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## Credits

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

STEP 0: Pre-Calculation Summary
Formula Used
density = ((8*Circumferential stress)/(Density*(Angular velocity^2)*(3+Poisson's ratio)*(Outer Radius^2)))
ρ = ((8*σc)/(ρ*(ω^2)*(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)
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)
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
Outer Radius: 10 Centimeter --> 0.1 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ρ = ((8*σc)/(ρ*(ω^2)*(3+𝛎)*(R^2))) --> ((8*1)/(997*(20^2)*(3+0.3)*(0.1^2)))
Evaluating ... ...
ρ = 0.000607884258837117
STEP 3: Convert Result to Output's Unit
0.000607884258837117 Kilogram per Meter³ --> No Conversion Required
0.000607884258837117 Kilogram per Meter³ <-- Density
(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

### Density of material in terms of maximum circumferential stress in solid disc Formula

density = ((8*Circumferential stress)/(Density*(Angular velocity^2)*(3+Poisson's ratio)*(Outer Radius^2)))
ρ = ((8*σc)/(ρ*(ω^2)*(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 maximum circumferential stress in solid disc?

Density of material in terms of maximum circumferential stress in solid disc calculator uses density = ((8*Circumferential stress)/(Density*(Angular velocity^2)*(3+Poisson's ratio)*(Outer Radius^2))) to calculate the Density, The Density of material in terms of maximum circumferential stress in solid 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 maximum circumferential stress in solid disc using this online calculator? To use this online calculator for Density of material in terms of maximum circumferential stress in solid disc, enter Circumferential stress c), Angular velocity (ω), Poisson's ratio (𝛎) and Outer Radius (R) and hit the calculate button. Here is how the Density of material in terms of maximum circumferential stress in solid disc calculation can be explained with given input values -> 0.000608 = ((8*1)/(997*(20^2)*(3+0.3)*(0.1^2))).

### FAQ

What is Density of material in terms of maximum circumferential stress in solid disc?
The Density of material in terms of maximum circumferential stress in solid 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)/(ρ*(ω^2)*(3+𝛎)*(R^2))) or density = ((8*Circumferential stress)/(Density*(Angular velocity^2)*(3+Poisson's ratio)*(Outer Radius^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 and Outer Radius is the radius of the larger of the two concentric circles that form its boundary.
How to calculate Density of material in terms of maximum circumferential stress in solid disc?
The Density of material in terms of maximum circumferential stress in solid 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)/(Density*(Angular velocity^2)*(3+Poisson's ratio)*(Outer Radius^2))). To calculate Density of material in terms of maximum circumferential stress in solid disc, you need Circumferential stress c), Angular velocity (ω), Poisson's ratio (𝛎) and Outer Radius (R). With our tool, you need to enter the respective value for Circumferential stress, Angular velocity, Poisson's ratio and Outer Radius 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 and Outer Radius. We can use 10 other way(s) to calculate the same, which is/are as follows -