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Froude Number Calculator: Open Channel Flow

This calculation tool is designed to help you quickly and accurately determine the hydraulic depth of a flowing body of water.

Calculation

Froude Number

Inputs



V1
:5m/s​



D1
:3m​


Output



Fr1
:0.92167​



Hydraulic Depth

Inputs



Fr2
:0.92​



V2
:5​


Output



D2
:3.011​


Explanation

The Froude number, Fr, is a dimensionless value that describes different flow regimes of open channel flow. The Froude number is a ratio of inertial and gravitational forces.
It's used in fluid dynamics to measure the relative importance of gravity and inertia forces in a flow. The Froude Number can range from 0 to infinity, with 0 representing a flow with no inertia and infinity representing a flow with no gravity.

The Froude number is calculated as the ratio of the inertial force of the flow to the gravitational force of the flow.

Fr=VgD{\displaystyle \mathrm {Fr} ={\frac {V}{\sqrt {gD}}}}

Where:

Fr=Froude NumberV=Water velocityg=gravityD=cross sectional area of flowtopwidth=Hydraulic depth{\displaystyle \mathrm {Fr}} = Froude \space Number \\ V = Water \space velocity \\ g = gravity \\ D= \frac{cross \space sectional \space area \space of \space flow}{top width} =Hydraulic \space depth
When:

Fr=1, critical flow,Fr>1, supercritical flow (fast rapid flow)Fr<1, subcritical flow (tranquil flow)\mathrm {Fr} = 1, \space critical \space flow, \\ \mathrm {Fr} > 1, \space supercritical \space flow \space (fast \space rapid \space flow) \\ \mathrm {Fr} < 1, \space subcritical \space flow \space (tranquil \space flow)

The hydraulic depth can be solved by rearranging the formula to solve for flow depth. This is shown below:

D=V2gFr2{\displaystyle D=\frac{V^2}{g\mathrm Fr^2}}

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