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))
Sf = ((n*vm,R)^2)/(RH^(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
Sf = ((n*vm,R)^2)/(RH^(4/3)) --> ((0.012*56.2)^2)/(1.6^(4/3))
Evaluating ... ...
Sf = 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 00.020 seconds)

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Integration of the Varied Flow Equation Calculators

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

Manning's Formula for Energy Slope Formula

​LaTeX ​Go
Energy Slope = ((Manning’s Roughness Coefficient*Mean Velocity for Varied Flow)^2)/(Hydraulic Radius of Channel^(4/3))
Sf = ((n*vm,R)^2)/(RH^(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 Sf 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 (vm,R) & Hydraulic Radius of Channel (RH) 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 Sf = ((n*vm,R)^2)/(RH^(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 (vm,R) & Hydraulic Radius of Channel (RH). 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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