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## Credits

National Institute Of Technology (NIT), Hamirpur
Anshika Arya has created this Calculator and 1000+ more calculators!
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## Circumferential stress in a solid disc in terms of outer radius of disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
circumferential_stress = ((Density*(Angular velocity^2))*(((3+Poisson's ratio)*Outer Radius^2)-(1+(3*Poisson's ratio)*Radius of element^2)))/8
σc = ((ρ*(ω^2))*(((3+𝛎)*R^2)-(1+(3*𝛎)*r^2)))/8
This formula uses 5 Variables
Variables Used
Density - The density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object. (Measured in Kilogram per Meter³)
Angular velocity- The angular velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.
Poisson's ratio- Poisson's ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.25 and 0.35.
Outer Radius - Outer Radius is the radius of the larger of the two concentric circles that form its boundary. (Measured in Centimeter)
Radius of element - Radius of element is the radius of the element considered in the disc at radius r from the center. (Measured in Millimeter)
STEP 1: Convert Input(s) to Base Unit
Density: 997 Kilogram per Meter³ --> 997 Kilogram per Meter³ No Conversion Required
Angular velocity: 20 --> No Conversion Required
Poisson's ratio: 0.3 --> No Conversion Required
Outer Radius: 10 Centimeter --> 0.1 Meter (Check conversion here)
Radius of element: 5 Millimeter --> 0.005 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σc = ((ρ*(ω^2))*(((3+𝛎)*R^2)-(1+(3*𝛎)*r^2)))/8 --> ((997*(20^2))*(((3+0.3)*0.1^2)-(1+(3*0.3)*0.005^2)))/8
Evaluating ... ...
σc = -48206.071625
STEP 3: Convert Result to Output's Unit
-48206.071625 Pascal -->-48206.071625 Newton per Square Meter (Check conversion here)
FINAL ANSWER
-48206.071625 Newton per Square Meter <-- Circumferential stress
(Calculation completed in 00.031 seconds)

## < 10+ Expression For Stresses In A Solid Disc Calculators

Angular velocity of disc in terms of circumferential stress in a solid disc
angular_velocity_1 = sqrt((((Constant at boundary condition/2)-Circumferential stress)*8)/(Density*(Radius^2)*((3*Poisson's ratio)+1))) Go
Angular velocity of the disc in terms of radial stress in a solid disc
angular_velocity_1 = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Radius^2)*(3+Poisson's ratio))) Go
Radius of the disc in terms of radial stress in a solid disc
radius = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Angular velocity^2)*(3+Poisson's ratio))) Go
Density of material in terms of circumferential stress in a solid disc
density = (((Constant at boundary condition/2)-Circumferential stress)*8)/((Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1)) Go
Constant at boundary condition in terms of circumferential stress in a solid disc
constant_at_boundary_condition = 2*(Circumferential stress+((Density*(Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))/8)) Go
Circumferential stress in a solid disc
circumferential_stress = (Constant at boundary condition/2)-((Density*(Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))/8) Go
Density of material in terms of radial stress in a solid disc
density = (((Constant at boundary condition/2)-Radial Stress)*8)/((Angular velocity^2)*(Radius^2)*(3+Poisson's ratio)) Go
Poisson's ratio in terms of radial stress in a solid disc
poissons_ratio = ((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Angular velocity^2)*(Radius^2)))-3 Go
Constant at boundary condition in terms of radial stress in a solid disc
constant_at_boundary_condition = 2*(Radial Stress+((Density*(Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))/8)) Go
Radial stress in a solid disc
radial_stress = (Constant at boundary condition/2)-((Density*(Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))/8) Go

### Circumferential stress in a solid disc in terms of outer radius of disc Formula

circumferential_stress = ((Density*(Angular velocity^2))*(((3+Poisson's ratio)*Outer Radius^2)-(1+(3*Poisson's ratio)*Radius of element^2)))/8
σc = ((ρ*(ω^2))*(((3+𝛎)*R^2)-(1+(3*𝛎)*r^2)))/8

## What is radial and tangential stress?

The “Hoop Stress” or “Tangential Stress” acts on a line perpendicular to the “longitudinal “and the “radial stress;” this stress attempts to separate the pipe wall in the circumferential direction. This stress is caused by internal pressure.

