Froude Number given Slope of Dynamic Equation of Gradually Varied Flow Solution

STEP 0: Pre-Calculation Summary
Formula Used
Froude No by Dynamic Equation = sqrt(1-((Bed Slope of Channel-Energy Slope)/Slope of Line))
Fr(d) = sqrt(1-((S0-Sf)/m))
This formula uses 1 Functions, 4 Variables
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
Froude No by Dynamic Equation - Froude No by Dynamic Equation is a measurement of bulk flow characteristics such as waves, sand bedforms, flow/depth interactions at a cross section or between boulders.
Bed Slope of Channel - Bed Slope of Channel is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow.
Energy Slope - Energy Slope is at a distance equal to the velocity head above the hydraulic gradient.
Slope of Line - The Slope of Line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.
STEP 1: Convert Input(s) to Base Unit
Bed Slope of Channel: 4.001 --> No Conversion Required
Energy Slope: 2.001 --> No Conversion Required
Slope of Line: 4 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Fr(d) = sqrt(1-((S0-Sf)/m)) --> sqrt(1-((4.001-2.001)/4))
Evaluating ... ...
Fr(d) = 0.707106781186547
STEP 3: Convert Result to Output's Unit
0.707106781186547 --> No Conversion Required
FINAL ANSWER
0.707106781186547 โ‰ˆ 0.707107 <-- Froude No by Dynamic Equation
(Calculation completed in 00.004 seconds)

Credits

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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

Froude Number given Slope of Dynamic Equation of Gradually Varied Flow Formula

Froude No by Dynamic Equation = sqrt(1-((Bed Slope of Channel-Energy Slope)/Slope of Line))
Fr(d) = sqrt(1-((S0-Sf)/m))

What is Gradually Varied Flow?

Gradually varied. flow (GVF), which is a form of steady. nonuniform flow characterized by gradual variations in flow depth and velocity (small slopes and no abrupt changes) and a free surface that always remains smooth (no discontinuities or zigzags).

How to Calculate Froude Number given Slope of Dynamic Equation of Gradually Varied Flow?

Froude Number given Slope of Dynamic Equation of Gradually Varied Flow calculator uses Froude No by Dynamic Equation = sqrt(1-((Bed Slope of Channel-Energy Slope)/Slope of Line)) to calculate the Froude No by Dynamic Equation, The Froude Number given Slope of Dynamic Equation of Gradually Varied Flow is defined as the ratio of two forces in fluid plane. Froude No by Dynamic Equation is denoted by Fr(d) symbol.

How to calculate Froude Number given Slope of Dynamic Equation of Gradually Varied Flow using this online calculator? To use this online calculator for Froude Number given Slope of Dynamic Equation of Gradually Varied Flow, enter Bed Slope of Channel (S0), Energy Slope (Sf) & Slope of Line (m) and hit the calculate button. Here is how the Froude Number given Slope of Dynamic Equation of Gradually Varied Flow calculation can be explained with given input values -> 0.707107 = sqrt(1-((4.001-2.001)/4)).

FAQ

What is Froude Number given Slope of Dynamic Equation of Gradually Varied Flow?
The Froude Number given Slope of Dynamic Equation of Gradually Varied Flow is defined as the ratio of two forces in fluid plane and is represented as Fr(d) = sqrt(1-((S0-Sf)/m)) or Froude No by Dynamic Equation = sqrt(1-((Bed Slope of Channel-Energy Slope)/Slope of Line)). Bed Slope of Channel is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow, Energy Slope is at a distance equal to the velocity head above the hydraulic gradient & The Slope of Line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.
How to calculate Froude Number given Slope of Dynamic Equation of Gradually Varied Flow?
The Froude Number given Slope of Dynamic Equation of Gradually Varied Flow is defined as the ratio of two forces in fluid plane is calculated using Froude No by Dynamic Equation = sqrt(1-((Bed Slope of Channel-Energy Slope)/Slope of Line)). To calculate Froude Number given Slope of Dynamic Equation of Gradually Varied Flow, you need Bed Slope of Channel (S0), Energy Slope (Sf) & Slope of Line (m). With our tool, you need to enter the respective value for Bed Slope of Channel, Energy Slope & Slope of Line and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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