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Density of material given Circumferential stress in solid disc Formula

GoDensity of disc material given Radial stress in solid disc and outer radius Formula

GoDensity of material given Circumferential stress at center of solid disc Formula

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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. Check FAQs

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

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

Density of material given Circumferential stress in solid disc Example

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

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

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

1.6783 = \frac{((\frac{300}{2}) - 100) \cdot 8}{({11.2}^{2}) \cdot (1000^{2}) \cdot ((3 \cdot 0.3) + 1)}

1.6783kg/m³ = \frac{((\frac{300}{2}) - 100N/m²) \cdot 8}{({11.2rad/s}^{2}) \cdot ({1000mm}^{2}) \cdot ((3 \cdot 0.3) + 1)}

1.6783 = \frac{((\frac{300}{2}) - 100) \cdot 8}{({11.2}^{2}) \cdot (1000^{2}) \cdot ((3 \cdot 0.3) + 1)}

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Density of material given Circumferential stress in solid disc Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ρ = \frac{((\frac{300}{2}) - 100N/m²) \cdot 8}{({11.2rad/s}^{2}) \cdot ({1000mm}^{2}) \cdot ((3 \cdot 0.3) + 1)}

Next Step Convert Units

∴

ρ = \frac{((\frac{300}{2}) - 100Pa) \cdot 8}{({11.2rad/s}^{2}) \cdot ({1m}^{2}) \cdot ((3 \cdot 0.3) + 1)}

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

ρ = 1.67830290010741kg/m³

LAST Step Rounding Answer

∴

ρ = 1.6783kg/m³

Density of material given Circumferential stress in solid disc Formula Elements

Variables

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

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

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

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

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 Density Of Disc

Go Density of disc material given Radial stress in solid disc and outer radius

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

Go Density of material given Circumferential stress at center of solid disc

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

Go Density of material given constant at boundary condition for circular disc

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

Go Density of material given Circumferential stress and Outer radius

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

How to Evaluate Density of material given Circumferential stress in solid disc?

Density of material given Circumferential stress in solid disc evaluator uses Density Of Disc = (((Constant at boundary condition/2)-Circumferential Stress)*8)/((Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1)) to evaluate the Density Of Disc, The Density of material given Circumferential stress in solid disc formula is defined as a measure of mass per volume. An object made from a comparatively dense material (such as iron) will have less volume than an object of equal mass made from some less dense substance (such as water). Density Of Disc is denoted by ρ symbol.

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

FAQs on Density of material given Circumferential stress in solid disc

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

The formula of Density of material given Circumferential stress in solid disc is expressed as Density Of Disc = (((Constant at boundary condition/2)-Circumferential Stress)*8)/((Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1)). Here is an example- 1.678303 = (((300/2)-100)*8)/((11.2^2)*(1^2)*((3*0.3)+1)).

How to calculate Density of material given Circumferential stress in solid disc?

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

What are the other ways to Calculate Density Of Disc?

Here are the different ways to Calculate Density Of Disc-

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

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

No, the Density of material given Circumferential stress in solid disc, measured in Density cannot be negative.

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

Density of material given Circumferential stress in solid disc is usually measured using the Kilogram per Cubic Meter[kg/m³] for Density. Kilogram per Cubic Centimeter[kg/m³], Gram per Cubic Meter[kg/m³], Gram per Cubic Centimeter[kg/m³] are the few other units in which Density of material given Circumferential stress in solid disc can be measured.

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Density of material given Circumferential stress in solid disc Formula

​GoDensity of disc material given Radial stress in solid disc and outer radius Formula

​GoDensity of material given Circumferential stress at center of solid disc Formula

Density of material given Circumferential stress in solid disc Example

Density of material given Circumferential stress in solid disc Solution

Density of material given Circumferential stress in solid disc Formula Elements

Other Formulas to find Density Of Disc

How to Evaluate Density of material given Circumferential stress in solid disc?

FAQs on Density of material given Circumferential stress in solid disc

Variable Name

GoDensity of disc material given Radial stress in solid disc and outer radius Formula

GoDensity of material given Circumferential stress at center of solid disc Formula