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## Credits

National Institute Of Technology (NIT), Hamirpur
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## Radius of the disc in terms of circumferential stress in a solid disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
radius = sqrt((((Constant at boundary condition/2)-Circumferential stress)*8)/(Density*(Angular velocity^2)*((3*Poisson's ratio)+1)))
r = sqrt((((C1/2)-σc)*8)/(ρ*(ω^2)*((3*𝛎)+1)))
This formula uses 1 Functions, 5 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
Constant at boundary condition- Constant at boundary condition is value obtained for stress in solid disc.
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
Constant at boundary condition: 5 --> No Conversion Required
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((((C1/2)-σc)*8)/(ρ*(ω^2)*((3*𝛎)+1))) --> sqrt((((5/2)-1)*8)/(997*(20^2)*((3*0.3)+1)))
Evaluating ... ...
r = 0.00397957091130751
STEP 3: Convert Result to Output's Unit
0.00397957091130751 Meter -->0.397957091130751 Centimeter (Check conversion here)
(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
Radius of the disc in terms of radial stress in a solid disc
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
Poisson's ratio in terms of radial stress in a solid disc
Constant at boundary condition in terms of radial stress in a solid disc
Radial stress in a solid disc

### Radius of the disc in terms of circumferential stress in a solid disc Formula

radius = sqrt((((Constant at boundary condition/2)-Circumferential stress)*8)/(Density*(Angular velocity^2)*((3*Poisson's ratio)+1)))
r = sqrt((((C1/2)-σc)*8)/(ρ*(ω^2)*((3*𝛎)+1)))

## 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 Radius of the disc in terms of circumferential stress in a solid disc?

Radius of the disc in terms of circumferential stress in a solid disc calculator uses radius = sqrt((((Constant at boundary condition/2)-Circumferential stress)*8)/(Density*(Angular velocity^2)*((3*Poisson's ratio)+1))) to calculate the Radius, The Radius of the disc in terms of circumferential stress in a solid disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Radius and is denoted by r symbol.

How to calculate Radius of the disc in terms of circumferential stress in a solid disc using this online calculator? To use this online calculator for Radius of the disc in terms of circumferential stress in a solid disc, enter Constant at boundary condition (C1), Circumferential stress c), Density (ρ), Angular velocity (ω) and Poisson's ratio (𝛎) and hit the calculate button. Here is how the Radius of the disc in terms of circumferential stress in a solid disc calculation can be explained with given input values -> 0.397957 = sqrt((((5/2)-1)*8)/(997*(20^2)*((3*0.3)+1))).

### FAQ

What is Radius of the disc in terms of circumferential stress in a solid disc?
The Radius of the disc in terms of circumferential stress in a 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((((C1/2)-σc)*8)/(ρ*(ω^2)*((3*𝛎)+1))) or radius = sqrt((((Constant at boundary condition/2)-Circumferential stress)*8)/(Density*(Angular velocity^2)*((3*Poisson's ratio)+1))). Constant at boundary condition is value obtained for stress in solid disc, 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 Radius of the disc in terms of circumferential stress in a solid disc?
The Radius of the disc in terms of circumferential stress in a 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 radius = sqrt((((Constant at boundary condition/2)-Circumferential stress)*8)/(Density*(Angular velocity^2)*((3*Poisson's ratio)+1))). To calculate Radius of the disc in terms of circumferential stress in a solid disc, you need Constant at boundary condition (C1), Circumferential stress c), Density (ρ), Angular velocity (ω) and Poisson's ratio (𝛎). With our tool, you need to enter the respective value for Constant at boundary condition, 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 Radius?
In this formula, Radius uses Constant at boundary condition, 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 -