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Manning's Formula for Energy Slope Formula

GoChezy Formula for Energy Slope Formula

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Energy Slope is at a distance equal to the velocity head above the hydraulic gradient. Check FAQs

S f = \frac{{(n \cdot v m,R)}^{2}}{{R H}^{\frac{4}{3}}}

S_f - Energy Slope?n - Manning’s Roughness Coefficient?v_m,R - Mean Velocity for Varied Flow?R_H - Hydraulic Radius of Channel?

Manning's Formula for Energy Slope Example

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Here is how the Manning's Formula for Energy Slope equation looks like with Values.

Here is how the Manning's Formula for Energy Slope equation looks like with Units.

Here is how the Manning's Formula for Energy Slope equation looks like.

0.243 = \frac{{(0.012 \cdot 56.2)}^{2}}{{1.6}^{\frac{4}{3}}}

0.243 = \frac{{(0.012 \cdot 56.2m/s)}^{2}}{{1.6m}^{\frac{4}{3}}}

0.243 = \frac{{(0.012 \cdot 56.2)}^{2}}{{1.6}^{\frac{4}{3}}}

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Manning's Formula for Energy Slope Solution

Follow our step by step solution on how to calculate Manning's Formula for Energy Slope?

FIRST Step Consider the formula

S f = \frac{{(n \cdot v m,R)}^{2}}{{R H}^{\frac{4}{3}}}

Next Step Substitute values of Variables

∴

S f = \frac{{(0.012 \cdot 56.2m/s)}^{2}}{{1.6m}^{\frac{4}{3}}}

Next Step Prepare to Evaluate

∴

S f = \frac{{(0.012 \cdot 56.2)}^{2}}{{1.6}^{\frac{4}{3}}}

Next Step Evaluate

∴

S f = 0.24303853930597

LAST Step Rounding Answer

∴

S f = 0.243

Manning's Formula for Energy Slope Formula Elements

Variables

Energy Slope

Energy Slope is at a distance equal to the velocity head above the hydraulic gradient.

Symbol: S_f

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Energy Slope

Manning’s Roughness Coefficient

Manning’s Roughness Coefficient represents the roughness or friction applied to the flow by the channel.

Symbol: n

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Manning’s Roughness Coefficient

Mean Velocity for Varied Flow

Mean velocity for Varied Flow is defined as the average velocity of a fluid at a point and over an arbitrary time T.

Symbol: v_m,R

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Mean Velocity for Varied Flow

Hydraulic Radius of Channel

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.

Symbol: R_H

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Hydraulic Radius of Channel

Other Formulas to find Energy Slope

Go Chezy Formula for Energy Slope

S f = \frac{{(\frac{v m,R}{C VF})}^{2}}{R H}

Other formulas in Integration of the Varied Flow Equation category

Go Manning's Formula for Roughness Coefficient given Energy Slope

n = {(\frac{S f}{\frac{{(v m,R)}^{2}}{{R H}^{\frac{4}{3}}}})}^{\frac{1}{2}}

Go Manning's Formula for Hydraulic Radius given Energy Slope

R H = {(\frac{{(n \cdot v m,R)}^{2}}{S f})}^{\frac{3}{4}}

Go Manning's Formula for Mean Velocity given Energy Slope

v m,R = {(\frac{S f}{\frac{{(n)}^{2}}{{R H}^{\frac{4}{3}}}})}^{\frac{1}{2}}

Go Chezy Formula for Mean Velocity given Energy Slope

v m,R = \sqrt{S f \cdot ({C VF}^{2}) \cdot R H}

How to Evaluate Manning's Formula for Energy Slope?

Manning's Formula for Energy Slope evaluator uses Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3)) to evaluate 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 evaluate Manning's Formula for Energy Slope using this online evaluator? To use this online evaluator 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.

FAQs on Manning's Formula for Energy Slope

What is the formula to find Manning's Formula for Energy Slope?

The formula of Manning's Formula for Energy Slope is expressed as Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3)). Here is an example- 0.243039 = ((0.012*56.2)^2)/(1.6^(4/3)).

How to calculate Manning's Formula for Energy Slope?

With Manning’s Roughness Coefficient (n), Mean Velocity for Varied Flow (v_m,R) & Hydraulic Radius of Channel (R_H) we can find Manning's Formula for Energy Slope using the formula - Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3)).

What are the other ways to Calculate Energy Slope?

Here are the different ways to Calculate Energy Slope-

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

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Manning's Formula for Energy Slope Formula

​GoChezy Formula for Energy Slope Formula

Manning's Formula for Energy Slope Example

Manning's Formula for Energy Slope Solution

Manning's Formula for Energy Slope Formula Elements

Other Formulas to find Energy Slope

Other formulas in Integration of the Varied Flow Equation category

How to Evaluate Manning's Formula for Energy Slope?

FAQs on Manning's Formula for Energy Slope

Variable Name

GoChezy Formula for Energy Slope Formula