Depth of Prism given Submerged Unit Weight and Shear Stress Calculator

✖Shear Stress for Submerged Slopes is the force per unit area parallel to the slope surface beneath water, causing deformation.ⓘ Shear Stress for Submerged Slopes [𝜏]			+10% -10%
✖Submerged Unit Weight is the unit weight of weight of soil as observed underwater in a saturated condition of course.ⓘ Submerged Unit Weight [γ^']			+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 Shear Stress [z]

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Depth of Prism given Submerged Unit Weight and Shear Stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
z = 𝜏/(γ^'*cos((i))*sin((i)))
This formula uses 2 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
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.
Shear Stress for Submerged Slopes - (Measured in Pascal) - Shear Stress for Submerged Slopes is the force per unit area parallel to the slope surface beneath water, causing deformation.
Submerged Unit Weight - (Measured in Newton per Cubic Meter) - Submerged Unit Weight is the unit weight of weight of soil as observed underwater 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

Shear Stress for Submerged Slopes: 5.9 Pascal --> 5.9 Pascal No Conversion Required
Submerged Unit Weight: 5.01 Newton per Cubic Meter --> 5.01 Newton per Cubic Meter No Conversion Required
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 = 𝜏/(γ^'*cos((i))*sin((i))) --> 5.9/(5.01*cos((1.11701072127616))*sin((1.11701072127616)))

Evaluating ... ...

z = 2.98890517721587

STEP 3: Convert Result to Output's Unit

2.98890517721587 Meter --> No Conversion Required

FINAL ANSWER

2.98890517721587 ≈ 2.988905 Meter <-- Depth of Prism

(Calculation completed in 00.007 seconds)

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2100+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< Stability Analysis of Submerged Slopes Calculators

Shear Stress Component given Submerged Unit Weight

LaTeX Go Shear Stress for Submerged Slopes = (Submerged Unit Weight*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil)))

Submerged Unit Weight given Normal Stress Component

LaTeX Go Submerged Unit Weight = Normal Stress/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2)

Depth of Prism given Submerged Unit Weight

LaTeX Go Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2)

Normal Stress Component given Submerged Unit Weight

LaTeX Go Normal Stress = Submerged Unit Weight*Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil)))^2

Depth of Prism given Submerged Unit Weight and Shear Stress Formula

LaTeX Go

What is Submerged Unit Weight?

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 Submerged Unit Weight and Shear Stress?

Depth of Prism given Submerged Unit Weight and Shear Stress calculator uses 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))) to calculate the Depth of Prism, The Depth of Prism given Submerged Unit Weight and Shear Stress is defined as the submerged unit weight and shear stress, reflecting material behavior in water. Depth of Prism is denoted by z symbol.

How to calculate Depth of Prism given Submerged Unit Weight and Shear Stress using this online calculator? To use this online calculator for Depth of Prism given Submerged Unit Weight and Shear Stress, enter Shear Stress for Submerged Slopes (𝜏), Submerged Unit Weight (γ^') & 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 Shear Stress calculation can be explained with given input values -> 2.994883 = 5.9/(5.01*cos((1.11701072127616))*sin((1.11701072127616))).

FAQ

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

The Depth of Prism given Submerged Unit Weight and Shear Stress is defined as the submerged unit weight and shear stress, reflecting material behavior in water and is represented as z = 𝜏/(γ^'*cos((i))*sin((i))) or 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))). Shear Stress for Submerged Slopes is the force per unit area parallel to the slope surface beneath water, causing deformation, Submerged Unit Weight is the unit weight of weight of soil as observed underwater 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 Shear Stress?

The Depth of Prism given Submerged Unit Weight and Shear Stress is defined as the submerged unit weight and shear stress, reflecting material behavior in water is calculated using 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))). To calculate Depth of Prism given Submerged Unit Weight and Shear Stress, you need Shear Stress for Submerged Slopes (𝜏), Submerged Unit Weight (γ^') & Angle of Inclination to Horizontal in Soil (i). With our tool, you need to enter the respective value for Shear Stress for Submerged Slopes, Submerged Unit Weight & 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 Shear Stress for Submerged Slopes, Submerged Unit Weight & Angle of Inclination to Horizontal in Soil. We can use 2 other way(s) to calculate the same, which is/are as follows -

Depth of Prism = Normal Stress/(Submerged Unit Weight*(cos((Angle of Inclination to Horizontal in Soil)))^2)
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))))

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