Depth of Prism given Upward Force Calculator

✖Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force.ⓘ Normal Stress in Soil Mechanics [σ_n]			+10% -10%
✖Upward Force in Seepage Analysis is due to seepage water.ⓘ Upward Force in Seepage Analysis [F_u]			+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 Upward Force [z]

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Depth of Prism given Upward Force Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
z = (σ_n-F_u)/(y_S*(cos((i*pi)/180))^2)
This formula uses 1 Constants, 1 Functions, 5 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.
Normal Stress in Soil Mechanics - (Measured in Pascal) - Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force.
Upward Force in Seepage Analysis - (Measured in Pascal) - Upward Force in Seepage Analysis is due to seepage water.
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

Normal Stress in Soil Mechanics: 77.36 Kilonewton per Square Meter --> 77360 Pascal (Check conversion here)
Upward Force in Seepage Analysis: 52.89 Kilonewton per Square Meter --> 52890 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_n-F_u)/(y_S*(cos((i*pi)/180))^2) --> (77360-52890)/(5000*(cos((1.11701072127616*pi)/180))^2)

Evaluating ... ...

z = 4.89586055895577

STEP 3: Convert Result to Output's Unit

4.89586055895577 Meter --> No Conversion Required

FINAL ANSWER

4.89586055895577 ≈ 4.895861 Meter <-- Depth of Prism

(Calculation completed in 00.004 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 Upward Force Formula

LaTeX Go

What is Submerged Density?

Submerged density or buoyant density is the density of a mass of soil as observed under water in a saturated condition of course.It is calculated as the difference of the soil density in air and the density of water, divided by the density of water.

How to Calculate Depth of Prism given Upward Force?

Depth of Prism given Upward Force calculator 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 calculate 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 calculate Depth of Prism given Upward Force using this online calculator? To use this online calculator 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. Here is how the Depth of Prism given Upward Force calculation can be explained with given input values -> -3.107181 = (77360-52890)/(5000*(cos((1.11701072127616*pi)/180))^2).

FAQ

What is Depth of Prism given Upward Force?

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 and is represented as z = (σ_n-F_u)/(y_S*(cos((i*pi)/180))^2) or 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). Normal Stress in Soil Mechanics is stress that occurs when a member is loaded by an axial force, Upward Force in Seepage Analysis is due to seepage water, 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 Upward Force?

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 is calculated using 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 calculate Depth of Prism given Upward Force, you need 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). With our tool, you need to enter the respective value for Normal Stress in Soil Mechanics, Upward Force in Seepage Analysis, 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 Normal Stress in Soil Mechanics, Upward Force in Seepage Analysis, 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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