Input data
Example data table
These sample rows show typical inputs and computed outputs for a quick cross-check.
| Unit | Shape | Q | b | z | S | n | Depth y | Velocity V |
|---|---|---|---|---|---|---|---|---|
| SI | Trapezoidal | 12.5 | 4 | 1.5 | 0.0012 | 0.022 | 1.19 | 1.55 |
| SI | Rectangular | 4.2 | 2.5 | 0 | 0.001 | 0.015 | 0.87 | 1.93 |
| US | Triangular | 180 | 0 | 2 | 0.0008 | 0.03 | 3.1 | 4.22 |
Formula used
The calculator solves for the normal depth in the approach channel using the Manning discharge equation:
- Q is discharge (flow rate).
- n is Manning roughness coefficient.
- A is flow area; R = A / P is hydraulic radius.
- P is wetted perimeter; S is bed slope.
- k is 1.0 (SI) or 1.486 (US customary).
Because depth appears inside A and R, the solution is obtained numerically using a bisection method to find y where computed Q matches the target discharge.
How to use this calculator
- Select the unit system that matches your project.
- Choose the channel shape for the approach section.
- Enter design discharge, slope, and roughness.
- Provide geometry: bottom width and side slope as required.
- Press Calculate depth to see results above the form.
- Download CSV or PDF to attach to submittals.
Technical note for approach channel depth design
1) Purpose of the normal-depth check
Approach channels guide flow into culverts, bridge openings, headwalls, and control structures. The depth computed here is the normal depth that satisfies Manning conveyance for the specified discharge and slope. It is a stable starting point for setting lining elevations, freeboard, and transition geometry.
2) Input data that drives the result
Depth sensitivity is highest to discharge, roughness, and slope. A small change in n can shift depth because Manning flow varies inversely with n. Typical n ranges are about 0.012–0.016 for finished concrete, 0.020–0.030 for clean earth, and 0.030–0.050 for dense vegetation. Bed slope S is often between 0.0005 and 0.005 for drainage approaches, but site grading should govern.
3) Geometry selection and dimensional meaning
The calculator supports rectangular, trapezoidal, and triangular sections. For trapezoids, bottom width b and side slope z (H:V) control area growth with depth. Increasing z widens the top width and usually reduces velocity at the same flow. For triangular channels, b is zero and z defines the V-shape.
4) Reading the output for hydraulic quality
In addition to depth, the tool reports area, velocity, hydraulic radius, and Froude number. Use the velocity as a lining check against permissible shear/velocity criteria. For many approach conditions, Fr < 1 indicates subcritical flow, supporting stable water-surface control and smoother transitions to structures.
5) Documentation and submission-ready reporting
Exported CSV and PDF outputs capture inputs, computed depth, and key section properties for design records. A good practice is to run at least two scenarios: a base roughness and a conservative roughness (higher n), then adopt the higher computed depth plus freeboard. Always confirm downstream tailwater and local losses separately.
FAQs
1) What depth does the calculator compute?
It computes the normal depth that satisfies Manning discharge for the entered flow, slope, roughness, and geometry. It does not automatically include freeboard, transitions, or local head losses.
2) When should I use SI versus US customary units?
Use SI when your project dimensions are in meters and flow is in cubic meters per second. Use US customary for feet and cubic feet per second. The Manning constant is applied automatically.
3) Why is the solution found numerically?
Depth appears inside the area and hydraulic radius terms, so the discharge equation is not linear in depth for most shapes. A bisection solver reliably finds the depth that matches the target flow.
4) How do I choose Manning n?
Select n based on lining material, vegetation, and surface irregularity. If uncertain, run a sensitivity check with a higher n to obtain a conservative depth and lower velocity.
5) What does the Froude number tell me?
Froude number compares flow inertia to gravity effects. Fr < 1 is subcritical and generally more stable for approach reaches. Fr > 1 indicates supercritical flow and may require additional checks.
6) Can I model a triangular channel with a bottom width?
A true triangular section has zero bottom width. If a small flat invert exists, model it as a trapezoid using the measured bottom width and the side slopes.
7) Is this adequate for culvert or bridge inlet design?
It provides approach normal depth and section properties. Inlet control, outlet control, tailwater, and losses through transitions require separate hydraulic analysis using the applicable design method or standard.