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Unprotected Side Slopes Shear Stress Required to Move Single Grain Formula

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The critical shear stress on horizontal bed is the magnitude of shear stress required to move a given particle. Check FAQs

ζc' = ζ c \cdot \sqrt{1 - (\frac{{\sin (θ)}^{2}}{{\sin (Φ)}^{2}})}

ζc^' - Critical Shear Stress on Horizontal Bed?ζ_c - Resisting Shear against Movement of Particle?θ - Side Slope?Φ - Angle of Repose of Soil?

Unprotected Side Slopes Shear Stress Required to Move Single Grain Example

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Here is how the Unprotected Side Slopes Shear Stress Required to Move Single Grain equation looks like with Values.

Here is how the Unprotected Side Slopes Shear Stress Required to Move Single Grain equation looks like with Units.

Here is how the Unprotected Side Slopes Shear Stress Required to Move Single Grain equation looks like.

0.0031 = 0.0054 \cdot \sqrt{1 - (\frac{{\sin (45)}^{2}}{{\sin (60)}^{2}})}

0.0031kN/m² = 0.0054kN/m² \cdot \sqrt{1 - (\frac{{\sin (45°)}^{2}}{{\sin (60°)}^{2}})}

0.0031 = 0.0054 \cdot \sqrt{1 - (\frac{{\sin (45)}^{2}}{{\sin (60)}^{2}})}

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Unprotected Side Slopes Shear Stress Required to Move Single Grain Solution

Follow our step by step solution on how to calculate Unprotected Side Slopes Shear Stress Required to Move Single Grain?

FIRST Step Consider the formula

ζc' = ζ c \cdot \sqrt{1 - (\frac{{\sin (θ)}^{2}}{{\sin (Φ)}^{2}})}

Next Step Substitute values of Variables

∴

ζc' = 0.0054kN/m² \cdot \sqrt{1 - (\frac{{\sin (45°)}^{2}}{{\sin (60°)}^{2}})}

Next Step Convert Units

∴

ζc' = 5.437Pa \cdot \sqrt{1 - (\frac{{\sin (0.7854rad)}^{2}}{{\sin (1.0472rad)}^{2}})}

Next Step Prepare to Evaluate

∴

ζc' = 5.437 \cdot \sqrt{1 - (\frac{{\sin (0.7854)}^{2}}{{\sin (1.0472)}^{2}})}

Next Step Evaluate

∴

ζc' = 3.1390534135842Pa

Next Step Convert to Output's Unit

∴

ζc' = 0.0031390534135842kN/m²

LAST Step Rounding Answer

∴

ζc' = 0.0031kN/m²

Unprotected Side Slopes Shear Stress Required to Move Single Grain Formula Elements

Variables

Functions

Critical Shear Stress on Horizontal Bed

The critical shear stress on horizontal bed is the magnitude of shear stress required to move a given particle.

Symbol: ζc^'

Measurement: StressUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Critical Shear Stress on Horizontal Bed

Resisting Shear against Movement of Particle

Resisting shear against movement of particle the ability of an adhesive to resist shear stress.

Symbol: ζ_c

Measurement: StressUnit: kN/m²

Note: Value can be positive or negative.

Formulas to find Resisting Shear against Movement of Particle

Side Slope

Side slope is the slope of the cut or fill expressed as the ratio of horizontal distance to vertical distance.

Symbol: θ

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Side Slope

Angle of Repose of Soil

The angle of repose of soil of a granular material is the steepest angle of descent relative to the horizontal plane to which a material can be piled without slumping. It ranges 0°-90°.

Symbol: Φ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Repose of Soil

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Design of Non Scouring Stable Channels having Protected Side Slopes (Shield's Entrainmnet Method) category

Go Drag Force Exerted by Flow

F 1 = K 1 \cdot (C D) \cdot (d^{2}) \cdot (0.5) \cdot (ρ w) \cdot (V °)

Go Resisting Shear against Movement of Particle

ζ c = 0.056 \cdot Γ w \cdot d \cdot (S s - 1)

Go General Relation between Resisting Shear and Diameter of Particle

ζ c = 0.155 + (0.409 \cdot \frac{d^{2}}{\sqrt{1 + 0.77 \cdot d^{2}}})

Go Manning's Rugosity Coefficient according to Stickler's Formula

n = (\frac{1}{24}) \cdot {(d)}^{\frac{1}{6}}

How to Evaluate Unprotected Side Slopes Shear Stress Required to Move Single Grain?

Unprotected Side Slopes Shear Stress Required to Move Single Grain evaluator uses Critical Shear Stress on Horizontal Bed = Resisting Shear against Movement of Particle*sqrt(1-(sin(Side Slope)^2/sin(Angle of Repose of Soil)^2)) to evaluate the Critical Shear Stress on Horizontal Bed, The Unprotected Side Slopes Shear Stress Required to Move Single Grain formula is defined as the product of shear stress required to move a similar grain to the square root of the ratio of side slope and angle of repose. Critical Shear Stress on Horizontal Bed is denoted by ζc^' symbol.

How to evaluate Unprotected Side Slopes Shear Stress Required to Move Single Grain using this online evaluator? To use this online evaluator for Unprotected Side Slopes Shear Stress Required to Move Single Grain, enter Resisting Shear against Movement of Particle (ζ_c), Side Slope (θ) & Angle of Repose of Soil (Φ) and hit the calculate button.

FAQs on Unprotected Side Slopes Shear Stress Required to Move Single Grain

What is the formula to find Unprotected Side Slopes Shear Stress Required to Move Single Grain?

The formula of Unprotected Side Slopes Shear Stress Required to Move Single Grain is expressed as Critical Shear Stress on Horizontal Bed = Resisting Shear against Movement of Particle*sqrt(1-(sin(Side Slope)^2/sin(Angle of Repose of Soil)^2)). Here is an example- 3.1E-6 = 5.437*sqrt(1-(sin(0.785398163397301)^2/sin(1.0471975511964)^2)).

How to calculate Unprotected Side Slopes Shear Stress Required to Move Single Grain?

With Resisting Shear against Movement of Particle (ζ_c), Side Slope (θ) & Angle of Repose of Soil (Φ) we can find Unprotected Side Slopes Shear Stress Required to Move Single Grain using the formula - Critical Shear Stress on Horizontal Bed = Resisting Shear against Movement of Particle*sqrt(1-(sin(Side Slope)^2/sin(Angle of Repose of Soil)^2)). This formula also uses Sine (sin), Square Root (sqrt) function(s).

Can the Unprotected Side Slopes Shear Stress Required to Move Single Grain be negative?

No, the Unprotected Side Slopes Shear Stress Required to Move Single Grain, measured in Stress cannot be negative.

Which unit is used to measure Unprotected Side Slopes Shear Stress Required to Move Single Grain?

Unprotected Side Slopes Shear Stress Required to Move Single Grain is usually measured using the Kilonewton per Square Meter[kN/m²] for Stress. Pascal[kN/m²], Newton per Square Meter[kN/m²], Newton per Square Millimeter[kN/m²] are the few other units in which Unprotected Side Slopes Shear Stress Required to Move Single Grain can be measured.

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