction factor f may be estimated using Reynolds number and roughness, or entered directly.

3) Open-channel Manning option

For uniform open-channel conditions: Q = (1/n) · A · R^2/3 · S^1/2

R is hydraulic radius A/P. For partial circular flow, the wetted geometry is computed from the segment angle.

How to use this calculator

1. Select your units and culvert shape.
2. Enter dimensions, length, and slope.
3. Provide roughness values and choose outlet method.
4. Enter headwater and tailwater depths to represent site conditions.
5. Press Calculate to compare inlet and outlet estimates.
6. Download CSV or PDF to archive your design check.

If you expect partially full flow, switch Flow state to Partially full and enter a depth.

Culvert flow article

1) Why culvert hydraulics matters

Culverts protect roads by passing storm runoff under embankments. Undersized barrels can raise headwater, overtop pavements, and accelerate approach erosion. A practical check compares inlet control versus outlet control, because the smaller capacity usually governs during peak events. This calculator provides quick capacity estimates for preliminary sizing and alternatives screening.

2) Inlet control in simple terms

Inlet control is driven mainly by entrance geometry and headwater depth. The tool uses an orifice-style estimate Q = C_d A √(2 g HW), where typical discharge coefficients often range from about 0.55 to 0.75. Improved entrances, bevels, or headwalls generally increase effective capacity by reducing contraction and turbulence losses.

3) Outlet control and energy losses

Outlet control depends on the full barrel losses plus minor losses at entrance and exit. The loss-based method applies H = (V²/2g)(K_e + K_exit + fL/D_h). Entrance loss coefficients commonly fall between roughly 0.2 and 1.0 depending on the inlet condition, while exit loss is often near 1.0 for a free discharge into tailwater.

4) Roughness, Reynolds number, and friction factor

For the loss-based option, the calculator can estimate Darcy friction factor using Reynolds number and absolute roughness. For water near 20°C, kinematic viscosity is about 1.0×10⁻⁶ m²/s, and many smooth materials have small roughness, while corrugated interiors behave effectively rougher. Longer barrels amplify friction losses because the fL/D_h term scales directly with length.

5) Manning approach for uniform flow

When flow behaves like uniform open-channel conditions, Manning’s equation is widely used: Q = (1/n) A R^2/3 S^1/2. Typical n values for smooth concrete may be near 0.012–0.015, while corrugated metal or rough surfaces can exceed 0.020 depending on diameter, joints, and deposits. For partially full flow, the tool computes wetted area and perimeter from the chosen depth.

6) Headwater, tailwater, and invert drop

Available head is modeled as HW − TW + SL. Tailwater can submerge the outlet and reduce the effective head driving flow, especially on flat grades. The invert drop term SL becomes important on steep installations, where a modest slope over a long barrel can add meaningful energy head even with similar water levels upstream and downstream.

7) Interpreting results for design decisions

If inlet control governs, focus on entrance improvement, debris management, and better alignment. If outlet control governs, capacity is limited by barrel losses, so increasing diameter/area, shortening length, reducing roughness, or decreasing minor losses can help. Always compare multiple sizes to see how controlling discharge responds to geometry changes.

8) Practical limits and recommended checks

This calculator is intended for preliminary evaluation. Final design often requires jurisdiction guidance, event frequency criteria, and checks for freeboard, roadway overtopping, fish passage, sediment transport, and inlet submergence. Field conditions such as partial blockage, skew, and outlet erosion can reduce performance, so apply conservative assumptions when screening alternatives.

FAQs

1) What is “controlling discharge”?

The controlling discharge is the smaller of the inlet-control estimate and outlet-control estimate. It represents the limiting capacity under the simplified assumptions used by this tool.

2) When should I use the loss-based outlet method?

Use it when headwater and tailwater are known and barrel losses are important, such as long culverts, steep flows, or cases with notable entrance and exit losses.

3) When is Manning more appropriate?

Manning is useful for uniform-flow style assessments, especially for partially full conditions. It is common in open-channel practice and gives quick sensitivity to slope and roughness.

4) How do I choose Manning n?

Select n based on material and condition. Smooth concrete is often about 0.012–0.015. Corrugated metal or rough interiors may be 0.020 or higher, especially with deposits.

5) What do Ke and Kexit represent?

Ke models entrance losses from contraction and turbulence. Kexit accounts for velocity head lost at the outlet, commonly near 1.0 for a free discharge. Use values consistent with your entrance type.

6) Why does tailwater reduce capacity?

Higher tailwater decreases the available head (HW − TW + SL). Less driving head lowers velocity and discharge for the same barrel and loss coefficients, particularly for loss-based outlet control.

7) Can I use this for final culvert permitting?

Use it for screening and early sizing. Final design typically requires agency charts or approved software, plus checks for blockage, submergence, erosion protection, and required overtopping criteria.

Practical guidance

• Use realistic Ke values for your inlet geometry and condition.
• Tailwater can submerge the outlet and reduce effective head.
• Long barrels and rough interiors increase friction losses.
• Check local design manuals for required freeboard and events.

Use results to size culverts and reduce flooding risk.