# Froude Number Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Feb 02, 2023

Froude number calculator helps you characterize the fluid flow in an open channel by estimating the Froude number for the given flow rate. The Froude number formula is critical in a wide range of fields relating to open channel flow (refer open channel flow calculator) such as waves, spillways, weirs, ripraps (see ripraps calculator), wind engineering, pipe flow, estimating hydraulic jump (see hydraulic jump calculator), partially submerged vessels moving through water, i.e., ship design. Scroll down to read more and understand how to calculate the Froude number.

## What is Froude number?

The Froude number is a dimensionless number which determines the effect of external forces (mostly, gravity) on a fluid flow. In other words, the ratio of inertia of flow to the gravity is known as Froude number. The Froude number $F_\mathrm{r}$ is affected by the acceleration due to gravity g, flow velocity u, and hydraulic depth $H_\mathrm{d}$, such that:

$F_\mathrm{r} = \frac{u}{\sqrt{g H_\mathrm{d}}}$

The hydraulic depth, $H_\mathrm{d}$ is defined as the ratio of area of the cross-section of the channel, A to the width of the channel, W. Mathematically,

$H = \frac{A}{W}$

For some applications such as ship hydrodynamics, the hydraulic depth is replaced by characteristic length L, which is the length of the ship at the waterline. Waterline is the point where the hull of the ship meets the surface of the water body.

## How to calculate Froude number?

Follow the steps below to learn how to calculate Froude number.

1. Enter the area of cross-section.

2. Use the width of the channel to estimate the hydraulic depth.

3. Input the flow velocity.

4. The calculator returns the Froude number.

## Example: Using the Froude number calculator

Determine the Froude number for a fluid flow in an open channel having area of cross-section, $1 ~\mathrm{m^2}$ and width 0.5 m. The flow velocity is 1 m/s. Use acceleration due to gravity as 9.81 m/s.

• Step 1 & 2: Enter the area of cross-section and width of the channel to estimate the hydraulic depth.
\scriptsize \begin{align*} \qquad H &= \frac{A}{W} \\ \qquad &= \frac{1}{0.5} = 2 \end{align*}
• Step 3: Input the flow velocity, 1 m/s.

• Step 4: The calculator produces the Froude number:

\scriptsize \begin{align*} \qquad F_\mathrm{r} &= \frac{u}{\sqrt{g H_\mathrm{d}}} \\ &= \frac{1}{\sqrt{9.81 \times 2}} = 0.22576 \end{align*}

Alternatively, you can also calculate the dimensions of the channel or flow velocity based on the Froude number.

For example, let's find the width of the channel given the area of cross-section is $1.5 \ \mathrm{m^2}$ and the fluid flow velocity is 2 m/s. The Froude number is 0.4.

• Step 1: Estimate the hydraulic depth using the Froude number formula.
\scriptsize \begin{align*} \qquad H_\mathrm{d} &= \frac{u^2}{F_\mathrm{r}^{2} g} \\ &= \frac{2^2}{0.4^{2} \times 9.81} = 2.5484 \ \mathrm{m} \end{align*}
• Step 2: Now use the hydraulic depth formula to calculate the width of the channel.

• Step 3: The width of the channel is returned by the calculator as 0.5886 m.

\scriptsize \begin{align*} \qquad W &= \frac{A}{H} \\ &= \frac{1.5}{2.5484} = 0.5886 \ \mathrm{ m} \end{align*}

Therefore, you can use the Froude number formula backwards to find out the channel dimensions.

## Using the Froude number

The flow is characterized as supercritical ($F_\mathrm{r} > 1$) or subcritical ($F_\mathrm{r} < 1$) based on the value of Froude number. If the Froude number is around 1, then it's called critical flow.

The number is crucial in the concept of hydraulic jump which is used to estimate the jump in water surface level occurring under different flow conditions. The Froude number is used similarly as Reynold's number is used to differentiate between the laminar and turbulent flow.

Rahul Dhari
Area of cross-section (A)
in²
Width of the channel (W)
in
Hydraulic mean depth (Hd)
in
Flow velocity (u)
m/s
Acceleration due to gravity (g)
ft/s²
Froude number (Fᵣ)
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