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Submerged Unit Weight given Effective Normal Stress Formula

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GoSubmerged Unit Weight given Factor of Safety Formula

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Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course. Check FAQs

y S = \frac{σ'}{z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

y_S - Submerged Unit Weight in KN per Cubic Meter?σ^' - Effective Normal Stress in Soil Mechanics?z - Depth of Prism?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

Submerged Unit Weight given Effective Normal Stress Example

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Here is how the Submerged Unit Weight given Effective Normal Stress equation looks like with Values.

Here is how the Submerged Unit Weight given Effective Normal Stress equation looks like with Units.

Here is how the Submerged Unit Weight given Effective Normal Stress equation looks like.

8.2265 = \frac{24.67}{3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

8.2265kN/m³ = \frac{24.67kN/m²}{3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

8.2265 = \frac{24.67}{3 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

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Submerged Unit Weight given Effective Normal Stress Solution

Follow our step by step solution on how to calculate Submerged Unit Weight given Effective Normal Stress?

FIRST Step Consider the formula

y S = \frac{σ'}{z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Next Step Substitute values of Variables

∴

y S = \frac{24.67kN/m²}{3m \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}}

Next Step Substitute values of Constants

∴

y S = \frac{24.67kN/m²}{3m \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

Next Step Convert Units

∴

y S = \frac{24670Pa}{3m \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}}

Next Step Prepare to Evaluate

∴

y S = \frac{24670}{3 \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}}

Next Step Evaluate

∴

y S = 8226.45960968797N/m³

Next Step Convert to Output's Unit

∴

y S = 8.22645960968797kN/m³

LAST Step Rounding Answer

∴

y S = 8.2265kN/m³

Submerged Unit Weight given Effective Normal Stress Formula Elements

Variables

Constants

Functions

Submerged Unit Weight in KN per Cubic Meter

Submerged Unit Weight in KN per Cubic Meter is the unit weight of a weight of soil as observed under water in a saturated condition of course.

Symbol: y_S

Measurement: Specific WeightUnit: kN/m³

Note: Value should be greater than 0.

Formulas to find Submerged Unit Weight in KN per Cubic Meter

Effective Normal Stress in Soil Mechanics

Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.

Symbol: σ^'

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Effective Normal Stress in Soil Mechanics

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

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

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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 Submerged Unit Weight in KN per Cubic Meter

Go Submerged Unit Weight given Upward Force

y S = \frac{σ n - F u}{z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Go Submerged Unit Weight given Factor of Safety

y S = \frac{F s}{\frac{\tan (\frac{Φ i \cdot π}{180})}{γ saturated \cdot \tan (\frac{i \cdot π}{180})}}

Go Submerged Unit Weight given Shear Strength

y S = \frac{\frac{τ f}{ζ soil}}{\frac{\tan ((Φ i))}{γ saturated \cdot \tan ((i))}}

Go Submerged Unit Weight for Steady Seepage along Slope

y S = \frac{(F s \cdot γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}) \cdot \sin (\frac{i \cdot π}{180})) - C}{z \cdot \tan (\frac{Φ i \cdot π}{180}) \cdot {(\cos (\frac{i \cdot π}{180}))}^{2}}

Other formulas in Steady State Seepage Analysis Along The Slopes category

Go Weight of Soil Prism given Saturated Unit Weight

W prism = (γ saturated \cdot z \cdot b \cdot \cos (\frac{i \cdot π}{180}))

Go Inclined Length of Prism given Saturated Unit Weight

b = \frac{W prism}{γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180})}

Go Vertical Stress on Prism given Saturated Unit Weight

σ zkp = (γ saturated \cdot z \cdot \cos (\frac{i \cdot π}{180}))

Go Normal Stress Component given Saturated Unit Weight

σ n = (γ saturated \cdot z \cdot {(\cos (\frac{i \cdot π}{180}))}^{2})

How to Evaluate Submerged Unit Weight given Effective Normal Stress?

Submerged Unit Weight given Effective Normal Stress evaluator uses Submerged Unit Weight in KN per Cubic Meter = Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to evaluate the Submerged Unit Weight in KN per Cubic Meter, Submerged Unit Weight given Effective Normal Stress is defined as the value of submerged unit weight when we have prior information of other parameters used. Submerged Unit Weight in KN per Cubic Meter is denoted by y_S symbol.

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

FAQs on Submerged Unit Weight given Effective Normal Stress

What is the formula to find Submerged Unit Weight given Effective Normal Stress?

The formula of Submerged Unit Weight given Effective Normal Stress is expressed as Submerged Unit Weight in KN per Cubic Meter = Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Here is an example- 0.008226 = 24670/(3*(cos((1.11701072127616*pi)/180))^2).

How to calculate Submerged Unit Weight given Effective Normal Stress?

With Effective Normal Stress in Soil Mechanics (σ^'), Depth of Prism (z) & Angle of Inclination to Horizontal in Soil (i) we can find Submerged Unit Weight given Effective Normal Stress using the formula - Submerged Unit Weight in KN per Cubic Meter = Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). This formula also uses Archimedes' constant and Cosine (cos) function(s).

What are the other ways to Calculate Submerged Unit Weight in KN per Cubic Meter?

Here are the different ways to Calculate Submerged Unit Weight in KN per Cubic Meter-

Submerged Unit Weight in KN per Cubic Meter=(Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Submerged Unit Weight in KN per Cubic Meter=Factor of Safety in Soil Mechanics/((tan((Angle of Internal Friction of Soil*pi)/180))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil*pi)/180)))
Submerged Unit Weight in KN per Cubic Meter=(Shear Strength in KN per Cubic Meter/Shear Stress in Soil Mechanics)/((tan((Angle of Internal Friction of Soil)))/(Saturated Unit Weight of Soil*tan((Angle of Inclination to Horizontal in Soil))))

Can the Submerged Unit Weight given Effective Normal Stress be negative?

No, the Submerged Unit Weight given Effective Normal Stress, measured in Specific Weight cannot be negative.

Which unit is used to measure Submerged Unit Weight given Effective Normal Stress?

Submerged Unit Weight given Effective Normal Stress is usually measured using the Kilonewton per Cubic Meter[kN/m³] for Specific Weight. Newton per Cubic Meter[kN/m³], Newton per Cubic Centimeter[kN/m³], Newton per Cubic Millimeter[kN/m³] are the few other units in which Submerged Unit Weight given Effective Normal Stress can be measured.

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Submerged Unit Weight given Effective Normal Stress Formula

​GoSubmerged Unit Weight given Upward Force Formula

​GoSubmerged Unit Weight given Factor of Safety Formula

Submerged Unit Weight given Effective Normal Stress Example

Submerged Unit Weight given Effective Normal Stress Solution

Submerged Unit Weight given Effective Normal Stress Formula Elements

Other Formulas to find Submerged Unit Weight in KN per Cubic Meter

Other formulas in Steady State Seepage Analysis Along The Slopes category

How to Evaluate Submerged Unit Weight given Effective Normal Stress?

FAQs on Submerged Unit Weight given Effective Normal Stress

Variable Name

GoSubmerged Unit Weight given Upward Force Formula

GoSubmerged Unit Weight given Factor of Safety Formula