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## Credits

National Institute Of Technology (NIT), Hamirpur
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## Density of material in terms of circumferential stress in a solid disc and outer radius of disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
density = ((8*Circumferential stress)/(((Angular velocity^2))*(((3+Poisson's ratio)*Outer Radius^2)-(1+(3*Poisson's ratio)*Radius of element^2))))
ρ = ((8*σc)/(((ω^2))*(((3+𝛎)*R^2)-(1+(3*𝛎)*r^2))))
This formula uses 5 Variables
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)
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
Circumferential stress: 1 Newton per Square Meter --> 1 Pascal (Check conversion here)
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
ρ = ((8*σc)/(((ω^2))*(((3+𝛎)*R^2)-(1+(3*𝛎)*r^2)))) --> ((8*1)/(((20^2))*(((3+0.3)*0.1^2)-(1+(3*0.3)*0.005^2))))
Evaluating ... ...
ρ = -0.020682042041421
STEP 3: Convert Result to Output's Unit
-0.020682042041421 Kilogram per Meter³ --> No Conversion Required
FINAL ANSWER
-0.020682042041421 Kilogram per Meter³ <-- Density
(Calculation completed in 00.066 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

### Density of material in terms of circumferential stress in a solid disc and outer radius of disc Formula

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

## 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 Density of material in terms of circumferential stress in a solid disc and outer radius of disc?

Density of material in terms of circumferential stress in a solid disc and outer radius of disc calculator uses density = ((8*Circumferential stress)/(((Angular velocity^2))*(((3+Poisson's ratio)*Outer Radius^2)-(1+(3*Poisson's ratio)*Radius of element^2)))) to calculate the Density, The Density of material in terms of circumferential stress in a solid disc and outer radius of disc formula is defined as a measure of mass per volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water). Density and is denoted by ρ symbol.

How to calculate Density of material in terms of circumferential stress in a solid disc and outer radius of disc using this online calculator? To use this online calculator for Density of material in terms of circumferential stress in a solid disc and outer radius of disc, enter Circumferential stress c), Angular velocity (ω), Poisson's ratio (𝛎), Outer Radius (R) and Radius of element (r) and hit the calculate button. Here is how the Density of material in terms of circumferential stress in a solid disc and outer radius of disc calculation can be explained with given input values -> -0.020682 = ((8*1)/(((20^2))*(((3+0.3)*0.1^2)-(1+(3*0.3)*0.005^2)))).

### FAQ

What is Density of material in terms of circumferential stress in a solid disc and outer radius of disc?
The Density of material in terms of circumferential stress in a solid disc and outer radius of disc formula is defined as a measure of mass per volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water) and is represented as ρ = ((8*σc)/(((ω^2))*(((3+𝛎)*R^2)-(1+(3*𝛎)*r^2)))) or density = ((8*Circumferential stress)/(((Angular velocity^2))*(((3+Poisson's ratio)*Outer Radius^2)-(1+(3*Poisson's ratio)*Radius of element^2)))). Circumferential stress is the force over area exerted circumferentially (perpendicular to the axis and the radius, 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 Density of material in terms of circumferential stress in a solid disc and outer radius of disc?
The Density of material in terms of circumferential stress in a solid disc and outer radius of disc formula is defined as a measure of mass per volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water) is calculated using density = ((8*Circumferential stress)/(((Angular velocity^2))*(((3+Poisson's ratio)*Outer Radius^2)-(1+(3*Poisson's ratio)*Radius of element^2)))). To calculate Density of material in terms of circumferential stress in a solid disc and outer radius of disc, you need Circumferential stress c), 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 Circumferential stress, 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 Density?
In this formula, Density uses Circumferential stress, 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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