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Constant at boundary condition given Radial stress in solid disc Formula

GoConstant at boundary condition given Circumferential stress in solid disc Formula

GoConstant at boundary condition for circular disc Formula

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Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain. Check FAQs

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

C₁ - Constant at Boundary Condition?σ_r - Radial Stress?ρ - Density Of Disc?ω - Angular Velocity?r_disc - Disc Radius?𝛎 - Poisson's Ratio?

Constant at boundary condition given Radial stress in solid disc Example

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Here is how the Constant at boundary condition given Radial stress in solid disc equation looks like with Values.

Here is how the Constant at boundary condition given Radial stress in solid disc equation looks like with Units.

Here is how the Constant at boundary condition given Radial stress in solid disc equation looks like.

406.976 = 2 \cdot (100 + (\frac{2 \cdot ({11.2}^{2}) \cdot (1000^{2}) \cdot (3 + 0.3)}{8}))

406.976 = 2 \cdot (100N/m² + (\frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({1000mm}^{2}) \cdot (3 + 0.3)}{8}))

406.976 = 2 \cdot (100 + (\frac{2 \cdot ({11.2}^{2}) \cdot (1000^{2}) \cdot (3 + 0.3)}{8}))

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Constant at boundary condition given Radial stress in solid disc Solution

Follow our step by step solution on how to calculate Constant at boundary condition given Radial stress in solid disc?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

C 1 = 2 \cdot (100N/m² + (\frac{2kg/m³ \cdot ({11.2rad/s}^{2}) \cdot ({1000mm}^{2}) \cdot (3 + 0.3)}{8}))

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

LAST Step Evaluate

∴

C 1 = 406.976

Constant at boundary condition given Radial stress in solid disc Formula Elements

Variables

Constant at Boundary Condition

Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.

Symbol: C₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant at Boundary Condition

Radial Stress

Radial stress refers to the stress that acts perpendicular to the longitudinal axis of a component, directed either towards or away from the central axis.

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 typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density Of Disc

Angular Velocity

Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.

Symbol: ω

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Angular Velocity

Disc Radius

Disc radius is the distance from the center of the disc to any point on its circumference.

Symbol: r_disc

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Disc Radius

Poisson's Ratio

Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.

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 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}))

Go Constant at boundary condition for circular disc

C 1 = \frac{ρ \cdot (ω^{2}) \cdot ({r outer}^{2}) \cdot (3 + 𝛎)}{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 given Radial stress in solid disc?

Constant at boundary condition given Radial stress in solid disc evaluator uses Constant at Boundary Condition = 2*(Radial Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8)) to evaluate the Constant at Boundary Condition, The Constant at boundary condition given Radial stress in solid 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 given Radial stress in solid disc using this online evaluator? To use this online evaluator for Constant at boundary condition given Radial stress in solid disc, enter Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Disc Radius (r_disc) & Poisson's Ratio (𝛎) and hit the calculate button.

FAQs on Constant at boundary condition given Radial stress in solid disc

What is the formula to find Constant at boundary condition given Radial stress in solid disc?

The formula of Constant at boundary condition given Radial stress in solid disc is expressed as Constant at Boundary Condition = 2*(Radial Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8)). Here is an example- 406.976 = 2*(100+((2*(11.2^2)*(1^2)*(3+0.3))/8)).

How to calculate Constant at boundary condition given Radial stress in solid disc?

With Radial Stress (σ_r), Density Of Disc (ρ), Angular Velocity (ω), Disc Radius (r_disc) & Poisson's Ratio (𝛎) we can find Constant at boundary condition given Radial stress in solid disc using the formula - Constant at Boundary Condition = 2*(Radial Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^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*(Circumferential Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8))
Constant at Boundary Condition=(Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8

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Constant at boundary condition given Radial stress in solid disc Formula

​GoConstant at boundary condition given Circumferential stress in solid disc Formula

​GoConstant at boundary condition for circular disc Formula

Constant at boundary condition given Radial stress in solid disc Example

Constant at boundary condition given Radial stress in solid disc Solution

Constant at boundary condition given Radial stress in solid disc Formula Elements

Other Formulas to find Constant at Boundary Condition

Other formulas in Stresses in Disc category

How to Evaluate Constant at boundary condition given Radial stress in solid disc?

FAQs on Constant at boundary condition given Radial stress in solid disc

Variable Name

GoConstant at boundary condition given Circumferential stress in solid disc Formula

GoConstant at boundary condition for circular disc Formula