Outer radius of disc given Circumferential stress Calculator

✖Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.ⓘ Circumferential Stress [σ_c]			+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 Disc [ρ]			+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%
✖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%

✖Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.ⓘ Outer radius of disc given Circumferential stress [r_outer]

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Formula

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Outer radius of disc given Circumferential stress

Formula

`"r"_{"outer"} = sqrt(((8*"σ"_{"c"})/(("ρ"*("ω"^2))*((1+(3*"𝛎")*"r"^2))))/(3+"𝛎"))`

Example

`"982.9923mm"=sqrt(((8*"100N/m²")/(("2kg/m³"*(("11.2rad/s")^2))*((1+(3*"0.3")*("5mm")^2))))/(3+"0.3"))`

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Outer radius of disc given Circumferential stress Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Outer Radius Disc - (Measured in Meter) - Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.
Circumferential Stress - (Measured in Pascal) - Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.
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.
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.
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)
Density Of Disc: 2 Kilogram per Cubic Meter --> 2 Kilogram per Cubic Meter No Conversion Required
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Poisson's Ratio: 0.3 --> No Conversion Required
Radius of Element: 5 Millimeter --> 0.005 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_outer = sqrt(((8*σ_c)/((ρ*(ω^2))*((1+(3*𝛎)*r^2))))/(3+𝛎)) --> sqrt(((8*100)/((2*(11.2^2))*((1+(3*0.3)*0.005^2))))/(3+0.3))

Evaluating ... ...

r_outer = 0.982992303118759

STEP 3: Convert Result to Output's Unit

0.982992303118759 Meter -->982.992303118759 Millimeter (Check conversion here)

FINAL ANSWER

982.992303118759 ≈ 982.9923 Millimeter <-- Outer Radius Disc

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Radius of Disc » Outer radius of disc given Circumferential stress

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National Institute Of Technology (NIT), Hamirpur

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< 9 Radius of Disc Calculators

Outer radius of disc given Circumferential stress

Go Outer Radius Disc = sqrt(((8*Circumferential Stress)/((Density Of Disc*(Angular Velocity^2))*((1+(3*Poisson's Ratio)*Radius of Element^2))))/(3+Poisson's Ratio))

Radius of disc given Circumferential stress in solid disc

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

Radius of Circular disc given Radial stress in solid disc

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

Disc outer radius given Radial stress in solid disc

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

Outer radius of disc given Constant at boundary condition for circular disc

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

Outer Radius of disc given Circumferential stress at center of solid disc

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

Outer radius of disc given max circumferential stress in solid disc

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

Outer radius of disc given Radial stress at center of solid disc

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

Outer radius of disc given Maximum radial stress in solid disc

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

Outer radius of disc given Circumferential stress Formula

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 Outer radius of disc given Circumferential stress?

Outer radius of disc given Circumferential stress calculator uses Outer Radius Disc = sqrt(((8*Circumferential Stress)/((Density Of Disc*(Angular Velocity^2))*((1+(3*Poisson's Ratio)*Radius of Element^2))))/(3+Poisson's Ratio)) to calculate the Outer Radius Disc, The Outer radius of disc given Circumferential stress formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Outer Radius Disc is denoted by r_outer symbol.

How to calculate Outer radius of disc given Circumferential stress using this online calculator? To use this online calculator for Outer radius of disc given Circumferential stress, enter Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Radius of Element (r) and hit the calculate button. Here is how the Outer radius of disc given Circumferential stress calculation can be explained with given input values -> 982992.3 = sqrt(((8*100)/((2*(11.2^2))*((1+(3*0.3)*0.005^2))))/(3+0.3)).

FAQ

What is Outer radius of disc given Circumferential stress?

The Outer radius of disc given Circumferential stress 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_outer = sqrt(((8*σ_c)/((ρ*(ω^2))*((1+(3*𝛎)*r^2))))/(3+𝛎)) or Outer Radius Disc = sqrt(((8*Circumferential Stress)/((Density Of Disc*(Angular Velocity^2))*((1+(3*Poisson's Ratio)*Radius of Element^2))))/(3+Poisson's Ratio)). Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius, 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, 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 & The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

How to calculate Outer radius of disc given Circumferential stress?

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

In this formula, Outer Radius Disc uses Circumferential Stress, Density Of Disc, Angular Velocity, Poisson's Ratio & Radius of Element. We can use 6 other way(s) to calculate the same, which is/are as follows -

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

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