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Depth of Prism given Submerged Unit Weight and Shear Stress Formula

GoDepth of Prism given Submerged Unit Weight Formula

GoDepth of Prism for Cohesive Soil given Submerged Slope Formula

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Depth of Prism is the length of prism along z direction. Check FAQs

z = \frac{𝜏}{γ' \cdot \cos ((i)) \cdot \sin ((i))}

z - Depth of Prism?𝜏 - Shear Stress for Submerged Slopes?γ^' - Submerged Unit Weight?i - Angle of Inclination to Horizontal in Soil?

Depth of Prism given Submerged Unit Weight and Shear Stress Example

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Here is how the Depth of Prism given Submerged Unit Weight and Shear Stress equation looks like with Values.

Here is how the Depth of Prism given Submerged Unit Weight and Shear Stress equation looks like with Units.

Here is how the Depth of Prism given Submerged Unit Weight and Shear Stress equation looks like.

2.9889 = \frac{5.9}{5.01 \cdot \cos ((64)) \cdot \sin ((64))}

2.9889m = \frac{5.9Pa}{5.01N/m³ \cdot \cos ((64°)) \cdot \sin ((64°))}

2.9889 = \frac{5.9}{5.01 \cdot \cos ((64)) \cdot \sin ((64))}

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Depth of Prism given Submerged Unit Weight and Shear Stress Solution

Follow our step by step solution on how to calculate Depth of Prism given Submerged Unit Weight and Shear Stress?

FIRST Step Consider the formula

z = \frac{𝜏}{γ' \cdot \cos ((i)) \cdot \sin ((i))}

Next Step Substitute values of Variables

∴

z = \frac{5.9Pa}{5.01N/m³ \cdot \cos ((64°)) \cdot \sin ((64°))}

Next Step Convert Units

∴

z = \frac{5.9Pa}{5.01N/m³ \cdot \cos ((1.117rad)) \cdot \sin ((1.117rad))}

Next Step Prepare to Evaluate

∴

z = \frac{5.9}{5.01 \cdot \cos ((1.117)) \cdot \sin ((1.117))}

Next Step Evaluate

∴

z = 2.98890517721587m

LAST Step Rounding Answer

∴

z = 2.9889m

Depth of Prism given Submerged Unit Weight and Shear Stress Formula Elements

Variables

Functions

Depth of Prism

Depth of Prism is the length of prism along z direction.

Symbol: z

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Depth of Prism

Shear Stress for Submerged Slopes

Shear Stress for Submerged Slopes is the force per unit area parallel to the slope surface beneath water, causing deformation.

Symbol: 𝜏

Measurement: StressUnit: Pa

Note: Value should be greater than 0.

Formulas to find Shear Stress for Submerged Slopes

Submerged Unit Weight

Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.

Symbol: γ^'

Measurement: Specific WeightUnit: N/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight

Angle of Inclination to Horizontal in Soil

Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

Symbol: i

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Angle of Inclination to Horizontal in 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)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Depth of Prism

Go Depth of Prism given Submerged Unit Weight

z = \frac{σ Normal}{γ' \cdot {(\cos ((i)))}^{2}}

Go Depth of Prism for Cohesive Soil given Submerged Slope

z = (\frac{C s}{(f s - (\frac{\tan ((φ))}{\tan ((i))})) \cdot γ' \cdot \cos ((i)) \cdot \sin ((i))})

Other formulas in Stability Analysis of Submerged Slopes category

Go Normal Stress Component given Submerged Unit Weight

σ Normal = γ' \cdot z \cdot {(\cos ((i)))}^{2}

Go Submerged Unit Weight given Normal Stress Component

γ' = \frac{σ Normal}{z \cdot {(\cos ((i)))}^{2}}

Go Shear Stress Component given Submerged Unit Weight

𝜏 = (γ' \cdot z \cdot \cos ((i)) \cdot \sin ((i)))

Go Submerged Unit Weight given Shear Stress Component

γ' = \frac{𝜏}{z \cdot \cos ((i)) \cdot \sin ((i))}

How to Evaluate Depth of Prism given Submerged Unit Weight and Shear Stress?

Depth of Prism given Submerged Unit Weight and Shear Stress evaluator uses Depth of Prism = Shear Stress for Submerged Slopes/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))) to evaluate the Depth of Prism, The Depth of Prism given Submerged Unit Weight and Shear Stress is defined as the submerged unit weight and shear stress, reflecting material behavior in water. Depth of Prism is denoted by z symbol.

How to evaluate Depth of Prism given Submerged Unit Weight and Shear Stress using this online evaluator? To use this online evaluator for Depth of Prism given Submerged Unit Weight and Shear Stress, enter Shear Stress for Submerged Slopes (𝜏), Submerged Unit Weight (γ^') & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Depth of Prism given Submerged Unit Weight and Shear Stress

What is the formula to find Depth of Prism given Submerged Unit Weight and Shear Stress?

The formula of Depth of Prism given Submerged Unit Weight and Shear Stress is expressed as Depth of Prism = Shear Stress for Submerged Slopes/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))). Here is an example- 2.994883 = 5.9/(5.01*cos((1.11701072127616))*sin((1.11701072127616))).

How to calculate Depth of Prism given Submerged Unit Weight and Shear Stress?

With Shear Stress for Submerged Slopes (𝜏), Submerged Unit Weight (γ^') & Angle of Inclination to Horizontal in Soil (i) we can find Depth of Prism given Submerged Unit Weight and Shear Stress using the formula - Depth of Prism = Shear Stress for Submerged Slopes/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))). This formula also uses Sine (sin), Cosine (cos) function(s).

What are the other ways to Calculate Depth of Prism?

Here are the different ways to Calculate Depth of Prism-

Depth of Prism=Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2)
Depth of Prism=(Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))

Can the Depth of Prism given Submerged Unit Weight and Shear Stress be negative?

No, the Depth of Prism given Submerged Unit Weight and Shear Stress, measured in Length cannot be negative.

Which unit is used to measure Depth of Prism given Submerged Unit Weight and Shear Stress?

Depth of Prism given Submerged Unit Weight and Shear Stress is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Depth of Prism given Submerged Unit Weight and Shear Stress can be measured.

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Depth of Prism given Submerged Unit Weight and Shear Stress Formula

​GoDepth of Prism given Submerged Unit Weight Formula

​GoDepth of Prism for Cohesive Soil given Submerged Slope Formula

Depth of Prism given Submerged Unit Weight and Shear Stress Example

Depth of Prism given Submerged Unit Weight and Shear Stress Solution

Depth of Prism given Submerged Unit Weight and Shear Stress Formula Elements

Other Formulas to find Depth of Prism

Other formulas in Stability Analysis of Submerged Slopes category

How to Evaluate Depth of Prism given Submerged Unit Weight and Shear Stress?

FAQs on Depth of Prism given Submerged Unit Weight and Shear Stress

Variable Name

GoDepth of Prism given Submerged Unit Weight Formula

GoDepth of Prism for Cohesive Soil given Submerged Slope Formula