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Depth of Prism given Upward Force Formula

GoDepth of Prism given Saturated Unit Weight Formula

GoDepth of Prism given Vertical Stress and Saturated Unit Weight Formula

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

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

z - Depth of Prism?σ_n - Normal Stress in Soil Mechanics?F_u - Upward Force in Seepage Analysis?y_S - Submerged Unit Weight in KN per Cubic Meter?i - Angle of Inclination to Horizontal in Soil?π - Archimedes' constant?

Depth of Prism given Upward Force Example

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Here is how the Depth of Prism given Upward Force equation looks like with Values.

Here is how the Depth of Prism given Upward Force equation looks like with Units.

Here is how the Depth of Prism given Upward Force equation looks like.

4.8959 = \frac{77.36 - 52.89}{5 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

4.8959m = \frac{77.36kN/m² - 52.89kN/m²}{5kN/m³ \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

4.8959 = \frac{77.36 - 52.89}{5 \cdot {(\cos (\frac{64 \cdot 3.1416}{180}))}^{2}}

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Depth of Prism given Upward Force Solution

Follow our step by step solution on how to calculate Depth of Prism given Upward Force?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

z = \frac{77.36kN/m² - 52.89kN/m²}{5kN/m³ \cdot {(\cos (\frac{64° \cdot π}{180}))}^{2}}

Next Step Substitute values of Constants

∴

z = \frac{77.36kN/m² - 52.89kN/m²}{5kN/m³ \cdot {(\cos (\frac{64° \cdot 3.1416}{180}))}^{2}}

Next Step Convert Units

∴

z = \frac{77360Pa - 52890Pa}{5000N/m³ \cdot {(\cos (\frac{1.117rad \cdot 3.1416}{180}))}^{2}}

Next Step Prepare to Evaluate

∴

z = \frac{77360 - 52890}{5000 \cdot {(\cos (\frac{1.117 \cdot 3.1416}{180}))}^{2}}

Next Step Evaluate

∴

z = 4.89586055895577m

LAST Step Rounding Answer

∴

z = 4.8959m

Depth of Prism given Upward Force Formula Elements

Variables

Constants

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 in Soil Mechanics

Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force.

Symbol: σ_n

Measurement: StressUnit: kN/m²

Note: Value can be positive or negative.

Formulas to find Normal Stress in Soil Mechanics

Upward Force in Seepage Analysis

Upward Force in Seepage Analysis is due to seepage water.

Symbol: F_u

Measurement: PressureUnit: kN/m²

Note: Value should be greater than 0.

Formulas to find Upward Force in Seepage Analysis

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

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 Depth of Prism

Go Depth of Prism given Saturated Unit Weight

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

Go Depth of Prism given Vertical Stress and Saturated Unit Weight

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

Go Depth of Prism given Normal Stress and Saturated Unit Weight

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

Go Depth of Prism given Shear Stress and Saturated Unit Weight

z = \frac{ζ soil}{γ saturated \cdot \cos (\frac{i \cdot π}{180}) \cdot \sin (\frac{i \cdot π}{180})}

Other formulas in Factor of Steady Seepage Along the Slope category

Go Saturated Unit Weight given Weight of Soil Prism

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

Go Angle of Inclination given Saturated Unit Weight

i = a \cos (\frac{W prism}{γ \cdot z \cdot b})

Go Saturated Unit Weight given Vertical Stress on Prism

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

Go Angle of Inclination given Vertical Stress and Saturated Unit Weight

i = a \cos (\frac{σ z}{γ \cdot z})

How to Evaluate Depth of Prism given Upward Force?

Depth of Prism given Upward Force evaluator uses Depth of Prism = (Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2) to evaluate the Depth of Prism, The Depth of Prism given Upward Force is defined as the value of depth of soil prism considered when we have prior information of other parameters used. Depth of Prism is denoted by z symbol.

How to evaluate Depth of Prism given Upward Force using this online evaluator? To use this online evaluator for Depth of Prism given Upward Force, enter Normal Stress in Soil Mechanics (σ_n), Upward Force in Seepage Analysis (F_u), Submerged Unit Weight in KN per Cubic Meter (y_S) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button.

FAQs on Depth of Prism given Upward Force

What is the formula to find Depth of Prism given Upward Force?

The formula of Depth of Prism given Upward Force is expressed as Depth of Prism = (Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Here is an example- -3.107181 = (77360-52890)/(5000*(cos((1.11701072127616*pi)/180))^2).

How to calculate Depth of Prism given Upward Force?

With Normal Stress in Soil Mechanics (σ_n), Upward Force in Seepage Analysis (F_u), Submerged Unit Weight in KN per Cubic Meter (y_S) & Angle of Inclination to Horizontal in Soil (i) we can find Depth of Prism given Upward Force using the formula - Depth of Prism = (Normal Stress in Soil Mechanics-Upward Force in Seepage Analysis)/(Submerged Unit Weight in KN per Cubic Meter*(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 Depth of Prism?

Here are the different ways to Calculate Depth of Prism-

Depth of Prism=Weight of Prism in Soil Mechanics/(Saturated Unit Weight in Newton per Cubic Meter*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism=Vertical Stress at a Point in Kilopascal/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism=Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)

Can the Depth of Prism given Upward Force be negative?

No, the Depth of Prism given Upward Force, measured in Length cannot be negative.

Which unit is used to measure Depth of Prism given Upward Force?

Depth of Prism given Upward Force 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 Upward Force can be measured.

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Depth of Prism given Upward Force Formula

​GoDepth of Prism given Saturated Unit Weight Formula

​GoDepth of Prism given Vertical Stress and Saturated Unit Weight Formula

Depth of Prism given Upward Force Example

Depth of Prism given Upward Force Solution

Depth of Prism given Upward Force Formula Elements

Other Formulas to find Depth of Prism

Other formulas in Factor of Steady Seepage Along the Slope category

How to Evaluate Depth of Prism given Upward Force?

FAQs on Depth of Prism given Upward Force

Variable Name

GoDepth of Prism given Saturated Unit Weight Formula

GoDepth of Prism given Vertical Stress and Saturated Unit Weight Formula