Froude Number Formula Calculator

\[ Fr = \frac{v}{\sqrt{gL}} \]

Flow Velocity (\(v\)):

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

Characteristic Length (\(L\)):

1. What is the Froude Number Formula Calculator?

Definition: This calculator computes the Froude number (\(Fr\)), a dimensionless quantity that compares the flow velocity to the speed of gravity-driven waves, using the formula \(Fr = \frac{v}{\sqrt{gL}}\).

Purpose: It is used in fluid dynamics to analyze open-channel flow, ship hydrodynamics, and other scenarios where inertial and gravitational forces are significant.

2. How Does the Calculator Work?

The calculator uses the Froude number formula:

Formula: \[ Fr = \frac{v}{\sqrt{gL}} \] where:

\(Fr\): Froude number (unitless)
\(v\): Flow velocity (m/s, cm/s)
\(g\): Acceleration due to gravity (m/s², cm/s²)
\(L\): Characteristic length (m, cm)

Unit Conversions:

Velocity:
- 1 m/s = 1 m/s
- 1 cm/s = 0.01 m/s
Gravity:
- 1 m/s² = 1 m/s²
- 1 cm/s² = 0.01 m/s²
Length:
- 1 m = 1 m
- 1 cm = 0.01 m

Steps:

Enter the flow velocity (\(v\)), acceleration due to gravity (\(g\)), and characteristic length (\(L\)) with their units (default: \(v = 1 \, \text{m/s}\), \(g = 9.81 \, \text{m/s}^2\), \(L = 1 \, \text{m}\)).
Convert inputs to SI units (m/s, m/s², m).
Validate that gravity and length are greater than 0.
Calculate the Froude number: \(Fr = \frac{v}{\sqrt{gL}}\).
Display the result, rounded to 4 decimal places.

3. Importance of Froude Number Calculation

Calculating the Froude number is crucial for:

Fluid Dynamics: Determining whether flow is subcritical (\(Fr < 1\)), critical (\(Fr = 1\)), or supercritical (\(Fr > 1\)) in channels or rivers.
Naval Architecture: Scaling ship models to predict wave patterns and resistance in full-scale vessels.
Education: Teaching dimensional analysis and the role of inertial versus gravitational forces in fluid mechanics.

4. Using the Calculator

Examples:

Example 1: Calculate the Froude number for \(v = 2 \, \text{m/s}\), \(g = 9.81 \, \text{m/s}^2\), \(L = 1 \, \text{m}\):
- Enter \(v = 2 \, \text{m/s}\), \(g = 9.81 \, \text{m/s}^2\), \(L = 1 \, \text{m}\).
- Froude number: \(Fr = \frac{v}{\sqrt{gL}} = \frac{2}{\sqrt{9.81 \times 1}} = \frac{2}{\sqrt{9.81}} \approx \frac{2}{3.132} \approx 0.6383\).
- Result: \( \text{Froude Number} = 0.6383 \).
Example 2: Calculate the Froude number for \(v = 50 \, \text{cm/s}\), \(g = 981 \, \text{cm/s}^2\), \(L = 100 \, \text{cm}\):
- Enter \(v = 50 \, \text{cm/s}\), \(g = 981 \, \text{cm/s}^2\), \(L = 100 \, \text{cm}\).
- Convert: \(v = 0.5 \, \text{m/s}\), \(g = 9.81 \, \text{m/s}^2\), \(L = 1 \, \text{m}\).
- Froude number: \(Fr = \frac{0.5}{\sqrt{9.81 \times 1}} = \frac{0.5}{\sqrt{9.81}} \approx \frac{0.5}{3.132} \approx 0.1596\).
- Result: \( \text{Froude Number} = 0.1596 \).

5. Frequently Asked Questions (FAQ)

Q: What is the Froude number?
A: The Froude number is a dimensionless quantity that represents the ratio of a fluid’s inertial forces to gravitational forces, used to characterize flow regimes.

Q: Why must gravity and length be greater than zero?
A: A zero or negative value for gravity or length would make the denominator undefined or physically meaningless, as these represent physical quantities in the system.

Q: What does the Froude number indicate?
A: A Froude number less than 1 indicates subcritical flow (slower than wave speed), equal to 1 indicates critical flow, and greater than 1 indicates supercritical flow (faster than wave speed).