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 = (σn-Fu)/(yS*(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 = (σn-Fu)/(yS*(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 00.020 seconds)

Credits

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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18 Factor of Steady Seepage Along the Slope Calculators

Saturated Unit Weight given Shear Strength
Go Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*Shear Stress in Soil Mechanics*tan((Angle of Internal Friction of Soil*pi)/180))/(Shear Strength in KN per Cubic Meter*tan((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight given Factor of Safety
Go Saturated Unit Weight of Soil = (Submerged Unit Weight in KN per Cubic Meter*tan((Angle of Internal Friction of Soil*pi)/180))/(Factor of Safety in Soil Mechanics*tan((Angle of Inclination to Horizontal in Soil*pi)/180))
Depth of Prism given Shear Stress and Saturated Unit Weight
Go Depth of Prism = Shear Stress in Soil Mechanics/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))
Saturated Unit Weight given Shear Stress Component
Go Saturated Unit Weight of Soil = Shear Stress in Soil Mechanics/(Depth of Prism*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))
Angle of Inclination given Shear Strength and Submerged Unit Weight
Go Angle of Inclination to Horizontal in Soil = atan((Submerged Unit Weight*tan((Angle of Internal Friction)))/(Saturated Unit Weight in Newton per Cubic Meter*(Shear Strength of Soil/Shear Stress in Soil Mechanics)))
Depth of Prism given Upward Force
Go 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)
Depth of Prism given Saturated Unit Weight
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 Effective Normal Stress
Go Saturated Unit Weight of Soil = Unit Weight of Water+(Effective Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2))
Depth of Prism given Effective Normal Stress
Go Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Saturated Unit Weight given Weight of Soil Prism
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))
Depth of Prism given Submerged Unit Weight and Effective Normal Stress
Go 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)
Depth of Prism given Vertical Stress and Saturated Unit Weight
Go 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))
Saturated Unit Weight given Vertical Stress on Prism
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
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 Normal Stress and Saturated Unit Weight
Go Depth of Prism = Normal Stress in Soil Mechanics/(Saturated Unit Weight of Soil*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Saturated Unit Weight given Normal Stress Component
Go Saturated Unit Weight of Soil = Normal Stress in Soil Mechanics/(Depth of Prism*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Depth of Prism given Upward Force due to Seepage Water
Go Depth of Prism = Upward Force in Seepage Analysis/(Unit Weight of Water*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
Angle of Inclination given Vertical Stress and Saturated Unit Weight
Go Angle of Inclination to Horizontal in Soil = acos(Vertical Stress at Point/(Unit Weight of Soil*Depth of Prism))

Depth of Prism given Upward Force 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)
z = (σn-Fu)/(yS*(cos((i*pi)/180))^2)

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 n), Upward Force in Seepage Analysis (Fu), Submerged Unit Weight in KN per Cubic Meter (yS) & 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 = (σn-Fu)/(yS*(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 n), Upward Force in Seepage Analysis (Fu), Submerged Unit Weight in KN per Cubic Meter (yS) & 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 7 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)
  • Depth of Prism = Shear Stress in Soil Mechanics/(Saturated Unit Weight of Soil*cos((Angle of Inclination to Horizontal in Soil*pi)/180)*sin((Angle of Inclination to Horizontal in Soil*pi)/180))
  • Depth of Prism = Upward Force in Seepage Analysis/(Unit Weight of Water*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
  • 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)
  • Depth of Prism = Effective Normal Stress in Soil Mechanics/((Saturated Unit Weight of Soil-Unit Weight of Water)*(cos((Angle of Inclination to Horizontal in Soil*pi)/180))^2)
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