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Disc outer radius given Radial stress in solid disc Formula

GoOuter radius of disc given Circumferential stress 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{8 \cdot σ r}{ρ \cdot (ω^{2}) \cdot (3 + 𝛎)}) + (r^{2})}

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

Disc outer radius given Radial stress in solid disc Example

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Here is how the Disc outer radius given Radial stress in solid disc equation looks like with Values.

Here is how the Disc outer radius given Radial stress in solid disc equation looks like with Units.

Here is how the Disc outer radius given Radial stress in solid disc equation looks like.

983.0161 = \sqrt{(\frac{8 \cdot 100}{2 \cdot ({11.2}^{2}) \cdot (3 + 0.3)}) + (5^{2})}

983.0161mm = \sqrt{(\frac{8 \cdot 100N/m²}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot (3 + 0.3)}) + ({5mm}^{2})}

983.0161 = \sqrt{(\frac{8 \cdot 100}{2 \cdot ({11.2}^{2}) \cdot (3 + 0.3)}) + (5^{2})}

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Disc outer radius given Radial stress in solid disc Solution

Follow our step by step solution on how to calculate Disc outer radius given Radial stress in solid disc?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r outer = 0.983016077769205m

Next Step Convert to Output's Unit

∴

r outer = 983.016077769205mm

LAST Step Rounding Answer

∴

r outer = 983.0161mm

Disc outer radius given Radial stress in solid disc 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

Radial Stress

Radial Stress induced by a bending moment in a member of constant cross section.

Symbol: σ_r

Measurement: PressureUnit: N/m²

Note: Value should be greater than 0.

Formulas to find Radial 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 Outer radius of disc given Circumferential stress

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

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 Disc outer radius given Radial stress in solid disc?

Disc outer radius given Radial stress in solid disc evaluator uses Outer Radius Disc = sqrt(((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2)) to evaluate the Outer Radius Disc, The Disc outer radius given Radial stress in solid disc 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 Disc outer radius given Radial stress in solid disc using this online evaluator? To use this online evaluator for Disc outer radius given Radial stress in solid disc, enter Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Radius of Element (r) and hit the calculate button.

FAQs on Disc outer radius given Radial stress in solid disc

What is the formula to find Disc outer radius given Radial stress in solid disc?

The formula of Disc outer radius given Radial stress in solid disc is expressed as Outer Radius Disc = sqrt(((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2)). Here is an example- 983016.1 = sqrt(((8*100)/(2*(11.2^2)*(3+0.3)))+(0.005^2)).

How to calculate Disc outer radius given Radial stress in solid disc?

With Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Poisson's Ratio (𝛎) & Radius of Element (r) we can find Disc outer radius given Radial stress in solid disc using the formula - Outer Radius Disc = sqrt(((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2)). 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*Circumferential Stress)/((Density Of Disc*(Angular Velocity^2))*((1+(3*Poisson's Ratio)*Radius of Element^2))))/(3+Poisson's Ratio))
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 Disc outer radius given Radial stress in solid disc be negative?

Yes, the Disc outer radius given Radial stress in solid disc, measured in Length can be negative.

Which unit is used to measure Disc outer radius given Radial stress in solid disc?

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

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Disc outer radius given Radial stress in solid disc Formula

​GoOuter radius of disc given Circumferential stress Formula

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

Disc outer radius given Radial stress in solid disc Example

Disc outer radius given Radial stress in solid disc Solution

Disc outer radius given Radial stress in solid disc Formula Elements

Other Formulas to find Outer Radius Disc

Other formulas in Radius of Disc category

How to Evaluate Disc outer radius given Radial stress in solid disc?

FAQs on Disc outer radius given Radial stress in solid disc

Variable Name

GoOuter radius of disc given Circumferential stress Formula

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