Energy Gradient given Slope Calculator

✖Discharge by Energy Gradient is rate of floe per unit time.ⓘ Discharge by Energy Gradient [Q_eg]			+10% -10%
✖Top Width is defined as width at top of section.ⓘ Top Width [T]			+10% -10%
✖Wetted Surface Area is the total area of outer surface in contact with the surrounding water.ⓘ Wetted Surface Area [S]			+10% -10%
✖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.ⓘ Slope of Line [m]			+10% -10%

✖Hydraulic Gradient to Head Loss is a specific measurement of liquid pressure above a vertical datum.ⓘ Energy Gradient given Slope [i]

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Formula

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Energy Gradient given Slope

Formula

`"i" = (1-("Q"_{"eg"}^2*"T"/("[g]"*"S"^3)))*"m"`

Example

`"2.02323"=(1-(("12.5m³/s")^2*"2m"/("[g]"*("4.01m²")^3)))*"4"`

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Download Gradually Varied Flow in Channels Formulas PDF

Energy Gradient given Slope Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hydraulic Gradient to Head Loss = (1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))*Slope of Line
i = (1-(Q_eg^2*T/([g]*S^3)))*m
This formula uses 1 Constants, 5 Variables

Constants Used

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

Variables Used

Hydraulic Gradient to Head Loss - Hydraulic Gradient to Head Loss is a specific measurement of liquid pressure above a vertical datum.
Discharge by Energy Gradient - (Measured in Cubic Meter per Second) - Discharge by Energy Gradient is rate of floe per unit time.
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.
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

Discharge by Energy Gradient: 12.5 Cubic Meter per Second --> 12.5 Cubic Meter per Second 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
Slope of Line: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

i = (1-(Q_eg^2*T/([g]*S^3)))*m --> (1-(12.5^2*2/([g]*4.01^3)))*4

Evaluating ... ...

i = 2.02322964452475

STEP 3: Convert Result to Output's Unit

2.02322964452475 --> No Conversion Required

FINAL ANSWER

2.02322964452475 ≈ 2.02323 <-- Hydraulic Gradient to Head Loss

(Calculation completed in 00.004 seconds)

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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

Energy Gradient given Slope Formula

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

Energy Gradient given Slope calculator uses Hydraulic Gradient to Head Loss = (1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))*Slope of Line to calculate the Hydraulic Gradient to Head Loss, The Energy Gradient given Slope formula is defined as slope of energy line in the channel taken at any point of channel. Hydraulic Gradient to Head Loss is denoted by i symbol.

How to calculate Energy Gradient given Slope using this online calculator? To use this online calculator for Energy Gradient given Slope, enter Discharge by Energy Gradient (Q_eg), Top Width (T), Wetted Surface Area (S) & Slope of Line (m) and hit the calculate button. Here is how the Energy Gradient given Slope calculation can be explained with given input values -> 2.008367 = (1-(12.5^2*2/([g]*4.01^3)))*4.

FAQ

What is Energy Gradient given Slope?

The Energy Gradient given Slope formula is defined as slope of energy line in the channel taken at any point of channel and is represented as i = (1-(Q_eg^2*T/([g]*S^3)))*m or Hydraulic Gradient to Head Loss = (1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))*Slope of Line. Discharge by Energy Gradient is rate of floe per unit time, 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 & 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 Energy Gradient given Slope?

The Energy Gradient given Slope formula is defined as slope of energy line in the channel taken at any point of channel is calculated using Hydraulic Gradient to Head Loss = (1-(Discharge by Energy Gradient^2*Top Width/([g]*Wetted Surface Area^3)))*Slope of Line. To calculate Energy Gradient given Slope, you need Discharge by Energy Gradient (Q_eg), Top Width (T), Wetted Surface Area (S) & Slope of Line (m). With our tool, you need to enter the respective value for Discharge by Energy Gradient, Top Width, Wetted Surface Area & Slope of Line 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 Hydraulic Gradient to Head Loss?

In this formula, Hydraulic Gradient to Head Loss uses Discharge by Energy Gradient, Top Width, Wetted Surface Area & Slope of Line. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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