Volume Per Unit Length of Prism Solution

STEP 0: Pre-Calculation Summary
Formula Used
Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Vl = (z*b*cos((I)))
This formula uses 1 Functions, 4 Variables
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
Volume per unit length of prism - (Measured in Square Meter) - Volume per unit length of prism means ratio of volume of prism to length of prism.
Depth of Prism - (Measured in Meter) - Depth of Prism is the length of prism along z direction.
Inclined Length - (Measured in Meter) - Inclined Length of prism is along the slope.
Angle of Inclination - (Measured in Radian) - Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.
STEP 1: Convert Input(s) to Base Unit
Depth of Prism: 3 Meter --> 3 Meter No Conversion Required
Inclined Length: 10 Meter --> 10 Meter No Conversion Required
Angle of Inclination: 80 Degree --> 1.3962634015952 Radian (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Vl = (z*b*cos((I))) --> (3*10*cos((1.3962634015952)))
Evaluating ... ...
Vl = 5.2094453300157
STEP 3: Convert Result to Output's Unit
5.2094453300157 Square Meter --> No Conversion Required
FINAL ANSWER
5.2094453300157 5.209445 Square Meter <-- Volume per unit length of prism
(Calculation completed in 00.004 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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23 Stability Analysis of Infinite Slopes in Prism Calculators

Unit Weight of Soil given Factor of Safety for Cohesive Soil
Go Unit Weight of Soil = Cohesion of Soil/((Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))
Cohesion given Factor of Safety for Cohesive Soil
Go Cohesion of Soil = (Factor of Safety-(tan((Angle of Internal Friction*pi)/180)/tan((Angle of Inclination*pi)/180)))*(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination*pi)/180)*sin((Angle of Inclination*pi)/180))
Depth of Prism given Factor of Safety for Cohesive Soil
Go Depth of Prism = Unit Cohesion/((Factor of Safety-(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination))))*Unit Weight of Soil*cos((Angle of Inclination))*sin((Angle of Inclination)))
Factor of Safety for Cohesive Soil given Cohesion
Go Factor of Safety = (Unit Cohesion/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination))*sin((Angle of Inclination))))+(tan((Angle of Internal Friction of Soil))/tan((Angle of Inclination)))
Inclined Length along Slope given Weight of Soil Prism
Go Inclined Length = Weight of Prism/(Unit Weight of Soil*Depth of Prism*cos((Angle of Inclination)))
Unit Weight of Soil given Weight of Soil Prism
Go Unit Weight of Soil = Weight of Prism/(Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Weight of Soil Prism in Stability Analysis
Go Weight of Prism = (Unit Weight of Soil*Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Depth of Prism given Weight of Soil Prism
Go Depth of Prism = Weight of Prism/(Unit Weight of Soil*Inclined Length*cos((Angle of Inclination)))
Angle of Inclination given Weight of Soil Prism
Go Angle of Inclination = acos(Weight of Prism/(Unit Weight of Soil*Depth of Prism*Inclined Length))
Unit Weight of Soil given Vertical Stress on Surface of Prism
Go Unit Weight of Soil = Vertical Stress at a Point in Pascal/(Depth of Prism*cos((Angle of Inclination)))
Depth of Prism given Vertical Stress on Surface of Prism
Go Depth of Prism = Vertical Stress at a Point in Pascal/(Unit Weight of Soil*cos((Angle of Inclination)))
Angle of Inclination given Vertical Stress on Surface of Prism
Go Angle of Inclination = acos(Vertical Stress at a Point in Pascal/(Depth of Prism*Unit Weight of Soil))
Inclined Length along Slope given Volume Per Unit Length of Prism
Go Inclined Length = Volume per unit length of prism/(Depth of Prism*cos((Angle of Inclination)))
Depth of Prism given Volume per Unit Length of Prism
Go Depth of Prism = Volume per unit length of prism/(Inclined Length*cos((Angle of Inclination)))
Volume Per Unit Length of Prism
Go Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Vertical Stress on Surface of Prism given Unit Weight of Soil
Go Vertical Stress at a Point = (Depth of Prism*Unit Weight of Soil*cos((Angle of Inclination)))
Angle of Inclination given Volume per Unit Length of Prism
Go Angle of Inclination = acos(Volume per unit length of prism/(Depth of Prism*Inclined Length))
Inclined Length along Slope given Horizontal Length of Prism
Go Inclined Length = Horizontal Length of Prism/cos((Angle of Inclination))
Horizontal Length of Prism
Go Horizontal Length of Prism = Inclined Length*cos((Angle of Inclination))
Angle of Inclination given Horizontal Length of Prism
Go Angle of Inclination = acos(Horizontal Length of Prism/Inclined Length)
Weight of Soil Prism given Vertical Stress on Surface of Prism
Go Weight of Prism = Vertical Stress at a Point in Pascal*Inclined Length
Inclined Length along Slope given Vertical Stress on Surface of Prism
Go Inclined Length = Weight of Prism/Vertical Stress at a Point*5
Vertical Stress on Surface of Prism
Go Vertical Stress at a Point = Weight of Prism/Inclined Length

Volume Per Unit Length of Prism Formula

Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination)))
Vl = (z*b*cos((I)))

What is Inclined Length?

The slope length is calculated using the Pythagorean Theorem, where the vertical distance is the rise and the horizontal distance is the run.

How to Calculate Volume Per Unit Length of Prism?

Volume Per Unit Length of Prism calculator uses Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination))) to calculate the Volume per unit length of prism, The Volume Per Unit Length of Prism is defined as the value of volume per unit length of soil prism when we have prior information of other parameters used. Volume per unit length of prism is denoted by Vl symbol.

How to calculate Volume Per Unit Length of Prism using this online calculator? To use this online calculator for Volume Per Unit Length of Prism, enter Depth of Prism (z), Inclined Length (b) & Angle of Inclination (I) and hit the calculate button. Here is how the Volume Per Unit Length of Prism calculation can be explained with given input values -> 5.209445 = (3*10*cos((1.3962634015952))).

FAQ

What is Volume Per Unit Length of Prism?
The Volume Per Unit Length of Prism is defined as the value of volume per unit length of soil prism when we have prior information of other parameters used and is represented as Vl = (z*b*cos((I))) or Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination))). Depth of Prism is the length of prism along z direction, Inclined Length of prism is along the slope & Angle of Inclination is defined as the angle measured from the horizontal surface of the wall or any object.
How to calculate Volume Per Unit Length of Prism?
The Volume Per Unit Length of Prism is defined as the value of volume per unit length of soil prism when we have prior information of other parameters used is calculated using Volume per unit length of prism = (Depth of Prism*Inclined Length*cos((Angle of Inclination))). To calculate Volume Per Unit Length of Prism, you need Depth of Prism (z), Inclined Length (b) & Angle of Inclination (I). With our tool, you need to enter the respective value for Depth of Prism, Inclined Length & Angle of Inclination and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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