Area of Section given Froude Number Calculator

✖Discharge for GVF Flow is rate of flow per unit time.ⓘ Discharge for GVF Flow [Q_f]			+10% -10%
✖Top Width is defined as width at top of section.ⓘ Top Width [T]			+10% -10%
✖Froude Number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.ⓘ Froude Number [Fr]			+10% -10%

✖Wetted Surface Area is the total area of outer surface in contact with the surrounding water.ⓘ Area of Section given Froude Number [S]

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Formula

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Area of Section given Froude Number

Formula

`"S" = (("Q"_{"f"}^2*"T"/("[g]"*"Fr"^2)))^(1/3)`

Example

`"3.997777m²"=((("177m³/s")^2*"2m"/("[g]"*("10")^2)))^(1/3)`

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Download Gradually Varied Flow in Channels Formulas PDF

Area of Section given Froude Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Wetted Surface Area = ((Discharge for GVF Flow^2*Top Width/([g]*Froude Number^2)))^(1/3)
S = ((Q_f^2*T/([g]*Fr^2)))^(1/3)
This formula uses 1 Constants, 4 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665

Variables Used

Wetted Surface Area - (Measured in Square Meter) - Wetted Surface Area is the total area of outer surface in contact with the surrounding water.
Discharge for GVF Flow - (Measured in Cubic Meter per Second) - Discharge for GVF Flow is rate of flow per unit time.
Top Width - (Measured in Meter) - Top Width is defined as width at top of section.
Froude Number - Froude Number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.

STEP 1: Convert Input(s) to Base Unit

Discharge for GVF Flow: 177 Cubic Meter per Second --> 177 Cubic Meter per Second No Conversion Required
Top Width: 2 Meter --> 2 Meter No Conversion Required
Froude Number: 10 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = ((Q_f^2*T/([g]*Fr^2)))^(1/3) --> ((177^2*2/([g]*10^2)))^(1/3)

Evaluating ... ...

S = 3.99777748351656

STEP 3: Convert Result to Output's Unit

3.99777748351656 Square Meter --> No Conversion Required

FINAL ANSWER

3.99777748351656 ≈ 3.997777 Square Meter <-- Wetted Surface Area

(Calculation completed in 00.004 seconds)

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National Institute of Technology Karnataka (NITK), Surathkal

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< 24 Gradually Varied Flow in Channels Calculators

Area of Section given Energy Gradient

Go Wetted Surface Area = (Discharge by Energy Gradient^2*Top Width/((1-(Hydraulic Gradient to Head Loss/Slope of Line))*([g])))^(1/3)

Discharge given Energy Gradient

Go Discharge by Energy Gradient = (((1-(Hydraulic Gradient to Head Loss/Slope of Line))*([g]*Wetted Surface Area^3)/Top Width))^0.5

Top Width given Energy Gradient

Go Top Width = ((1-(Hydraulic Gradient to Head Loss/Slope of Line))*([g]*Wetted Surface Area^3)/Discharge by Energy Gradient^2)

Slope of Dynamic Equation of Gradually Varied Flow given Energy Gradient

Go Slope of Line = Hydraulic Gradient to Head Loss/(1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))

Energy Gradient given Slope

Go Hydraulic Gradient to Head Loss = (1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))*Slope of Line

Froude Number given Top Width

Go Froude Number = sqrt(Discharge for GVF Flow^2*Top Width/([g]*Wetted Surface Area^3))

Discharge given Froude Number

Go Discharge for GVF Flow = Froude Number/(sqrt(Top Width/([g]*Wetted Surface Area^3)))

Area of Section given Total Energy

Go Wetted Surface Area = ((Discharge for GVF Flow^2)/(2*[g]*(Total Energy in Open Channel-Depth of Flow)))^0.5

Depth of Flow given Total Energy

Go Depth of Flow = Total Energy in Open Channel-((Discharge for GVF Flow^2)/(2*[g]*Wetted Surface Area^2))

Discharge given Total Energy

Go Discharge for GVF Flow = ((Total Energy in Open Channel-Depth of Flow)*2*[g]*Wetted Surface Area^2)^0.5

Total Energy of Flow

Go Total Energy in Open Channel = Depth of Flow+(Discharge for GVF Flow^2)/(2*[g]*Wetted Surface Area^2)

Froude Number given Slope of Dynamic Equation of Gradually Varied Flow

Go Froude No by Dynamic Equation = sqrt(1-((Bed Slope of Channel-Energy Slope)/Slope of Line))

Area of Section given Froude Number

Go Wetted Surface Area = ((Discharge for GVF Flow^2*Top Width/([g]*Froude Number^2)))^(1/3)