## How to Calculate Circumferential stress in a solid disc in terms of outer radius of disc?

Circumferential stress in a solid disc in terms of outer radius of disc calculator uses circumferential_stress = ((Density*(Angular velocity^2))*(((3+Poisson's ratio)*Outer Radius^2)-(1+(3*Poisson's ratio)*Radius of element^2)))/8 to calculate the Circumferential stress, The Circumferential stress in a solid disc in terms of outer radius of disc formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction. Circumferential stress and is denoted by σc symbol.

How to calculate Circumferential stress in a solid disc in terms of outer radius of disc using this online calculator? To use this online calculator for Circumferential stress in a solid disc in terms of outer radius of disc, enter Density (ρ), Angular velocity (ω), Poisson's ratio (𝛎), Outer Radius (R) and Radius of element (r) and hit the calculate button. Here is how the Circumferential stress in a solid disc in terms of outer radius of disc calculation can be explained with given input values -> -0.048206 = ((997*(20^2))*(((3+0.3)*0.1^2)-(1+(3*0.3)*0.005^2)))/8.

### FAQ

What is Circumferential stress in a solid disc in terms of outer radius of disc?
The Circumferential stress in a solid disc in terms of outer radius of disc formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction and is represented as σc = ((ρ*(ω^2))*(((3+𝛎)*R^2)-(1+(3*𝛎)*r^2)))/8 or circumferential_stress = ((Density*(Angular velocity^2))*(((3+Poisson's ratio)*Outer Radius^2)-(1+(3*Poisson's ratio)*Radius of element^2)))/8. The density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object, The angular velocity refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time, Poisson's ratio is defined as the ratio of the lateral and axial strain. For many metals and alloys, values of Poisson’s ratio range between 0.25 and 0.35, Outer Radius is the radius of the larger of the two concentric circles that form its boundary and Radius of element is the radius of the element considered in the disc at radius r from the center.
How to calculate Circumferential stress in a solid disc in terms of outer radius of disc?
The Circumferential stress in a solid disc in terms of outer radius of disc formula is defined as hoop stress, a normal stress in the tangential (azimuth) direction is calculated using circumferential_stress = ((Density*(Angular velocity^2))*(((3+Poisson's ratio)*Outer Radius^2)-(1+(3*Poisson's ratio)*Radius of element^2)))/8. To calculate Circumferential stress in a solid disc in terms of outer radius of disc, you need Density (ρ), Angular velocity (ω), Poisson's ratio (𝛎), Outer Radius (R) and Radius of element (r). With our tool, you need to enter the respective value for Density, Angular velocity, Poisson's ratio, Outer Radius and Radius of element 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 Circumferential stress?
In this formula, Circumferential stress uses Density, Angular velocity, Poisson's ratio, Outer Radius and Radius of element. We can use 10 other way(s) to calculate the same, which is/are as follows -
• radial_stress = (Constant at boundary condition/2)-((Density*(Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))/8)
• constant_at_boundary_condition = 2*(Radial Stress+((Density*(Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))/8))
• density = (((Constant at boundary condition/2)-Radial Stress)*8)/((Angular velocity^2)*(Radius^2)*(3+Poisson's ratio))
• angular_velocity_1 = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Radius^2)*(3+Poisson's ratio)))
• radius = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Angular velocity^2)*(3+Poisson's ratio)))
• poissons_ratio = ((((Constant at boundary condition/2)-Radial Stress)*8)/(Density*(Angular velocity^2)*(Radius^2)))-3
• circumferential_stress = (Constant at boundary condition/2)-((Density*(Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))/8)
• constant_at_boundary_condition = 2*(Circumferential stress+((Density*(Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))/8))
• density = (((Constant at boundary condition/2)-Circumferential stress)*8)/((Angular velocity^2)*(Radius^2)*((3*Poisson's ratio)+1))
• angular_velocity_1 = sqrt((((Constant at boundary condition/2)-Circumferential stress)*8)/(Density*(Radius^2)*((3*Poisson's ratio)+1)))
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