Discharge given Froude Number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Discharge for GVF Flow = Froude Number/(sqrt(Top Width/([g]*Wetted Surface Area^3)))
Qf = Fr/(sqrt(T/([g]*S^3)))
This formula uses 1 Constants, 1 Functions, 4 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Discharge for GVF Flow - (Measured in Cubic Meter per Second) - Discharge for GVF Flow is rate of flow per unit time.
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.
Top Width - (Measured in Meter) - Top Width is defined as width at top of section.
Wetted Surface Area - (Measured in Square Meter) - Wetted Surface Area is the total area of outer surface in contact with the surrounding water.
STEP 1: Convert Input(s) to Base Unit
Froude Number: 10 --> No Conversion Required
Top Width: 2 Meter --> 2 Meter No Conversion Required
Wetted Surface Area: 4.01 Square Meter --> 4.01 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Qf = Fr/(sqrt(T/([g]*S^3))) --> 10/(sqrt(2/([g]*4.01^3)))
Evaluating ... ...
Qf = 177.812340655345
STEP 3: Convert Result to Output's Unit
177.812340655345 Cubic Meter per Second --> No Conversion Required
FINAL ANSWER
177.812340655345 177.8123 Cubic Meter per Second <-- Discharge for GVF Flow
(Calculation completed in 00.004 seconds)

Credits

Created by Rithik Agrawal
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

Discharge given Froude Number Formula

Discharge for GVF Flow = Froude Number/(sqrt(Top Width/([g]*Wetted Surface Area^3)))
Qf = Fr/(sqrt(T/([g]*S^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 Discharge given Froude Number?

Discharge given Froude Number calculator uses Discharge for GVF Flow = Froude Number/(sqrt(Top Width/([g]*Wetted Surface Area^3))) to calculate the Discharge for GVF Flow, The Discharge given Froude Number formula is defined as the amount of fluid flowing in the channel at any point of time. Discharge for GVF Flow is denoted by Qf symbol.

How to calculate Discharge given Froude Number using this online calculator? To use this online calculator for Discharge given Froude Number, enter Froude Number (Fr), Top Width (T) & Wetted Surface Area (S) and hit the calculate button. Here is how the Discharge given Froude Number calculation can be explained with given input values -> 177.1476 = 10/(sqrt(2/([g]*4.01^3))).

FAQ

What is Discharge given Froude Number?
The Discharge given Froude Number formula is defined as the amount of fluid flowing in the channel at any point of time and is represented as Qf = Fr/(sqrt(T/([g]*S^3))) or Discharge for GVF Flow = Froude Number/(sqrt(Top Width/([g]*Wetted Surface Area^3))). Froude Number is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders, Top Width is defined as width at top of section & Wetted Surface Area is the total area of outer surface in contact with the surrounding water.
How to calculate Discharge given Froude Number?
The Discharge given Froude Number formula is defined as the amount of fluid flowing in the channel at any point of time is calculated using Discharge for GVF Flow = Froude Number/(sqrt(Top Width/([g]*Wetted Surface Area^3))). To calculate Discharge given Froude Number, you need Froude Number (Fr), Top Width (T) & Wetted Surface Area (S). With our tool, you need to enter the respective value for Froude Number, Top Width & Wetted Surface Area 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 Discharge for GVF Flow?
In this formula, Discharge for GVF Flow uses Froude Number, Top Width & Wetted Surface Area. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Discharge for GVF Flow = ((Total Energy in Open Channel-Depth of Flow)*2*[g]*Wetted Surface Area^2)^0.5
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