Discharge given Energy Gradient Solution

STEP 0: Pre-Calculation Summary
Formula Used
Discharge by Energy Gradient = (((1-(Hydraulic Gradient to Head Loss/Slope of Line))*([g]*Wetted Surface Area^3)/Top Width))^0.5
Qeg = (((1-(i/m))*([g]*S^3)/T))^0.5
This formula uses 1 Constants, 5 Variables
Constants Used
[g] - Gravitational acceleration on Earth Value Taken As 9.80665
Variables Used
Discharge by Energy Gradient - (Measured in Cubic Meter per Second) - Discharge by Energy Gradient is rate of floe per unit time.
Hydraulic Gradient to Head Loss - Hydraulic Gradient to Head Loss is a specific measurement of liquid pressure above a vertical datum.
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.
Wetted Surface Area - (Measured in Square Meter) - Wetted Surface Area is the total area of outer surface in contact with the surrounding water.
Top Width - (Measured in Meter) - Top Width is defined as width at top of section.
STEP 1: Convert Input(s) to Base Unit
Hydraulic Gradient to Head Loss: 2.02 --> No Conversion Required
Slope of Line: 4 --> No Conversion Required
Wetted Surface Area: 4.01 Square Meter --> 4.01 Square Meter No Conversion Required
Top Width: 2 Meter --> 2 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Qeg = (((1-(i/m))*([g]*S^3)/T))^0.5 --> (((1-(2.02/4))*([g]*4.01^3)/2))^0.5
Evaluating ... ...
Qeg = 12.5102070735138
STEP 3: Convert Result to Output's Unit
12.5102070735138 Cubic Meter per Second --> No Conversion Required
FINAL ANSWER
12.5102070735138 12.51021 Cubic Meter per Second <-- Discharge by Energy Gradient
(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

Discharge given Energy Gradient Formula

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

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 Discharge given Energy Gradient?

Discharge given Energy Gradient calculator uses Discharge by Energy Gradient = (((1-(Hydraulic Gradient to Head Loss/Slope of Line))*([g]*Wetted Surface Area^3)/Top Width))^0.5 to calculate the Discharge by Energy Gradient, The Discharge given Energy Gradient formula is defined as the amount of fluid in the channel in open channel section. Discharge by Energy Gradient is denoted by Qeg symbol.

How to calculate Discharge given Energy Gradient using this online calculator? To use this online calculator for Discharge given Energy Gradient, enter Hydraulic Gradient to Head Loss (i), Slope of Line (m), Wetted Surface Area (S) & Top Width (T) and hit the calculate button. Here is how the Discharge given Energy Gradient calculation can be explained with given input values -> 12.46344 = (((1-(2.02/4))*([g]*4.01^3)/2))^0.5.

FAQ

What is Discharge given Energy Gradient?
The Discharge given Energy Gradient formula is defined as the amount of fluid in the channel in open channel section and is represented as Qeg = (((1-(i/m))*([g]*S^3)/T))^0.5 or Discharge by Energy Gradient = (((1-(Hydraulic Gradient to Head Loss/Slope of Line))*([g]*Wetted Surface Area^3)/Top Width))^0.5. Hydraulic Gradient to Head Loss is a specific measurement of liquid pressure above a vertical datum, 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, Wetted Surface Area is the total area of outer surface in contact with the surrounding water & Top Width is defined as width at top of section.
How to calculate Discharge given Energy Gradient?
The Discharge given Energy Gradient formula is defined as the amount of fluid in the channel in open channel section is calculated using Discharge by Energy Gradient = (((1-(Hydraulic Gradient to Head Loss/Slope of Line))*([g]*Wetted Surface Area^3)/Top Width))^0.5. To calculate Discharge given Energy Gradient, you need Hydraulic Gradient to Head Loss (i), Slope of Line (m), Wetted Surface Area (S) & Top Width (T). With our tool, you need to enter the respective value for Hydraulic Gradient to Head Loss, Slope of Line, Wetted Surface Area & Top Width 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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