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Outer radius of disc given Circumferential stress Formula

GoDisc outer radius given Radial stress in solid disc Formula

GoOuter radius of disc given Constant at boundary condition for circular disc Formula

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Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary. Check FAQs

r outer = \sqrt{\frac{\frac{8 \cdot σ c}{(ρ \cdot (ω^{2})) \cdot ((1 + (3 \cdot 𝛎) \cdot r^{2}))}}{3 + 𝛎}}

r_outer - Outer Radius Disc?σ_c - Circumferential Stress?ρ - Density Of Disc?ω - Angular Velocity?𝛎 - Poisson's Ratio?r - Radius of Element?

Outer radius of disc given Circumferential stress Example

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Here is how the Outer radius of disc given Circumferential stress equation looks like with Values.

Here is how the Outer radius of disc given Circumferential stress equation looks like with Units.

Here is how the Outer radius of disc given Circumferential stress equation looks like.

982.9923 = \sqrt{\frac{\frac{8 \cdot 100}{(2 \cdot ({11.2}^{2})) \cdot ((1 + (3 \cdot 0.3) \cdot 5^{2}))}}{3 + 0.3}}

982.9923mm = \sqrt{\frac{\frac{8 \cdot 100N/m²}{(2kg/m³ \cdot ({11.2rad/s}^{2})) \cdot ((1 + (3 \cdot 0.3) \cdot {5mm}^{2}))}}{3 + 0.3}}

982.9923 = \sqrt{\frac{\frac{8 \cdot 100}{(2 \cdot ({11.2}^{2})) \cdot ((1 + (3 \cdot 0.3) \cdot 5^{2}))}}{3 + 0.3}}

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Outer radius of disc given Circumferential stress Solution

Follow our step by step solution on how to calculate Outer radius of disc given Circumferential stress?

FIRST Step Consider the formula

r outer = \sqrt{\frac{\frac{8 \cdot σ c}{(ρ \cdot (ω^{2})) \cdot ((1 + (3 \cdot 𝛎) \cdot r^{2}))}}{3 + 𝛎}}

Next Step Substitute values of Variables

∴

r outer = \sqrt{\frac{\frac{8 \cdot 100N/m²}{(2kg/m³ \cdot ({11.2rad/s}^{2})) \cdot ((1 + (3 \cdot 0.3) \cdot {5mm}^{2}))}}{3 + 0.3}}

Next Step Convert Units

∴

r outer = \sqrt{\frac{\frac{8 \cdot 100Pa}{(2kg/m³ \cdot ({11.2rad/s}^{2})) \cdot ((1 + (3 \cdot 0.3) \cdot {0.005m}^{2}))}}{3 + 0.3}}

Next Step Prepare to Evaluate

∴

r outer = \sqrt{\frac{\frac{8 \cdot 100}{(2 \cdot ({11.2}^{2})) \cdot ((1 + (3 \cdot 0.3) \cdot {0.005}^{2}))}}{3 + 0.3}}

Next Step Evaluate

∴

r outer = 0.982992303118759m

Next Step Convert to Output's Unit

∴

r outer = 982.992303118759mm

LAST Step Rounding Answer

∴

r outer = 982.9923mm

Outer radius of disc given Circumferential stress Formula Elements

Variables

Functions

Outer Radius Disc

Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.

Symbol: r_outer

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Outer Radius Disc

Circumferential Stress

Circumferential Stress is the force over area exerted circumferentially perpendicular to the axis and the radius.

Symbol: σ_c

Measurement: StressUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Circumferential Stress

Density Of Disc

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.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Of Disc

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.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

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.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 10.

Formulas to find Poisson's Ratio

Radius of Element

The Radius of Element is the radius of the element considered in the disc at radius r from the centre.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Element

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.

Syntax: sqrt(Number)

Other Formulas to find Outer Radius Disc

Go Disc outer radius given Radial stress in solid disc

r outer = \sqrt{(\frac{8 \cdot σ r}{ρ \cdot (ω^{2}) \cdot (3 + 𝛎)}) + (r^{2})}

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

r outer = \sqrt{\frac{8 \cdot C 1}{ρ \cdot (ω^{2}) \cdot (3 + 𝛎)}}

Go Outer radius of disc given max circumferential stress in solid disc

r outer = \sqrt{\frac{8 \cdot σ c}{ρ \cdot (ω^{2}) \cdot (3 + 𝛎)}}

Go Outer radius of disc given Maximum radial stress in solid disc

r outer = \sqrt{\frac{8 \cdot σ r}{ρ \cdot (ω^{2}) \cdot (3 + 𝛎)}}

Other formulas in Radius of Disc category

Go Radius of disc given Circumferential stress in solid disc

r disc = \sqrt{\frac{((\frac{C 1}{2}) - σ c) \cdot 8}{ρ \cdot (ω^{2}) \cdot ((3 \cdot 𝛎) + 1)}}

Go Radius of Circular disc given Radial stress in solid disc

r disc = \sqrt{\frac{((\frac{C 1}{2}) - σ r) \cdot 8}{ρ \cdot (ω^{2}) \cdot (3 + 𝛎)}}

How to Evaluate Outer radius of disc given Circumferential stress?

Outer radius of disc given Circumferential stress evaluator 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 evaluate 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 evaluate Outer radius of disc given Circumferential stress using this online evaluator? To use this online evaluator 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.

FAQs on Outer radius of disc given Circumferential stress

What is the formula to find Outer radius of disc given Circumferential stress?

The formula of Outer radius of disc given Circumferential stress is expressed as 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)). Here is an example- 982992.3 = sqrt(((8*100)/((2*(11.2^2))*((1+(3*0.3)*0.005^2))))/(3+0.3)).

How to calculate Outer radius of disc given Circumferential stress?

With Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Radius of Element (r) we can find Outer radius of disc given Circumferential stress using the formula - 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)). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Outer Radius Disc?

Here are the different ways to Calculate Outer Radius Disc-

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)))

Can the Outer radius of disc given Circumferential stress be negative?

Yes, the Outer radius of disc given Circumferential stress, measured in Length can be negative.

Which unit is used to measure Outer radius of disc given Circumferential stress?

Outer radius of disc given Circumferential stress is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Outer radius of disc given Circumferential stress can be measured.

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Outer radius of disc given Circumferential stress Formula

​GoDisc outer radius given Radial stress in solid disc Formula

​GoOuter radius of disc given Constant at boundary condition for circular disc Formula

Outer radius of disc given Circumferential stress Example

Outer radius of disc given Circumferential stress Solution

Outer radius of disc given Circumferential stress Formula Elements

Other Formulas to find Outer Radius Disc

Other formulas in Radius of Disc category

How to Evaluate Outer radius of disc given Circumferential stress?

FAQs on Outer radius of disc given Circumferential stress

Variable Name

GoDisc outer radius given Radial stress in solid disc Formula

GoOuter radius of disc given Constant at boundary condition for circular disc Formula