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Density of material given constant at boundary condition for circular 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{8 \cdot C 1}{(ω^{2}) \cdot ({r outer}^{2}) \cdot (3 + 𝛎)}

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

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

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Here is how the Density of material given constant at boundary condition for circular disc equation looks like with Values.

Here is how the Density of material given constant at boundary condition for circular disc equation looks like with Units.

Here is how the Density of material given constant at boundary condition for circular disc equation looks like.

7.1577 = \frac{8 \cdot 300}{({11.2}^{2}) \cdot (900^{2}) \cdot (3 + 0.3)}

7.1577kg/m³ = \frac{8 \cdot 300}{({11.2rad/s}^{2}) \cdot ({900mm}^{2}) \cdot (3 + 0.3)}

7.1577 = \frac{8 \cdot 300}{({11.2}^{2}) \cdot (900^{2}) \cdot (3 + 0.3)}

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

Follow our step by step solution on how to calculate Density of material given constant at boundary condition for circular disc?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

ρ = \frac{8 \cdot 300}{({11.2rad/s}^{2}) \cdot ({900mm}^{2}) \cdot (3 + 0.3)}

Next Step Convert Units

∴

ρ = \frac{8 \cdot 300}{({11.2rad/s}^{2}) \cdot ({0.9m}^{2}) \cdot (3 + 0.3)}

Next Step Prepare to Evaluate

∴

ρ = \frac{8 \cdot 300}{({11.2}^{2}) \cdot ({0.9}^{2}) \cdot (3 + 0.3)}

Next Step Evaluate

∴

ρ = 7.15774525298335kg/m³

LAST Step Rounding Answer

∴

ρ = 7.1577kg/m³

Density of material given constant at boundary condition for circular 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

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 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 Circumferential stress in solid disc

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

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 constant at boundary condition for circular disc?

Density of material given constant at boundary condition for circular disc evaluator uses Density Of Disc = (8*Constant at boundary condition)/((Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio)) to evaluate the Density Of Disc, The Density of material given constant at boundary condition for circular 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 constant at boundary condition for circular disc using this online evaluator? To use this online evaluator for Density of material given constant at boundary condition for circular disc, enter Constant at boundary condition (C₁), Angular Velocity (ω), Outer Radius Disc (r_outer) & Poisson's Ratio (𝛎) and hit the calculate button.

FAQs on Density of material given constant at boundary condition for circular disc

What is the formula to find Density of material given constant at boundary condition for circular disc?

The formula of Density of material given constant at boundary condition for circular disc is expressed as Density Of Disc = (8*Constant at boundary condition)/((Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio)). Here is an example- 7.157745 = (8*300)/((11.2^2)*(0.9^2)*(3+0.3)).

How to calculate Density of material given constant at boundary condition for circular disc?

With Constant at boundary condition (C₁), Angular Velocity (ω), Outer Radius Disc (r_outer) & Poisson's Ratio (𝛎) we can find Density of material given constant at boundary condition for circular disc using the formula - Density Of Disc = (8*Constant at boundary condition)/((Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio)).

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

Can the Density of material given constant at boundary condition for circular disc be negative?

No, the Density of material given constant at boundary condition for circular disc, measured in Density cannot be negative.

Which unit is used to measure Density of material given constant at boundary condition for circular disc?

Density of material given constant at boundary condition for circular 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 constant at boundary condition for circular disc can be measured.

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