Froude Number Calculator
Result
What Is a Froude Number Calculator?
A Froude number calculator compares the mean water velocity with the speed at which shallow surface waves travel. The resulting dimensionless number helps describe whether open-channel flow is subcritical, near-critical, or supercritical.
This calculator finds the Froude number using velocity, gravity, and hydraulic depth. You may enter velocity and hydraulic depth directly, or provide flow rate and channel geometry so the calculator can determine flow area, top width, hydraulic depth, and mean velocity before calculating the final Froude number.
The geometry method supports rectangular, trapezoidal, triangular, part-full circular, parabolic, and custom cross sections. The result also includes a flow-regime label and, for supercritical flow, a conditional description of the type of hydraulic jump that could form.
How the Froude Number Calculation Works
The calculator uses the open-channel Froude number relationship:
In this formula, Fr is the Froude number, V is mean flow velocity, g is gravitational acceleration, and D is hydraulic depth. The Froude number has no unit because the units cancel in the ratio.
Hydraulic depth is calculated as flow area divided by water-surface top width:
Here, A is the flow cross-sectional area and T is the top width of the water surface. For a rectangular channel, this relationship makes hydraulic depth equal to the entered flow depth.
When you choose the discharge and channel geometry method, the calculator first obtains mean velocity from discharge and flow area:
Here, Q is flow rate. The calculator also reports surface wave speed using:
Channel Geometry Formulas
For the geometry method, the selected channel shape determines how flow area and top width are calculated.
Rectangular channel:
Trapezoidal channel:
Triangular channel:
In these equations, b is bottom width, y is flow depth, and z is horizontal side slope per one unit of vertical rise.
For a part-full circular pipe, the calculator first determines the wetted central angle:
It then calculates flow area and water-surface top width as:
Here, Dp is pipe diameter. The entered flow depth must be less than the pipe diameter because the calculator treats this option as part-full open-channel flow.
For a parabolic channel, the calculator uses the entered water-surface top width and flow depth:
For the custom option, you enter flow area and top width directly rather than having the calculator derive them from a predefined shape.
Worked Example
Suppose the direct method uses the default SI values: a velocity of 2.4 m/s, hydraulic depth of 0.8 m, and gravity of 9.80665 m/s².
The calculator therefore displays a Froude number of 0.8569. Because this is below 0.95, it labels the result Subcritical (Tranquil Flow). It also displays hydraulic depth as 0.8 m, mean velocity as 2.4 m/s, and surface wave speed as 2.8009 m/s.
How to Use the Froude Number Calculator
- Choose an input method: Velocity + Hydraulic Depth or Discharge + Channel Geometry.
- Select either SI (Metric) or US Customary units.
- For the direct method, enter flow velocity and a positive hydraulic depth.
- For the geometry method, enter a positive flow rate and select the channel shape.
- Enter the dimensions requested for the selected shape, such as bottom width, side slope, flow depth, pipe diameter, top width, or custom area.
- Enter the gravitational acceleration. The default is 9.80665 m/s² in SI units or 32.174 ft/s² in U.S. Customary units.
- Select Calculate Froude Number to display the results.
The main result is the dimensionless Froude number. The calculator also shows its flow-regime classification, hydraulic depth, mean velocity, surface wave speed, and an explanation based on the relationship between water velocity and wave speed. With the geometry method, it additionally reports the calculated flow area and top width.
Selecting Reset restores the calculator's original SI settings and default input values.
How to Read Your Froude Number Result
The calculator uses a band of 0.05 around a Froude number of 1 when assigning its main flow-regime labels.
| Froude Number | Calculator Classification |
|---|---|
| Fr < 0.95 | Subcritical (Tranquil Flow) |
| 0.95 ≤ Fr ≤ 1.05 | Near-Critical (Unstable Zone) |
| Fr > 1.05 | Supercritical (Rapid Flow) |
For subcritical results, the calculated mean velocity is lower than the surface wave speed. In the near-critical band, the two speeds are close. For supercritical results, mean velocity exceeds surface wave speed.
When the result is supercritical, the calculator also displays an If a Hydraulic Jump Formed interpretation. It uses the following Froude-number ranges: below 1.7 for an undular jump, 1.7 to below 2.5 for a weak jump, 2.5 to below 4.5 for an oscillating jump, 4.5 to below 9 for a steady jump, and 9 or higher for a strong jump.
This hydraulic-jump output is conditional. It describes the calculator's jump category if a hydraulic jump forms; it does not determine that a jump will actually occur at a particular location.
Displayed numerical values are rounded to no more than four decimal places, with unnecessary trailing zeros removed. When you change between SI and U.S. Customary units, the calculator converts existing length, velocity, flow-rate, area, and gravity entries to the selected unit system.
These results are for informational calculation purposes. Actual open-channel behavior can depend on channel conditions and other design factors not entered into this calculator. Engineering applications should be checked against site conditions and applicable design standards.
Frequently Asked Questions
What does a Froude number of 1 mean?
A Froude number of 1 means the calculated mean flow velocity equals the surface wave speed because Fr = V/c. This calculator treats values from 0.95 through 1.05 as its near-critical zone rather than requiring the value to equal exactly 1.
What is hydraulic depth?
Hydraulic depth is flow area divided by the water-surface top width, or D = A/T. It is the length value used in this calculator's Froude number equation. In a rectangular channel, the calculator's geometry formulas make hydraulic depth equal to the flow depth.
Can I calculate Froude number from discharge instead of velocity?
Yes. Select Discharge + Channel Geometry. The calculator divides flow rate by the calculated cross-sectional area to obtain mean velocity. It then calculates hydraulic depth from area and top width before applying the Froude number formula.
Which channel shapes does the calculator support?
The geometry method includes rectangular, trapezoidal, triangular or V-notch, circular part-full pipe, parabolic, and custom sections. The custom option requires you to enter the flow area and water-surface top width directly.
Can flow velocity be zero?
Yes, the direct-input method accepts a flow velocity of zero or greater. Hydraulic depth and gravity must be positive. Under the geometry method, flow rate must also be positive, and the applicable channel dimensions must satisfy the calculator's validation rules.
Why must a circular pipe be only part full?
The circular option is specifically implemented for a part-full pipe with a free water surface. The calculator rejects a flow depth equal to or greater than the pipe diameter and states that the open-channel Froude number is undefined for a full pipe in this calculation.
Does changing units change the Froude number?
The Froude number itself is dimensionless. When you switch unit systems, the calculator converts the existing dimensional inputs so they represent the same quantities in the new units. Small visible differences can occur from its input and result formatting to four decimal places.