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Depth of Prism given Submerged Unit Weight Formula

GoDepth of Prism given Submerged Unit Weight and Shear Stress 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{σ Normal}{γ' \cdot {(\cos ((i)))}^{2}}

z - Depth of Prism?σ_Normal - Normal Stress?γ^' - Submerged Unit Weight?i - Angle of Inclination to Horizontal in Soil?

Depth of Prism given Submerged Unit Weight Example

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

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

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

0.8309 = \frac{0.8}{5.01 \cdot {(\cos ((64)))}^{2}}

0.8309m = \frac{0.8Pa}{5.01N/m³ \cdot {(\cos ((64°)))}^{2}}

0.8309 = \frac{0.8}{5.01 \cdot {(\cos ((64)))}^{2}}

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Depth of Prism given Submerged Unit Weight Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

z = \frac{0.8Pa}{5.01N/m³ \cdot {(\cos ((64°)))}^{2}}

Next Step Convert Units

∴

z = \frac{0.8Pa}{5.01N/m³ \cdot {(\cos ((1.117rad)))}^{2}}

Next Step Prepare to Evaluate

∴

z = \frac{0.8}{5.01 \cdot {(\cos ((1.117)))}^{2}}

Next Step Evaluate

∴

z = 0.830937459926598m

LAST Step Rounding Answer

∴

z = 0.8309m

Depth of Prism given Submerged Unit Weight 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

Normal Stress

Normal stress is defined as the stress produced by the perpendicular action of a force on a given area.

Symbol: σ_Normal

Measurement: PressureUnit: Pa

Note: Value can be positive or negative.

Formulas to find Normal Stress

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

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 and Shear Stress

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

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?

Depth of Prism given Submerged Unit Weight evaluator uses Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2) to evaluate the Depth of Prism, The Depth of Prism given Submerged Unit Weight is defined as its weight per unit volume, expressed as submerged unit weight. Depth of Prism is denoted by z symbol.

How to evaluate Depth of Prism given Submerged Unit Weight using this online evaluator? To use this online evaluator for Depth of Prism given Submerged Unit Weight, enter Normal Stress (σ_Normal), 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

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

The formula of Depth of Prism given Submerged Unit Weight is expressed as Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2). Here is an example- 0.832599 = 0.8/(5.01*(cos((1.11701072127616)))^2).

How to calculate Depth of Prism given Submerged Unit Weight?

With Normal Stress (σ_Normal), Submerged Unit Weight (γ^') & Angle of Inclination to Horizontal in Soil (i) we can find Depth of Prism given Submerged Unit Weight using the formula - Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2). This formula also uses 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=Shear Stress for Submerged Slopes/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))
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 be negative?

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

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

Depth of Prism given Submerged Unit Weight 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 can be measured.

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Depth of Prism given Submerged Unit Weight Formula

​GoDepth of Prism given Submerged Unit Weight and Shear Stress Formula

​GoDepth of Prism for Cohesive Soil given Submerged Slope Formula

Depth of Prism given Submerged Unit Weight Example

Depth of Prism given Submerged Unit Weight Solution

Depth of Prism given Submerged Unit Weight 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?

FAQs on Depth of Prism given Submerged Unit Weight

Variable Name

GoDepth of Prism given Submerged Unit Weight and Shear Stress Formula

GoDepth of Prism for Cohesive Soil given Submerged Slope Formula