Manning's Formula for Energy Slope Calculator

✖Manning’s Roughness Coefficient represents the roughness or friction applied to the flow by the channel.ⓘ Manning’s Roughness Coefficient [n]			+10% -10%
✖Mean velocity for Varied Flow is defined as the average velocity of a fluid at a point and over an arbitrary time T.ⓘ Mean Velocity for Varied Flow [v_m,R]			+10% -10%
✖Hydraulic Radius of Channel is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit.ⓘ Hydraulic Radius of Channel [R_H]			+10% -10%

✖Energy Slope is at a distance equal to the velocity head above the hydraulic gradient.ⓘ Manning's Formula for Energy Slope [S_f]

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Formula

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Manning's Formula for Energy Slope

Formula

`"S"_{"f"} = (("n"*"v"_{"m,R"})^2)/("R"_{"H"}^(4/3))`

Example

`"0.243039"=(("0.012"*"56.2m/s")^2)/(("1.6m")^(4/3))`

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Manning's Formula for Energy Slope Solution

STEP 0: Pre-Calculation Summary

Formula Used

Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3))
S_f = ((n*v_m,R)^2)/(R_H^(4/3))
This formula uses 4 Variables

Variables Used

Energy Slope - Energy Slope is at a distance equal to the velocity head above the hydraulic gradient.
Manning’s Roughness Coefficient - Manning’s Roughness Coefficient represents the roughness or friction applied to the flow by the channel.
Mean Velocity for Varied Flow - (Measured in Meter per Second) - Mean velocity for Varied Flow is defined as the average velocity of a fluid at a point and over an arbitrary time T.
Hydraulic Radius of Channel - (Measured in Meter) - Hydraulic Radius of Channel is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit.

STEP 1: Convert Input(s) to Base Unit

Manning’s Roughness Coefficient: 0.012 --> No Conversion Required
Mean Velocity for Varied Flow: 56.2 Meter per Second --> 56.2 Meter per Second No Conversion Required
Hydraulic Radius of Channel: 1.6 Meter --> 1.6 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_f = ((n*v_m,R)^2)/(R_H^(4/3)) --> ((0.012*56.2)^2)/(1.6^(4/3))

Evaluating ... ...

S_f = 0.24303853930597

STEP 3: Convert Result to Output's Unit

0.24303853930597 --> No Conversion Required

FINAL ANSWER

0.24303853930597 ≈ 0.243039 <-- Energy Slope

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Hydraulics and Waterworks » Non-uniform Flow in Channels » Integration of the Varied Flow Equation » Manning's Formula for Energy Slope

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National Institute of Technology Karnataka (NITK), Surathkal

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< 12 Integration of the Varied Flow Equation Calculators

Chezy Constant using Chezy Formula given Normal Depth of Wide Rectangular Channel

Go Chézy’s Coefficients for Varied Flow = sqrt(((Critical Depth of Channel/Normal Depth of Varied Flow)^3)*[g]/Bed Slope of Channel)

Chezy Formula for Critical Depth given Normal Depth of Wide Rectangular Channel

Go Critical Depth of Channel = (((Normal Depth of Varied Flow^3)*((Chézy’s Coefficients for Varied Flow^2)*Bed Slope of Channel))/[g])^(1/3)

Chezy Formula for Normal Depth of Wide Rectangular Channel

Go Normal Depth of Varied Flow = (((Critical Depth of Channel^3)*[g])/((Chézy’s Coefficients for Varied Flow^2)*Bed Slope of Channel))^(1/3)

Chezy Formula for Bed Slope given Normal Depth of Wide Rectangular Channel

Go Bed Slope of Channel = (((Critical Depth of Channel/Normal Depth of Varied Flow)^3)*[g]/Chézy’s Coefficients for Varied Flow^2)

