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Slope of Gradient of Stream Bed given Discharge in Manning's Equation Formula

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Bed Slope also called channel slope is the difference in elevation between two points on a stream divided by the distance between them measured along the stream channel. Check FAQs

S̄ = {(\frac{v \cdot n}{{r H}^{\frac{2}{3}}})}^{2}

S̄ - Bed Slope?v - Stream Velocity?n - Manning’s Roughness Coefficient?r_H - Hydraulic Radius?

Slope of Gradient of Stream Bed given Discharge in Manning's Equation Example

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Here is how the Slope of Gradient of Stream Bed given Discharge in Manning's Equation equation looks like with Values.

Here is how the Slope of Gradient of Stream Bed given Discharge in Manning's Equation equation looks like with Units.

Here is how the Slope of Gradient of Stream Bed given Discharge in Manning's Equation equation looks like.

5.974 = {(\frac{2.227 \cdot 0.412}{{0.23}^{\frac{2}{3}}})}^{2}

5.974 = {(\frac{2.227m/s \cdot 0.412}{{0.23m}^{\frac{2}{3}}})}^{2}

5.974 = {(\frac{2.227 \cdot 0.412}{{0.23}^{\frac{2}{3}}})}^{2}

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Slope of Gradient of Stream Bed given Discharge in Manning's Equation Solution

Follow our step by step solution on how to calculate Slope of Gradient of Stream Bed given Discharge in Manning's Equation?

FIRST Step Consider the formula

S̄ = {(\frac{v \cdot n}{{r H}^{\frac{2}{3}}})}^{2}

Next Step Substitute values of Variables

∴

S̄ = {(\frac{2.227m/s \cdot 0.412}{{0.23m}^{\frac{2}{3}}})}^{2}

Next Step Prepare to Evaluate

∴

S̄ = {(\frac{2.227 \cdot 0.412}{{0.23}^{\frac{2}{3}}})}^{2}

Next Step Evaluate

∴

S̄ = 5.97398899333278

LAST Step Rounding Answer

∴

S̄ = 5.974

Slope of Gradient of Stream Bed given Discharge in Manning's Equation Formula Elements

Variables

Bed Slope

Bed Slope also called channel slope is the difference in elevation between two points on a stream divided by the distance between them measured along the stream channel.

Symbol: S̄

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Bed Slope

Stream Velocity

Stream Velocity is the speed of the water in the stream. It is greatest in midstream near the surface and is slowest along the stream bed and banks due to friction.

Symbol: v

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Stream Velocity

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 can be positive or negative.

Formulas to find Manning’s Roughness Coefficient

Hydraulic Radius

Hydraulic Radius 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 can be positive or negative.

Formulas to find Hydraulic Radius

Other formulas in Manning's Equation category

Go Hydraulic radius in Manning's formula

r H = \frac{A}{P}

Go Hydraulic Radius using Manning Equation

r H = {(\frac{v \cdot n}{{S̄}^{\frac{1}{2}}})}^{\frac{3}{2}}

Go Manning's Equation

v = (\frac{1}{n}) \cdot {(r H)}^{\frac{2}{3}} \cdot {(S̄)}^{\frac{1}{2}}

How to Evaluate Slope of Gradient of Stream Bed given Discharge in Manning's Equation?

Slope of Gradient of Stream Bed given Discharge in Manning's Equation evaluator uses Bed Slope = ((Stream Velocity*Manning’s Roughness Coefficient)/Hydraulic Radius^(2/3))^2 to evaluate the Bed Slope, The Slope of Gradient of Stream Bed given Discharge in Manning's Equation formula is defined as the slope measured by the difference in elevation between two points on a stream divided by the distance between the two points that the water flows. Bed Slope is denoted by S̄ symbol.

How to evaluate Slope of Gradient of Stream Bed given Discharge in Manning's Equation using this online evaluator? To use this online evaluator for Slope of Gradient of Stream Bed given Discharge in Manning's Equation, enter Stream Velocity (v), Manning’s Roughness Coefficient (n) & Hydraulic Radius (r_H) and hit the calculate button.

FAQs on Slope of Gradient of Stream Bed given Discharge in Manning's Equation

What is the formula to find Slope of Gradient of Stream Bed given Discharge in Manning's Equation?

The formula of Slope of Gradient of Stream Bed given Discharge in Manning's Equation is expressed as Bed Slope = ((Stream Velocity*Manning’s Roughness Coefficient)/Hydraulic Radius^(2/3))^2. Here is an example- 5.805118 = ((2.227*0.412)/0.23^(2/3))^2.

How to calculate Slope of Gradient of Stream Bed given Discharge in Manning's Equation?

With Stream Velocity (v), Manning’s Roughness Coefficient (n) & Hydraulic Radius (r_H) we can find Slope of Gradient of Stream Bed given Discharge in Manning's Equation using the formula - Bed Slope = ((Stream Velocity*Manning’s Roughness Coefficient)/Hydraulic Radius^(2/3))^2.

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Slope of Gradient of Stream Bed given Discharge in Manning's Equation Formula

Slope of Gradient of Stream Bed given Discharge in Manning's Equation Example

Slope of Gradient of Stream Bed given Discharge in Manning's Equation Solution

Slope of Gradient of Stream Bed given Discharge in Manning's Equation Formula Elements

Other formulas in Manning's Equation category

How to Evaluate Slope of Gradient of Stream Bed given Discharge in Manning's Equation?

FAQs on Slope of Gradient of Stream Bed given Discharge in Manning's Equation

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