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 = ๐œ/(ฮณ'*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 = ๐œ/(ฮณ'*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 โ‰ˆ 2.988905 Meter <-- Depth of Prism
(Calculation completed in 00.004 seconds)

Credits

Created by Suraj Kumar
Birsa Institute of Technology (BIT), Sindri
Suraj Kumar has created this Calculator and 2200+ more calculators!
Verified by Ishita Goyal
Meerut Institute of Engineering and Technology (MIET), Meerut
Ishita Goyal has verified this Calculator and 2600+ more calculators!

14 Stability Analysis Of Submerged Slopes Calculators

Cohesion given Submerged Unit Weight
Go Cohesion of Soil = (Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination to Horizontal in Soil))))*(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 Factor of Safety for Cohesive Soil
Go Submerged Unit Weight = (Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil))))*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))
Depth of Prism for Cohesive Soil given Submerged Slope
Go 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))))
Factor of Safety for Cohesive Soil given Depth of Prism
Go Factor of Safety = (Cohesion of Soil/(Submerged Unit Weight*Depth of Prism*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))+(tan((Angle of Internal Friction))/tan((Angle of Inclination to Horizontal in Soil)))
Angle of Internal Friction given Factor of Safety for Submerged Slope
Go Angle of Internal Friction of Soil = atan(tan((Angle of Inclination to Horizontal in Soil))*(Factor of Safety-(Cohesion in Soil as Kilopascal/(Submerged Unit Weight*cos((Angle of Inclination to Horizontal in Soil))*sin((Angle of Inclination to Horizontal in Soil))))))
Cohesion of Soil given Submerged Unit Weight
Go Cohesion of Soil = Critical Depth/(((sec((Angle of Inclination to Horizontal in Soil)))^2)/(Submerged Unit Weight*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction)))))
Critical Depth given Submerged Unit Weight
Go Critical Depth = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Submerged Unit Weight*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction))))
Submerged Unit Weight given Critical Depth
Go Submerged Unit Weight = (Cohesion of Soil*(sec((Angle of Inclination to Horizontal in Soil)))^2)/(Critical Depth*(tan((Angle of Inclination to Horizontal in Soil))-tan((Angle of Internal Friction))))
Depth of Prism given Submerged Unit Weight and Shear Stress
Go 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 Component given Submerged Unit Weight
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 Shear Stress Component
Go Submerged Unit Weight = Shear Stress for Submerged Slopes/(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
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
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
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

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 = ๐œ/(ฮณ'*cos((i))*sin((i)))

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 (๐œ), Submerged Unit Weight (ฮณ') & 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 = ๐œ/(ฮณ'*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 (๐œ), Submerged Unit Weight (ฮณ') & 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))))
Let Others Know
โœ–
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!