Calculated Results
Results appear here after you press calculate.
Calculator Inputs
Single-column page layout with a responsive input grid.
Plotly Graph
The chart shows discharge versus depth for the current shape and roughness settings.
Formula Used
Manning velocity equation:
V = (k / n) × R2/3 × S1/2
Discharge equation:
Q = A × V
Where:
- V = mean flow velocity
- Q = discharge
- A = flow area
- R = hydraulic radius = A / P
- P = wetted perimeter
- S = slope of energy grade line, approximated here by bed slope
- n = Manning roughness coefficient
- k = 1.0 for metric units and 1.49 for US customary units
The calculator also reports top width, hydraulic depth, and Froude number using F = V / √(g × Dh).
How to Use This Calculator
- Select the unit system that matches your project data.
- Choose the channel shape: rectangular, trapezoidal, triangular, or circular.
- Enter Manning roughness, slope, and flow depth.
- Provide the shape dimensions such as bottom width, side slope, or pipe diameter.
- Click Calculate Manning Flow to update the result panel above the form.
- Review velocity, discharge, hydraulic radius, and flow regime indicators.
- Use the CSV or PDF buttons to export the result summary.
- Check the chart to compare how discharge changes with depth.
Example Data Table
| Case | Shape | n | Slope | Depth | Base / Diameter | Side Slope | Estimated Discharge |
|---|---|---|---|---|---|---|---|
| 1 | Rectangular | 0.015 | 0.0020 | 1.20 m | 2.50 m | – | 5.84 m³/s |
| 2 | Trapezoidal | 0.018 | 0.0015 | 1.00 m | 3.00 m | 1.5 | 5.23 m³/s |
| 3 | Triangular | 0.020 | 0.0030 | 0.80 m | – | 2.0 | 1.67 m³/s |
| 4 | Circular | 0.013 | 0.0025 | 0.90 m | 1.80 m | – | 3.54 m³/s |
Frequently Asked Questions
1. What does the Manning equation calculate?
It estimates average velocity and discharge in open-channel flow using roughness, hydraulic radius, and slope. Engineers use it for drains, channels, sewers, and partially full circular conduits.
2. What is a typical Manning roughness value?
Smooth concrete may use values near 0.012 to 0.015. Earth channels, rock, grass, or debris increase roughness. Choose n from a reliable hydraulic reference for the actual surface condition.
3. Is bed slope the same as energy slope?
Not always. For uniform flow, engineers often assume the energy slope, water surface slope, and bed slope are approximately equal. This calculator uses bed slope as the common practical approximation.
4. Can this calculator handle partially full circular pipes?
Yes. Select the circular option and enter pipe diameter and flow depth. The calculator computes the wetted angle, area, wetted perimeter, hydraulic radius, and resulting discharge.
5. Why is hydraulic radius important?
Hydraulic radius is area divided by wetted perimeter. It captures how efficiently a section conveys flow. Larger hydraulic radius usually means lower resistance and higher velocity for the same slope and roughness.
6. What does the Froude number show?
The Froude number compares flow inertia with gravity effects. Values below one suggest subcritical flow, about one indicates critical flow, and above one suggests supercritical flow.
7. How accurate are the chart values?
The chart is generated from the same entered roughness, slope, and geometry assumptions. It is useful for screening and comparison, but final design should still include professional hydraulic checks.
8. When should I avoid using Manning results alone?
Avoid relying on Manning alone when flow is rapidly varied, pressurized, heavily backwater-controlled, sediment-laden, or strongly unsteady. In those situations, more detailed hydraulic analysis is usually needed.