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Radius of disc given Circumferential stress in solid disc Formula

GoRadius of Circular disc given Radial stress in solid disc Formula

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Disc Radius is a radial line from the focus to any point of a curve. Check FAQs

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

r_disc - Disc Radius?C₁ - Constant at boundary condition?σ_c - Circumferential Stress?ρ - Density Of Disc?ω - Angular Velocity?𝛎 - Poisson's Ratio?

Radius of disc given Circumferential stress in solid disc Example

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Here is how the Radius of disc given Circumferential stress in solid disc equation looks like with Values.

Here is how the Radius of disc given Circumferential stress in solid disc equation looks like with Units.

Here is how the Radius of disc given Circumferential stress in solid disc equation looks like.

916.0521 = \sqrt{\frac{((\frac{300}{2}) - 100) \cdot 8}{2 \cdot ({11.2}^{2}) \cdot ((3 \cdot 0.3) + 1)}}

916.0521mm = \sqrt{\frac{((\frac{300}{2}) - 100N/m²) \cdot 8}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ((3 \cdot 0.3) + 1)}}

916.0521 = \sqrt{\frac{((\frac{300}{2}) - 100) \cdot 8}{2 \cdot ({11.2}^{2}) \cdot ((3 \cdot 0.3) + 1)}}

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Radius of disc given Circumferential stress in solid disc Solution

Follow our step by step solution on how to calculate Radius of disc given Circumferential stress in solid disc?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r disc = \sqrt{\frac{((\frac{300}{2}) - 100N/m²) \cdot 8}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ((3 \cdot 0.3) + 1)}}

Next Step Convert Units

∴

r disc = \sqrt{\frac{((\frac{300}{2}) - 100Pa) \cdot 8}{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ((3 \cdot 0.3) + 1)}}

Next Step Prepare to Evaluate

∴

r disc = \sqrt{\frac{((\frac{300}{2}) - 100) \cdot 8}{2 \cdot ({11.2}^{2}) \cdot ((3 \cdot 0.3) + 1)}}

Next Step Evaluate

∴

r disc = 0.916052100076031m

Next Step Convert to Output's Unit

∴

r disc = 916.052100076031mm

LAST Step Rounding Answer

∴

r disc = 916.0521mm

Radius of disc given Circumferential stress in solid disc Formula Elements

Variables

Functions

Disc Radius

Disc Radius is a radial line from the focus to any point of a curve.

Symbol: r_disc

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Disc Radius

Constant at boundary condition

Constant at boundary condition is value obtained for stress in solid disc.

Symbol: C₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant at boundary condition

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

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 Disc Radius

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)}}

Other formulas in Radius of Disc category

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 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)}}

How to Evaluate Radius of disc given Circumferential stress in solid disc?

Radius of disc given Circumferential stress in solid disc evaluator uses Disc Radius = sqrt((((Constant at boundary condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*((3*Poisson's Ratio)+1))) to evaluate the Disc Radius, The Radius of disc given Circumferential 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. Disc Radius is denoted by r_disc symbol.

How to evaluate Radius of disc given Circumferential stress in solid disc using this online evaluator? To use this online evaluator for Radius of disc given Circumferential stress in solid disc, enter Constant at boundary condition (C₁), Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω) & Poisson's Ratio (𝛎) and hit the calculate button.

FAQs on Radius of disc given Circumferential stress in solid disc

What is the formula to find Radius of disc given Circumferential stress in solid disc?

The formula of Radius of disc given Circumferential stress in solid disc is expressed as Disc Radius = sqrt((((Constant at boundary condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*((3*Poisson's Ratio)+1))). Here is an example- 916052.1 = sqrt((((300/2)-100)*8)/(2*(11.2^2)*((3*0.3)+1))).

How to calculate Radius of disc given Circumferential stress in solid disc?

With Constant at boundary condition (C₁), Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω) & Poisson's Ratio (𝛎) we can find Radius of disc given Circumferential stress in solid disc using the formula - Disc Radius = sqrt((((Constant at boundary condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*((3*Poisson's Ratio)+1))). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Disc Radius?

Here are the different ways to Calculate Disc Radius-

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

Can the Radius of disc given Circumferential stress in solid disc be negative?

No, the Radius of disc given Circumferential stress in solid disc, measured in Length cannot be negative.

Which unit is used to measure Radius of disc given Circumferential stress in solid disc?

Radius of disc given Circumferential 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 Radius of disc given Circumferential stress in solid disc can be measured.

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Radius of disc given Circumferential stress in solid disc Formula

​GoRadius of Circular disc given Radial stress in solid disc Formula

Radius of disc given Circumferential stress in solid disc Example

Radius of disc given Circumferential stress in solid disc Solution

Radius of disc given Circumferential stress in solid disc Formula Elements

Other Formulas to find Disc Radius

Other formulas in Radius of Disc category

How to Evaluate Radius of disc given Circumferential stress in solid disc?

FAQs on Radius of disc given Circumferential stress in solid disc

Variable Name

GoRadius of Circular disc given Radial stress in solid disc Formula