Froude Number Calculator

Area of Cross-Section (\( A \)):

Width of the Channel (\( W \)):

Flow Velocity (\( u \)):

Acceleration Due to Gravity (\( g \)):

1. What is Froude Number Calculator?

Definition: This calculator computes the Froude number (\( F_r \)) and hydraulic depth (\( H_d \)) for a fluid flow in an open channel using the Froude number equation, based on the area of the cross-section, width of the channel, flow velocity, and acceleration due to gravity.

Purpose: It is used in fluid dynamics and hydraulic engineering to determine the flow regime (subcritical, critical, or supercritical) in open channels, aiding in the design of channels, rivers, and spillways.

2. How Does the Calculator Work?

The calculator uses the Froude number equation in SI units:

\( H_d = \frac{A}{W} \)
\( F_r = \frac{u}{\sqrt{g H_d}} \)

Where:

\( H_d \): Hydraulic depth (m, converted to selected unit);
\( A \): Area of the cross-section (m²);
\( W \): Width of the channel (m);
\( F_r \): Froude number (dimensionless);
\( u \): Flow velocity (m/s);
\( g \): Acceleration due to gravity (m/s²).

Steps:

Enter the area of the cross-section (\( A \)) with its unit.
Enter the width of the channel (\( W \)) with its unit.
Enter the flow velocity (\( u \)) with its unit.
Enter the acceleration due to gravity (\( g \)) with its unit (default is 9.81 m/s²).
Convert \( A \), \( W \), \( u \), and \( g \) to SI units (m², m, m/s, m/s²).
Calculate the hydraulic depth: \( H_d = \frac{A}{W} \).
Convert \( H_d \) to the selected output unit.
Calculate the Froude number: \( F_r = \frac{u}{\sqrt{g H_d}} \).
Display the results, formatted in scientific notation if the absolute value is less than 0.001, otherwise with 5 decimal places.

3. Importance of Froude Number Calculation

Calculating the Froude number is crucial for:

Flow Regime Analysis: Determining whether the flow is subcritical (\( F_r < 1 \)), critical (\( F_r = 1 \)), or supercritical (\( F_r > 1 \)), which affects channel design and stability.
Hydraulic Design: Designing open channels, spillways, and weirs to manage flow behavior and prevent issues like erosion or flooding.
Wave Propagation: Understanding wave behavior in channels, as the Froude number influences wave speed relative to the flow.

4. Using the Calculator

Example 1 (SI Units): Calculate \( H_d \) and \( F_r \) for a channel:

Area of Cross-Section: \( A = 2 \, \text{m}^2 \);
Width of the Channel: \( W = 4 \, \text{m} \);
Flow Velocity: \( u = 3 \, \text{m/s} \);
Acceleration Due to Gravity: \( g = 9.81 \, \text{m/s}^2 \);
Hydraulic Depth: \( H_d = \frac{A}{W} = \frac{2}{4} = 0.5 \, \text{m} \);
Froude Number: \( F_r = \frac{u}{\sqrt{g H_d}} = \frac{3}{\sqrt{9.81 \times 0.5}} \approx 1.353 \);
Result: \( H_d = 0.50000 \, \text{m} \), \( F_r = 1.35300 \).

Example 2 (Mixed Units): Calculate \( H_d \) and \( F_r \) for a channel:

Area of Cross-Section: \( A = 144 \, \text{in}^2 \);
Convert \( A \): \( A = 144 \times 0.00064516 = 0.092903 \, \text{m}^2 \);
Width of the Channel: \( W = 3 \, \text{ft} \);
Convert \( W \): \( W = 3 \times 0.3048 = 0.9144 \, \text{m} \);
Flow Velocity: \( u = 5 \, \text{ft/s} \);
Convert \( u \): \( u = 5 \times 0.3048 = 1.524 \, \text{m/s} \);
Acceleration Due to Gravity: \( g = 32.2 \, \text{ft/s}^2 \);
Convert \( g \): \( g = 32.2 \times 0.3048 = 9.81456 \, \text{m/s}^2 \);
Hydraulic Depth: \( H_d = \frac{A}{W} = \frac{0.092903}{0.9144} \approx 0.1016 \, \text{m} \);
Convert \( H_d \) to ft: \( H_d = 0.1016 \times 3.28084 \approx 0.3333 \, \text{ft} \);
Froude Number: \( F_r = \frac{u}{\sqrt{g H_d}} = \frac{1.524}{\sqrt{9.81456 \times 0.1016}} \approx 1.526 \);
Result: \( H_d = 0.33330 \, \text{ft} \), \( F_r = 1.52600 \).

5. Frequently Asked Questions (FAQ)

Q: What does the Froude number indicate?
A: The Froude number indicates the flow regime: \( F_r < 1 \) (subcritical, tranquil flow), \( F_r = 1 \) (critical flow), or \( F_r > 1 \) (supercritical, rapid flow).

Q: Why is the calculator using only the SI formula?
A: The SI formula ensures consistency, but the calculator allows input and output in various units, converting them to SI units (m², m, m/s, m/s²) for calculation, ensuring accurate results.

Q: Can this calculator be used for closed conduits?
A: The Froude number is typically used for open channel flows. For closed conduits, other dimensionless numbers like the Reynolds number may be more appropriate.