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## Credits

National Institute Of Technology (NIT), Hamirpur
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## Constant at boundary condition for the circular disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
constant_at_boundary_condition = (Density*(Angular velocity^2)*(Outer Radius^2)*(3+Poisson's ratio))/8
C1 = (ρ*(ω^2)*(R^2)*(3+𝛎))/8
This formula uses 4 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.
Outer Radius - Outer Radius is the radius of the larger of the two concentric circles that form its boundary. (Measured in Centimeter)
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
Density: 997 Kilogram per Meter³ --> 997 Kilogram per Meter³ No Conversion Required
Angular velocity: 20 --> No Conversion Required
Outer Radius: 10 Centimeter --> 0.1 Meter (Check conversion here)
Poisson's ratio: 0.3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
C1 = (ρ*(ω^2)*(R^2)*(3+𝛎))/8 --> (997*(20^2)*(0.1^2)*(3+0.3))/8
Evaluating ... ...
C1 = 1645.05
STEP 3: Convert Result to Output's Unit
1645.05 --> No Conversion Required
FINAL ANSWER
1645.05 <-- Constant at boundary condition
(Calculation completed in 00.015 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

### Constant at boundary condition for the circular disc Formula

constant_at_boundary_condition = (Density*(Angular velocity^2)*(Outer Radius^2)*(3+Poisson's ratio))/8
C1 = (ρ*(ω^2)*(R^2)*(3+𝛎))/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 Constant at boundary condition for the circular disc?

Constant at boundary condition for the circular disc calculator uses constant_at_boundary_condition = (Density*(Angular velocity^2)*(Outer Radius^2)*(3+Poisson's ratio))/8 to calculate the Constant at boundary condition, The Constant at boundary condition for the circular disc formula is defined as the value obtained at boundary condition for the equation of stresses in the solid disc. Constant at boundary condition and is denoted by C1 symbol.

How to calculate Constant at boundary condition for the circular disc using this online calculator? To use this online calculator for Constant at boundary condition for the circular disc, enter Density (ρ), Angular velocity (ω), Outer Radius (R) and Poisson's ratio (𝛎) and hit the calculate button. Here is how the Constant at boundary condition for the circular disc calculation can be explained with given input values -> 1645.05 = (997*(20^2)*(0.1^2)*(3+0.3))/8.

### FAQ

What is Constant at boundary condition for the circular disc?
The Constant at boundary condition for the circular disc formula is defined as the value obtained at boundary condition for the equation of stresses in the solid disc and is represented as C1 = (ρ*(ω^2)*(R^2)*(3+𝛎))/8 or constant_at_boundary_condition = (Density*(Angular velocity^2)*(Outer Radius^2)*(3+Poisson's ratio))/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, Outer Radius is the radius of the larger of the two concentric circles that form its boundary 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 Constant at boundary condition for the circular disc?
The Constant at boundary condition for the circular disc formula is defined as the value obtained at boundary condition for the equation of stresses in the solid disc is calculated using constant_at_boundary_condition = (Density*(Angular velocity^2)*(Outer Radius^2)*(3+Poisson's ratio))/8. To calculate Constant at boundary condition for the circular disc, you need Density (ρ), Angular velocity (ω), Outer Radius (R) and Poisson's ratio (𝛎). With our tool, you need to enter the respective value for Density, Angular velocity, Outer Radius 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 Constant at boundary condition?
In this formula, Constant at boundary condition uses Density, Angular velocity, Outer Radius 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)))
Where is the Constant at boundary condition for the circular disc calculator used?
Among many, Constant at boundary condition for the circular disc calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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