Density of material given Circumferential stress and Outer radius Calculator

✖Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.ⓘ Circumferential Stress [σ_c]			+10% -10%
✖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.ⓘ Angular Velocity [ω]			+10% -10%
✖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 0.1 and 0.5.ⓘ Poisson's Ratio [𝛎]			+10% -10%
✖Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.ⓘ Outer Radius Disc [r_outer]			+10% -10%
✖The Radius of Element is the radius of the element considered in the disc at radius r from the centre.ⓘ Radius of Element [r]			+10% -10%

✖Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.ⓘ Density of material given Circumferential stress and Outer radius [ρ]

⎘ Copy

👎

Formula

LaTeX

Reset

👍

Download Strength of Materials Formula PDF PDF Image

Density of material given Circumferential stress and Outer radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density Of Disc = ((8*Circumferential Stress)/(((Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2))))
ρ = ((8*σ_c)/(((ω^2))*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*r^2))))
This formula uses 6 Variables

Variables Used

Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density Of Disc shows the denseness of disc in a specific given area. This is taken as mass per unit volume of a given disc.
Circumferential Stress - (Measured in Pascal) - Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.
Angular Velocity - (Measured in Radian per Second) - 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 0.1 and 0.5.
Outer Radius Disc - (Measured in Meter) - Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.
Radius of Element - (Measured in Meter) - The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

STEP 1: Convert Input(s) to Base Unit

Circumferential Stress: 100 Newton per Square Meter --> 100 Pascal (Check conversion here)
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Poisson's Ratio: 0.3 --> No Conversion Required
Outer Radius Disc: 900 Millimeter --> 0.9 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*σ_c)/(((ω^2))*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*r^2)))) --> ((8*100)/(((11.2^2))*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2))))

Evaluating ... ...

ρ = 3.81209611032316

STEP 3: Convert Result to Output's Unit

3.81209611032316 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

3.81209611032316 ≈ 3.812096 Kilogram per Cubic Meter <-- Density Of Disc

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Mechanical » Density of Disc » Density of material given Circumferential stress and Outer radius

Credits

Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has created this Calculator and 2000+ more calculators!

Verified by Payal Priya

Birsa Institute of Technology (BIT), Sindri

Payal Priya has verified this Calculator and 1900+ more calculators!

< Density of Disc Calculators

Density of material given Circumferential stress in solid disc

LaTeX Go Density Of Disc = (((Constant at boundary condition/2)-Circumferential Stress)*8)/((Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))

Density of disc material given Radial stress in solid disc and outer radius

LaTeX Go Density Of Disc = ((8*Radial Stress)/((Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2))))

Density of material given constant at boundary condition for circular disc

LaTeX Go Density Of Disc = (8*Constant at boundary condition)/((Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))

Density of material given Circumferential stress at center of solid disc

LaTeX Go Density Of Disc = ((8*Circumferential Stress)/((Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2)))

Density of material given Circumferential stress and Outer radius Formula

LaTeX Go

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 given Circumferential stress and Outer radius?

Density of material given Circumferential stress and Outer radius calculator uses Density Of Disc = ((8*Circumferential Stress)/(((Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))) to calculate the Density Of Disc, The Density of material given Circumferential stress and Outer radius 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 Of Disc is denoted by ρ symbol.

How to calculate Density of material given Circumferential stress and Outer radius using this online calculator? To use this online calculator for Density of material given Circumferential stress and Outer radius, enter Circumferential Stress (σ_c), Angular Velocity (ω), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (r) and hit the calculate button. Here is how the Density of material given Circumferential stress and Outer radius calculation can be explained with given input values -> 3.812096 = ((8*100)/(((11.2^2))*(((3+0.3)*0.9^2)-(1+(3*0.3)*0.005^2)))).

FAQ

What is Density of material given Circumferential stress and Outer radius?

The Density of material given Circumferential stress and Outer radius 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*σ_c)/(((ω^2))*(((3+𝛎)*r_outer^2)-(1+(3*𝛎)*r^2)))) or Density Of Disc = ((8*Circumferential Stress)/(((Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^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 0.1 and 0.5, Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary & The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

How to calculate Density of material given Circumferential stress and Outer radius?

The Density of material given Circumferential stress and Outer radius 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 Of Disc = ((8*Circumferential Stress)/(((Angular Velocity^2))*(((3+Poisson's Ratio)*Outer Radius Disc^2)-(1+(3*Poisson's Ratio)*Radius of Element^2)))). To calculate Density of material given Circumferential stress and Outer radius, you need Circumferential Stress (σ_c), Angular Velocity (ω), Poisson's Ratio (𝛎), Outer Radius Disc (r_outer) & Radius of Element (r). With our tool, you need to enter the respective value for Circumferential Stress, Angular Velocity, Poisson's Ratio, Outer Radius Disc & 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 Of Disc?

In this formula, Density Of Disc uses Circumferential Stress, Angular Velocity, Poisson's Ratio, Outer Radius Disc & Radius of Element. We can use 3 other way(s) to calculate the same, which is/are as follows -

Density Of Disc = ((8*Radial Stress)/((Angular Velocity^2)*(3+Poisson's Ratio)*((Outer Radius Disc^2)-(Radius of Element^2))))
Density Of Disc = ((8*Circumferential Stress)/((Angular Velocity^2)*(3+Poisson's Ratio)*(Outer Radius Disc^2)))
Density Of Disc = (8*Constant at boundary condition)/((Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))

Home

FREE PDFs

🔍 Search