Open Channel Flow

This calculation tool is designed to help you quickly and accurately determine the hydraulic depth of a flowing body of water.
CalculationFroude NumberInputs﻿﻿V1
:5m/s​
﻿
﻿﻿D1
:3m​
﻿
Output﻿﻿Fr1
:0.92167​
﻿
﻿
Hydraulic DepthInputs﻿﻿Fr2
:0.92​
﻿
﻿﻿V2
:5​
﻿
Output﻿﻿D2
:3.011​
﻿
ExplanationThe 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}}}}Fr=gD​V​
﻿
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 depthFr=Froude NumberV=Water velocityg=gravityD=topwidthcross sectional area of flow​=Hydraulic 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)Fr=1, critical flow,Fr>1, supercritical flow (fast rapid flow)Fr<1, subcritical flow (tranquil 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}}D=gFr2V2​
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