Open Channel Flow Calculator
Flow Analysis
What Is an Open Channel Flow Calculator?
An open channel flow calculator estimates how much water moves through a channel with a free surface exposed to the atmosphere. This calculator applies Manning’s equation to a trapezoidal cross-section. Setting the side slope to zero creates a rectangular channel, while setting the bottom width to zero creates a triangular channel.
To calculate open channel flow, enter the bottom width, side slope, flow depth, channel bed slope, and Manning’s roughness coefficient. The tool calculates discharge in cubic meters per second, velocity in meters per second, hydraulic geometry, and the Froude number used to identify the flow regime.
The calculator is intended for uniform, steady-flow estimates. Although the target audience may include users in the United States, all input and output units are metric. It does not convert dimensions to feet or discharge to cubic feet per second.
How the Open Channel Flow Calculator Formula Works
The calculation begins with the geometry of the channel. For a trapezoidal section, the cross-sectional flow area is:
The wetted perimeter is the length of the channel boundary touching the water:
Hydraulic radius equals the flow area divided by the wetted perimeter:
The calculator then applies Manning’s equation in metric units:
- b is the bottom width in meters.
- z is the horizontal side slope for each one unit of vertical rise.
- y is the flow depth in meters.
- S is the bed slope in meters per meter.
- n is Manning’s roughness coefficient.
- V is average flow velocity in meters per second.
- Q is volumetric flow rate in cubic meters per second.
Worked Example
Assume a bottom width of 3 meters, a side slope of 2:1, a depth of 1.5 meters, a bed slope of 0.001, and a Manning’s n value of 0.015.
Because values below 100 use scientific notation in the displayed flow and velocity fields, the calculator shows approximately 1.80e+1 m³/s and 2.00e+0 m/s. Depth, slope, and Manning’s n must be greater than zero or the result remains hidden.
How to Use the Open Channel Flow Calculator: Step by Step
- Enter the Bottom Width in meters. This is the flat width across the base of the channel.
- Enter the Side Slope as a horizontal-to-vertical ratio. For example, enter 2 for a 2:1 side slope.
- Use a side slope of 0 for a rectangular channel. Use a bottom width of 0 with a positive side slope for a triangular channel.
- Enter the Flow Depth in meters. This must be greater than zero for the calculator to display results.
- Enter the Bed Slope in meters per meter. A slope of 0.001 represents a vertical drop of 0.001 meter per horizontal meter.
- Enter Manning’s Roughness. This dimensionless value represents resistance caused by the channel surface.
- Select Calculate to view discharge, velocity, flow regime, Froude number, and channel metrics.
- Select Reset to clear every input and hide the previous result.
The main result is the volumetric flow rate in cubic meters per second. The next output shows velocity and classifies the flow as subcritical, critical, or supercritical. The channel metrics provide area, wetted perimeter, hydraulic radius, top width, and hydraulic depth. These values help explain how the calculator reached its result.
How to Read Your Open Channel Flow Calculator Results
Flow Rate and Velocity
Flow rate measures the volume of water passing through the section each second. Velocity measures the average speed of that water. A larger flow area, steeper bed slope, larger hydraulic radius, or lower Manning’s n can increase the calculated discharge under the model used by the tool.
Froude Number and Flow Regime
The calculator finds top width and hydraulic depth before calculating the Froude number:
| Froude Number | Calculator Classification | Interpretation |
|---|---|---|
| Fr < 1 | Subcritical | Tranquil flow controlled mainly by downstream conditions. Gravity waves can travel upstream. |
| Fr = 1 | Critical | The flow is at the threshold between subcritical and supercritical conditions. |
| Fr > 1 | Supercritical | Rapid flow controlled mainly by upstream conditions. Downstream disturbances cannot travel upstream. |
Channel Shape
A positive bottom width and positive side slope produce a trapezoidal channel. A zero side slope produces vertical sides and is treated as rectangular. A zero bottom width with sloped sides produces a triangular section. Use physically valid, nonnegative dimensions even though the calculation script does not separately reject negative width or side-slope entries.
Important Model Limitations
Manning’s equation assumes steady, uniform flow. The channel shape, depth, slope, and roughness are treated as constant at the analyzed section. The calculator does not model gradually varied flow, changing water depth, wind shear, sediment transport, culvert control, hydraulic jumps, or backwater effects. Field conditions may therefore produce different results.
Frequently Asked Questions
What is Manning’s equation for open channel flow?
Manning’s equation estimates average velocity from hydraulic radius, bed slope, and surface roughness. This calculator uses the metric form: velocity equals one divided by Manning’s n, multiplied by hydraulic radius to the two-thirds power and slope to the one-half power. Discharge then equals area multiplied by velocity.
How do you calculate flow through a trapezoidal channel?
Calculate the cross-sectional area and wetted perimeter from the bottom width, side slope, and water depth. Divide area by wetted perimeter to find hydraulic radius. Manning’s equation then gives velocity from hydraulic radius, bed slope, and roughness. Multiply velocity by area to find the volumetric flow rate.
Can this calculator handle rectangular channels?
Yes. Enter zero for the side slope to model a rectangular channel with vertical walls. The calculator still uses the entered bottom width, depth, slope, and Manning’s n. Its summary identifies the section as rectangular whenever the side-slope value is exactly zero.
Can this calculator handle triangular channels?
Yes. Enter zero for the bottom width and a positive value for the side slope. The area and wetted perimeter formulas then represent a triangular section. Do not set both the bottom width and side slope to zero because that creates a channel with no valid flow area.
What Manning’s roughness value should I enter?
Enter the Manning’s n value that represents the channel surface being analyzed. The calculator does not select a value based on material or condition. Users must supply the coefficient. Since discharge changes with roughness, an unsuitable n value can noticeably change the calculated velocity and flow rate.
What does a Froude number below 1 mean?
A Froude number below 1 means the calculator classifies the flow as subcritical. The water is moving slowly enough for gravity waves to travel upstream. Such flow is described as tranquil and is mainly influenced by downstream conditions, including control structures that affect the water depth.
How accurate is an open channel flow calculator?
The calculator accurately applies its programmed geometry and Manning formulas to the entered values. Real accuracy depends on correct dimensions, slope, depth, and roughness. Results may differ where flow is not steady and uniform or where sediment, backwater, changing geometry, wind, or other hydraulic effects are important.