Depth of Prism given Submerged Unit Weight and Effective Normal Stress Calculator

✖Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.ⓘ Effective Normal Stress in Soil Mechanics [σ^']			+10% -10%
✖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.ⓘ Submerged Unit Weight in KN per Cubic Meter [y_S]			+10% -10%
✖Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.ⓘ Angle of Inclination to Horizontal in Soil [i]			+10% -10%

✖Depth of Prism is the length of prism along z direction.ⓘ Depth of Prism given Submerged Unit Weight and Effective Normal Stress [z]

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Depth of Prism given Submerged Unit Weight and Effective Normal Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

Depth of Prism = Effective Normal Stress in Soil Mechanics/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
z = σ^'/(y_S*(cos((i*pi)/180))^2)
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Effective Normal Stress in Soil Mechanics - (Measured in Pascal) - Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure.
Submerged Unit Weight in KN per Cubic Meter - (Measured in Newton 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.
Angle of Inclination to Horizontal in Soil - (Measured in Radian) - Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

STEP 1: Convert Input(s) to Base Unit

Effective Normal Stress in Soil Mechanics: 24.67 Kilonewton per Square Meter --> 24670 Pascal (Check conversion here)
Submerged Unit Weight in KN per Cubic Meter: 5 Kilonewton per Cubic Meter --> 5000 Newton per Cubic Meter (Check conversion here)
Angle of Inclination to Horizontal in Soil: 64 Degree --> 1.11701072127616 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = σ^'/(y_S*(cos((i*pi)/180))^2) --> 24670/(5000*(cos((1.11701072127616*pi)/180))^2)

Evaluating ... ...

z = 4.93587576581278

STEP 3: Convert Result to Output's Unit

4.93587576581278 Meter --> No Conversion Required

FINAL ANSWER

4.93587576581278 ≈ 4.935876 Meter <-- Depth of Prism

(Calculation completed in 00.020 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

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Meerut Institute of Engineering and Technology (MIET), Meerut

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< Factor of Steady Seepage Along the Slope Calculators

Depth of Prism given Saturated Unit Weight

LaTeX Go 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))

Saturated Unit Weight given Weight of Soil Prism

LaTeX Go Saturated Unit Weight of Soil = Weight of Prism in Soil Mechanics/(Depth of Prism*Inclined Length of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Saturated Unit Weight given Vertical Stress on Prism

LaTeX Go Saturated Unit Weight of Soil = Vertical Stress at a Point in Kilopascal/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180))

Angle of Inclination given Saturated Unit Weight

LaTeX Go Angle of Inclination to Horizontal in Soil = acos(Weight of Prism in Soil Mechanics/(Unit Weight of Soil*Depth of Prism*Inclined Length of Prism))

Depth of Prism given Submerged Unit Weight and Effective Normal Stress Formula

LaTeX Go

What is Submerged Unit Weight?

The weight of the solids in air minus the weight of water displaced by the solids per unit of volume of soil mass; the saturated unit weight minus the unit weight of water.

How to Calculate Depth of Prism given Submerged Unit Weight and Effective Normal Stress?

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

How to calculate Depth of Prism given Submerged Unit Weight and Effective Normal Stress using this online calculator? To use this online calculator for Depth of Prism given Submerged Unit Weight and Effective Normal Stress, enter Effective Normal Stress in Soil Mechanics (σ^'), Submerged Unit Weight in KN per Cubic Meter (y_S) & Angle of Inclination to Horizontal in Soil (i) and hit the calculate button. Here is how the Depth of Prism given Submerged Unit Weight and Effective Normal Stress calculation can be explained with given input values -> 4.935876 = 24670/(5000*(cos((1.11701072127616*pi)/180))^2).

FAQ

What is Depth of Prism given Submerged Unit Weight and Effective Normal Stress?

The Depth of Prism given Submerged Unit Weight and Effective Normal Stress is defined as the value of depth of prism when we have prior information of other parameters used and is represented as z = σ^'/(y_S*(cos((i*pi)/180))^2) or Depth of Prism = Effective Normal Stress in Soil Mechanics/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). Effective Normal Stress in Soil Mechanics is related to total stress and pore pressure, 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 & Angle of Inclination to Horizontal in Soil is defined as the angle measured from the horizontal surface of the wall or any object.

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

The Depth of Prism given Submerged Unit Weight and Effective Normal Stress is defined as the value of depth of prism when we have prior information of other parameters used is calculated using Depth of Prism = Effective Normal Stress in Soil Mechanics/(Submerged Unit Weight in KN per Cubic Meter*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2). To calculate Depth of Prism given Submerged Unit Weight and Effective Normal Stress, you need Effective Normal Stress in Soil Mechanics (σ^'), Submerged Unit Weight in KN per Cubic Meter (y_S) & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Effective Normal Stress in Soil Mechanics, Submerged Unit Weight in KN per Cubic Meter & Angle of Inclination to Horizontal in Soil and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Depth of Prism?

In this formula, Depth of Prism uses Effective Normal Stress in Soil Mechanics, Submerged Unit Weight in KN per Cubic Meter & Angle of Inclination to Horizontal in Soil. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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