Chezy Formula for Mean Velocity given Energy Slope

Go Mean Velocity for Varied Flow = sqrt(Energy Slope*(Chézy’s Coefficients for Varied Flow^2)*Hydraulic Radius of Channel)

Manning's Formula for Roughness Coefficient given Energy Slope

Go Manning’s Roughness Coefficient = (Energy Slope/(((Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3))))^(1/2)

Manning's Formula for Mean Velocity given Energy Slope

Go Mean Velocity for Varied Flow = (Energy Slope/(((Manning’s Roughness Coefficient)^2)/(Hydraulic Radius of Channel^(4/3))))^(1/2)

Chezy's Constant using Chezy Formula given Energy Slope

Go Chézy’s Coefficients for Varied Flow = (((Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel*Energy Slope))^(1/2)

Manning's Formula for Hydraulic Radius given Energy Slope

Go Hydraulic Radius of Channel = (((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/Energy Slope)^(3/4)

Manning's Formula for Energy Slope

Go Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3))

Chezy Formula for Hydraulic Radius given Energy Slope

Go Hydraulic Radius of Channel = ((Mean Velocity for Varied Flow/Chézy’s Coefficients for Varied Flow)^2)/Energy Slope

Chezy Formula for Energy Slope

Go Energy Slope = ((Mean Velocity for Varied Flow/Chézy’s Coefficients for Varied Flow)^2)/Hydraulic Radius of Channel

Manning's Formula for Energy Slope Formula

Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3))
S_f = ((n*v_m,R)^2)/(R_H^(4/3))

What does Energy Gradient mean?

The energy gradient is equal to the height of the velocity head (the velocity of a fluid expressed in terms of the static pressure required to produce that velocity) above the hydraulic gradient – the distance water free flows downward from a height.

How to Calculate Manning's Formula for Energy Slope?

Manning's Formula for Energy Slope calculator uses Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3)) to calculate the Energy Slope, The Manning's Formula for Energy Slope is defined as the channel energy slope in the section at any point. Energy Slope is denoted by S_f symbol.

How to calculate Manning's Formula for Energy Slope using this online calculator? To use this online calculator for Manning's Formula for Energy Slope, enter Manning’s Roughness Coefficient (n), Mean Velocity for Varied Flow (v_m,R) & Hydraulic Radius of Channel (R_H) and hit the calculate button. Here is how the Manning's Formula for Energy Slope calculation can be explained with given input values -> 0.243039 = ((0.012*56.2)^2)/(1.6^(4/3)).

FAQ

What is Manning's Formula for Energy Slope?

The Manning's Formula for Energy Slope is defined as the channel energy slope in the section at any point and is represented as S_f = ((n*v_m,R)^2)/(R_H^(4/3)) or Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3)). Manning’s Roughness Coefficient represents the roughness or friction applied to the flow by the channel, Mean velocity for Varied Flow is defined as the average velocity of a fluid at a point and over an arbitrary time T & Hydraulic Radius of Channel is the ratio of the cross-sectional area of a channel or pipe in which a fluid is flowing to the wet perimeter of the conduit.

How to calculate Manning's Formula for Energy Slope?

The Manning's Formula for Energy Slope is defined as the channel energy slope in the section at any point is calculated using Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3)). To calculate Manning's Formula for Energy Slope, you need Manning’s Roughness Coefficient (n), Mean Velocity for Varied Flow (v_m,R) & Hydraulic Radius of Channel (R_H). With our tool, you need to enter the respective value for Manning’s Roughness Coefficient, Mean Velocity for Varied Flow & Hydraulic Radius of Channel 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 Energy Slope?

In this formula, Energy Slope uses Manning’s Roughness Coefficient, Mean Velocity for Varied Flow & Hydraulic Radius of Channel. We can use 1 other way(s) to calculate the same, which is/are as follows -

Energy Slope = ((Mean Velocity for Varied Flow/Chézy’s Coefficients for Varied Flow)^2)/Hydraulic Radius of Channel

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