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## Credits

National Institute Of Technology (NIT), Hamirpur
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## Outer radius of disc in terms of maximum circumferential stress in solid disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
outer_radius = sqrt((8*Circumferential stress)/(Density*(Angular velocity^2)*(3+Poisson's ratio)))
R = sqrt((8*σc)/(ρ*(ω^2)*(3+𝛎)))
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Circumferential stress - Circumferential stress is the force over area exerted circumferentially (perpendicular to the axis and the radius. (Measured in Newton per Square Meter)
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.
STEP 1: Convert Input(s) to Base Unit
Circumferential stress: 1 Newton per Square Meter --> 1 Pascal (Check conversion here)
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
STEP 2: Evaluate Formula
Substituting Input Values in Formula
R = sqrt((8*σc)/(ρ*(ω^2)*(3+𝛎))) --> sqrt((8*1)/(997*(20^2)*(3+0.3)))
Evaluating ... ...
R = 0.00246553089381804
STEP 3: Convert Result to Output's Unit
0.00246553089381804 Meter -->0.246553089381804 Centimeter (Check conversion here)
FINAL ANSWER
0.246553089381804 Centimeter <-- Outer Radius
(Calculation completed in 00.016 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

### Outer radius of disc in terms of maximum circumferential stress in solid disc Formula

outer_radius = sqrt((8*Circumferential stress)/(Density*(Angular velocity^2)*(3+Poisson's ratio)))
R = sqrt((8*σc)/(ρ*(ω^2)*(3+𝛎)))

## 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 Outer radius of disc in terms of maximum circumferential stress in solid disc?

Outer radius of disc in terms of maximum circumferential stress in solid disc calculator uses outer_radius = sqrt((8*Circumferential stress)/(Density*(Angular velocity^2)*(3+Poisson's ratio))) to calculate the Outer Radius, The Outer radius of disc in terms of maximum circumferential stress in solid disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Outer Radius and is denoted by R symbol.

How to calculate Outer radius of disc in terms of maximum circumferential stress in solid disc using this online calculator? To use this online calculator for Outer radius of disc in terms of maximum circumferential stress in solid disc, enter Circumferential stress c), Density (ρ), Angular velocity (ω) and Poisson's ratio (𝛎) and hit the calculate button. Here is how the Outer radius of disc in terms of maximum circumferential stress in solid disc calculation can be explained with given input values -> 0.246553 = sqrt((8*1)/(997*(20^2)*(3+0.3))).

### FAQ

What is Outer radius of disc in terms of maximum circumferential stress in solid disc?
The Outer radius of disc in terms of maximum circumferential stress in solid disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface and is represented as R = sqrt((8*σc)/(ρ*(ω^2)*(3+𝛎))) or outer_radius = sqrt((8*Circumferential stress)/(Density*(Angular velocity^2)*(3+Poisson's ratio))). Circumferential stress is the force over area exerted circumferentially (perpendicular to the axis and the radius, 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 and 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.
How to calculate Outer radius of disc in terms of maximum circumferential stress in solid disc?
The Outer radius of disc in terms of maximum circumferential stress in solid disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface is calculated using outer_radius = sqrt((8*Circumferential stress)/(Density*(Angular velocity^2)*(3+Poisson's ratio))). To calculate Outer radius of disc in terms of maximum circumferential stress in solid disc, you need Circumferential stress c), Density (ρ), Angular velocity (ω) and Poisson's ratio (𝛎). With our tool, you need to enter the respective value for Circumferential stress, Density, Angular velocity and Poisson's ratio 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 Outer Radius?
In this formula, Outer Radius uses Circumferential stress, Density, Angular velocity and Poisson's ratio. 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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