Top Width given Froude Number

Go Top Width = (Froude Number^2*Wetted Surface Area^3*[g])/(Discharge for GVF Flow^2)

Bed Slope given Slope of Dynamic Equation of Gradually Varied Flow

Go Bed Slope of Channel = Energy Slope+(Slope of Line*(1-(Froude No by Dynamic Equation^2)))

Slope of Dynamic Equation of Gradually Varied Flows

Go Slope of Line = (Bed Slope of Channel-Energy Slope)/(1-(Froude No by Dynamic Equation^2))

Depth of Flow given Energy Slope of Rectangular channel

Go Depth of Flow = Critical Depth of Channel/((Energy Slope/Bed Slope of Channel)^(3/10))

Normal Depth given Energy Slope of Rectangular channel

Go Critical Depth of Channel = ((Energy Slope/Bed Slope of Channel)^(3/10))*Depth of Flow

Chezy Formula for Depth of Flow given Energy Slope of Rectangular Channel

Go Depth of Flow = Critical Depth of Channel/((Energy Slope/Bed Slope of Channel)^(1/3))

Chezy Formula for Normal Depth given Energy Slope of Rectangular Channel

Go Critical Depth of Channel = ((Energy Slope/Bed Slope of Channel)^(1/3))*Depth of Flow

Bed Slope given Energy Slope of Rectangular channel

Go Bed Slope of Channel = Energy Slope/(Critical Depth of Channel/Depth of Flow)^(10/3)

Chezy Formula for Bed Slope given Energy Slope of Rectangular Channel

Go Bed Slope of Channel = Energy Slope/(Critical Depth of Channel/Depth of Flow)^(3)

Bottom Slope of Channel given Energy Gradient

Go Bed Slope of Channel = Hydraulic Gradient to Head Loss+Energy Slope

Energy Gradient given Bed Slope

Go Hydraulic Gradient to Head Loss = Bed Slope of Channel-Energy Slope

Area of Section given Froude Number Formula

Wetted Surface Area = ((Discharge for GVF Flow^2*Top Width/([g]*Froude Number^2)))^(1/3)
S = ((Q_f^2*T/([g]*Fr^2)))^(1/3)

What is Froude Number?

In continuum mechanics, the Froude number is a dimensionless number defined as the ratio of the flow inertia to the external field.

How to Calculate Area of Section given Froude Number?

Area of Section given Froude Number calculator uses Wetted Surface Area = ((Discharge for GVF Flow^2*Top Width/([g]*Froude Number^2)))^(1/3) to calculate the Wetted Surface Area, The Area of Section given Froude Number is defined as the amount of surface which in contact with water at any time. Wetted Surface Area is denoted by S symbol.

How to calculate Area of Section given Froude Number using this online calculator? To use this online calculator for Area of Section given Froude Number, enter Discharge for GVF Flow (Q_f), Top Width (T) & Froude Number (Fr) and hit the calculate button. Here is how the Area of Section given Froude Number calculation can be explained with given input values -> 3.997777 = ((177^2*2/([g]*10^2)))^(1/3).

FAQ

What is Area of Section given Froude Number?

The Area of Section given Froude Number is defined as the amount of surface which in contact with water at any time and is represented as S = ((Q_f^2*T/([g]*Fr^2)))^(1/3) or Wetted Surface Area = ((Discharge for GVF Flow^2*Top Width/([g]*Froude Number^2)))^(1/3). Discharge for GVF Flow is rate of flow per unit time, Top Width is defined as width at top of section & Froude Number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.

How to calculate Area of Section given Froude Number?

The Area of Section given Froude Number is defined as the amount of surface which in contact with water at any time is calculated using Wetted Surface Area = ((Discharge for GVF Flow^2*Top Width/([g]*Froude Number^2)))^(1/3). To calculate Area of Section given Froude Number, you need Discharge for GVF Flow (Q_f), Top Width (T) & Froude Number (Fr). With our tool, you need to enter the respective value for Discharge for GVF Flow, Top Width & Froude Number and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Wetted Surface Area?

In this formula, Wetted Surface Area uses Discharge for GVF Flow, Top Width & Froude Number. We can use 2 other way(s) to calculate the same, which is/are as follows -

Wetted Surface Area = ((Discharge for GVF Flow^2)/(2*[g]*(Total Energy in Open Channel-Depth of Flow)))^0.5
Wetted Surface Area = (Discharge by Energy Gradient^2*Top Width/((1-(Hydraulic Gradient to Head Loss/Slope of Line))*([g])))^(1/3)

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