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Constant at boundary condition for circular disc Formula

GoConstant at boundary condition given Radial stress in solid disc Formula

GoConstant at boundary condition given Circumferential stress in solid disc Formula

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

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

C₁ - Constant at boundary condition?ρ - Density Of Disc?ω - Angular Velocity?r_outer - Outer Radius Disc?𝛎 - Poisson's Ratio?

Constant at boundary condition for circular disc Example

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Here is how the Constant at boundary condition for circular disc equation looks like with Values.

Here is how the Constant at boundary condition for circular disc equation looks like with Units.

Here is how the Constant at boundary condition for circular disc equation looks like.

83.8253 = \frac{2 \cdot ({11.2}^{2}) \cdot (900^{2}) \cdot (3 + 0.3)}{8}

83.8253 = \frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({900mm}^{2}) \cdot (3 + 0.3)}{8}

83.8253 = \frac{2 \cdot ({11.2}^{2}) \cdot (900^{2}) \cdot (3 + 0.3)}{8}

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Constant at boundary condition for circular disc Solution

Follow our step by step solution on how to calculate Constant at boundary condition for circular disc?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C 1 = \frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({900mm}^{2}) \cdot (3 + 0.3)}{8}

Next Step Convert Units

∴

C 1 = \frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({0.9m}^{2}) \cdot (3 + 0.3)}{8}

Next Step Prepare to Evaluate

∴

C 1 = \frac{2 \cdot ({11.2}^{2}) \cdot ({0.9}^{2}) \cdot (3 + 0.3)}{8}

Next Step Evaluate

∴

C 1 = 83.82528

LAST Step Rounding Answer

∴

C 1 = 83.8253

Constant at boundary condition for circular disc Formula Elements

Variables

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

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

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

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

Other Formulas to find Constant at boundary condition

Go Constant at boundary condition given Radial stress in solid disc

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

Go Constant at boundary condition given Circumferential stress in solid disc

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

Other formulas in Stresses in Disc category

Go Radial stress in solid disc

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

Go Poisson's ratio given Radial stress in solid disc

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

Go Circumferential stress in solid disc

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

Go Poisson's ratio given Circumferential stress in solid disc

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

How to Evaluate Constant at boundary condition for circular disc?

Constant at boundary condition for circular disc evaluator uses Constant at boundary condition = (Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8 to evaluate the Constant at boundary condition, The Constant at boundary condition for circular disc formula is defined as the value obtained at boundary condition for the equation of stresses in the solid disc. Constant at boundary condition is denoted by C₁ symbol.

How to evaluate Constant at boundary condition for circular disc using this online evaluator? To use this online evaluator for Constant at boundary condition for circular disc, enter Density Of Disc (ρ), Angular Velocity (ω), Outer Radius Disc (r_outer) & Poisson's Ratio (𝛎) and hit the calculate button.

FAQs on Constant at boundary condition for circular disc

What is the formula to find Constant at boundary condition for circular disc?

The formula of Constant at boundary condition for circular disc is expressed as Constant at boundary condition = (Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8. Here is an example- 83.82528 = (2*(11.2^2)*(0.9^2)*(3+0.3))/8.

How to calculate Constant at boundary condition for circular disc?

With Density Of Disc (ρ), Angular Velocity (ω), Outer Radius Disc (r_outer) & Poisson's Ratio (𝛎) we can find Constant at boundary condition for circular disc using the formula - Constant at boundary condition = (Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8.

What are the other ways to Calculate Constant at boundary condition?

Here are the different ways to Calculate Constant at boundary condition-

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

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