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Slope of Channel Bottom given Boundary Shear Stress Formula

GoSlope of Channel Bed given Average Velocity in Channel Formula

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Bed Slope is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow. Check FAQs

S = \frac{ζ 0}{γ l \cdot R H}

S - Bed Slope?ζ₀ - Shear Stress of Wall?γ_l - Liquid Specific Weight?R_H - Hydraulic Radius of Channel?

Slope of Channel Bottom given Boundary Shear Stress Example

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Here is how the Slope of Channel Bottom given Boundary Shear Stress equation looks like with Values.

Here is how the Slope of Channel Bottom given Boundary Shear Stress equation looks like with Units.

Here is how the Slope of Channel Bottom given Boundary Shear Stress equation looks like.

0.0004 = \frac{6.3}{9.81 \cdot 1.6}

0.0004 = \frac{6.3Pa}{9.81kN/m³ \cdot 1.6m}

0.0004 = \frac{6.3}{9.81 \cdot 1.6}

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Slope of Channel Bottom given Boundary Shear Stress Solution

Follow our step by step solution on how to calculate Slope of Channel Bottom given Boundary Shear Stress?

FIRST Step Consider the formula

S = \frac{ζ 0}{γ l \cdot R H}

Next Step Substitute values of Variables

∴

S = \frac{6.3Pa}{9.81kN/m³ \cdot 1.6m}

Next Step Convert Units

∴

S = \frac{6.3Pa}{9810N/m³ \cdot 1.6m}

Next Step Prepare to Evaluate

∴

S = \frac{6.3}{9810 \cdot 1.6}

Next Step Evaluate

∴

S = 0.000401376146788991

LAST Step Rounding Answer

∴

S = 0.0004

Slope of Channel Bottom given Boundary Shear Stress Formula Elements

Variables

Bed Slope

Bed Slope is used to calculate the shear stress at the bed of an open channel containing fluid that is undergoing steady, uniform flow.

Symbol: S

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Bed Slope

Shear Stress of Wall

Shear Stress of Wall is defined as the shear stress in the layer of fluid next to the wall of a pipe.

Symbol: ζ₀

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Stress of Wall

Liquid Specific Weight

Liquid Specific Weight is also known as the unit weight, is the weight per unit volume of the liquid. For Example - Specific weight of water on Earth at 4°C is 9.807 kN/m3 or 62.43 lbf/ft3.

Symbol: γ_l

Measurement: Specific WeightUnit: kN/m³

Note: Value can be positive or negative.

Formulas to find Liquid Specific Weight

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 Bed Slope

Go Slope of Channel Bed given Average Velocity in Channel

S = {(\frac{V avg}{\sqrt{8 \cdot [g] \cdot \frac{R H}{f}}})}^{2}

Other formulas in Average Velocity in Uniform Flow in Channels category

Go Boundary Shear Stress

ζ 0 = γ l \cdot R H \cdot S

Go Specific Weight of Liquid given Boundary Shear Stress

γ l = \frac{ζ 0}{R H \cdot S}

Go Hydraulic Radius given Boundary Shear Stress

R H = \frac{ζ 0}{γ l \cdot S}

Go Average Velocity in Channel

V avg = \sqrt{8 \cdot [g] \cdot R H \cdot \frac{S}{f}}

How to Evaluate Slope of Channel Bottom given Boundary Shear Stress?

Slope of Channel Bottom given Boundary Shear Stress evaluator uses Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel) to evaluate the Bed Slope, The Slope of Channel Bottom given Boundary Shear Stress is defined as the elevation of the channel from the bottom. Bed Slope is denoted by S symbol.

How to evaluate Slope of Channel Bottom given Boundary Shear Stress using this online evaluator? To use this online evaluator for Slope of Channel Bottom given Boundary Shear Stress, enter Shear Stress of Wall (ζ₀), Liquid Specific Weight (γ_l) & Hydraulic Radius of Channel (R_H) and hit the calculate button.

FAQs on Slope of Channel Bottom given Boundary Shear Stress

What is the formula to find Slope of Channel Bottom given Boundary Shear Stress?

The formula of Slope of Channel Bottom given Boundary Shear Stress is expressed as Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel). Here is an example- 0.000401 = 6.3/(9810*1.6).

How to calculate Slope of Channel Bottom given Boundary Shear Stress?

With Shear Stress of Wall (ζ₀), Liquid Specific Weight (γ_l) & Hydraulic Radius of Channel (R_H) we can find Slope of Channel Bottom given Boundary Shear Stress using the formula - Bed Slope = Shear Stress of Wall/(Liquid Specific Weight*Hydraulic Radius of Channel).

What are the other ways to Calculate Bed Slope?

Here are the different ways to Calculate Bed Slope-

Bed Slope=(Average Velocity of Flow/(sqrt(8*[g]*Hydraulic Radius of Channel/Darcy Friction Factor)))^2

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Slope of Channel Bottom given Boundary Shear Stress Formula

​GoSlope of Channel Bed given Average Velocity in Channel Formula

Slope of Channel Bottom given Boundary Shear Stress Example

Slope of Channel Bottom given Boundary Shear Stress Solution

Slope of Channel Bottom given Boundary Shear Stress Formula Elements

Other Formulas to find Bed Slope

Other formulas in Average Velocity in Uniform Flow in Channels category

How to Evaluate Slope of Channel Bottom given Boundary Shear Stress?

FAQs on Slope of Channel Bottom given Boundary Shear Stress

Variable Name

GoSlope of Channel Bed given Average Velocity in Channel Formula