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Radial Stress in Rotating Flywheel at given Radius Formula

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Radial Stress in Flywheel is the stress that occurs in the rim of a flywheel due to the centrifugal force of the rotating wheel. Check FAQs

σ r = ρ \cdot {V p}^{2} \cdot (\frac{3 + u}{8}) \cdot (1 - {(\frac{r}{R})}^{2})

σ_r - Radial Stress in Flywheel?ρ - Mass Density of Flywheel?V_p - Peripheral Speed of Flywheel?u - Poisson Ratio for Flywheel?r - Distance from Flywheel Centre?R - Outer Radius of Flywheel?

Radial Stress in Rotating Flywheel at given Radius Example

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Here is how the Radial Stress in Rotating Flywheel at given Radius equation looks like with Values.

Here is how the Radial Stress in Rotating Flywheel at given Radius equation looks like with Units.

Here is how the Radial Stress in Rotating Flywheel at given Radius equation looks like.

0.2288 = 7800 \cdot {10.35}^{2} \cdot (\frac{3 + 0.3}{8}) \cdot (1 - {(\frac{200}{345})}^{2})

0.2288N/mm² = 7800kg/m³ \cdot {10.35m/s}^{2} \cdot (\frac{3 + 0.3}{8}) \cdot (1 - {(\frac{200mm}{345mm})}^{2})

0.2288 = 7800 \cdot {10.35}^{2} \cdot (\frac{3 + 0.3}{8}) \cdot (1 - {(\frac{200}{345})}^{2})

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Radial Stress in Rotating Flywheel at given Radius Solution

Follow our step by step solution on how to calculate Radial Stress in Rotating Flywheel at given Radius?

FIRST Step Consider the formula

σ r = ρ \cdot {V p}^{2} \cdot (\frac{3 + u}{8}) \cdot (1 - {(\frac{r}{R})}^{2})

Next Step Substitute values of Variables

∴

σ r = 7800kg/m³ \cdot {10.35m/s}^{2} \cdot (\frac{3 + 0.3}{8}) \cdot (1 - {(\frac{200mm}{345mm})}^{2})

Next Step Convert Units

∴

σ r = 7800kg/m³ \cdot {10.35m/s}^{2} \cdot (\frac{3 + 0.3}{8}) \cdot (1 - {(\frac{0.2m}{0.345m})}^{2})

Next Step Prepare to Evaluate

∴

σ r = 7800 \cdot {10.35}^{2} \cdot (\frac{3 + 0.3}{8}) \cdot (1 - {(\frac{0.2}{0.345})}^{2})

Next Step Evaluate

∴

σ r = 228836.64375Pa

Next Step Convert to Output's Unit

∴

σ r = 0.22883664375N/mm²

LAST Step Rounding Answer

∴

σ r = 0.2288N/mm²

Radial Stress in Rotating Flywheel at given Radius Formula Elements

Variables

Radial Stress in Flywheel

Radial Stress in Flywheel is the stress that occurs in the rim of a flywheel due to the centrifugal force of the rotating wheel.

Symbol: σ_r

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Radial Stress in Flywheel

Mass Density of Flywheel

Mass Density of Flywheel is the measure of mass per unit volume of a flywheel, which affects its rotational inertia and overall performance.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Mass Density of Flywheel

Peripheral Speed of Flywheel

Peripheral Speed of Flywheel is the linear velocity of the flywheel's rim, which is a critical parameter in designing and optimizing flywheel performance.

Symbol: V_p

Measurement: SpeedUnit: m/s

Note: Value should be greater than 0.

Formulas to find Peripheral Speed of Flywheel

Poisson Ratio for Flywheel

Poisson Ratio for Flywheel is the ratio of lateral contraction to longitudinal extension of a material in the flywheel's rim and hub under different loads.

Symbol: u

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Poisson Ratio for Flywheel

Distance from Flywheel Centre

Distance from Flywheel Centre is the length of the line segment from the centre of the flywheel to a point on its circumference.

Symbol: r

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance from Flywheel Centre

Outer Radius of Flywheel

Outer Radius of Flywheel is the distance from the axis of rotation to the outer edge of the flywheel, affecting its moment of inertia and energy storage.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Outer Radius of Flywheel

Other formulas in Design of Flywheel category

Go Moment of Inertia of Flywheel

I = \frac{T 1 - T 2}{α}

Go Mean Angular Velocity of Flywheel

ω = \frac{n max + n min}{2}

Go Energy Output from Flywheel

U o = I \cdot ω^{2} \cdot C s

Go Coefficient of Fluctuation of Flywheel Speed given Mean Speed

C s = \frac{n max - n min}{ω}

How to Evaluate Radial Stress in Rotating Flywheel at given Radius?

Radial Stress in Rotating Flywheel at given Radius evaluator uses Radial Stress in Flywheel = Mass Density of Flywheel*Peripheral Speed of Flywheel^2*((3+Poisson Ratio for Flywheel)/8)*(1-(Distance from Flywheel Centre/Outer Radius of Flywheel)^2) to evaluate the Radial Stress in Flywheel, Radial Stress in Rotating Flywheel at given Radius formula is defined as a measure of the stress experienced by a rotating flywheel at a specific radius, which is critical in determining the flywheel's structural integrity and performance in various mechanical systems. Radial Stress in Flywheel is denoted by σ_r symbol.

How to evaluate Radial Stress in Rotating Flywheel at given Radius using this online evaluator? To use this online evaluator for Radial Stress in Rotating Flywheel at given Radius, enter Mass Density of Flywheel (ρ), Peripheral Speed of Flywheel (V_p), Poisson Ratio for Flywheel (u), Distance from Flywheel Centre (r) & Outer Radius of Flywheel (R) and hit the calculate button.

FAQs on Radial Stress in Rotating Flywheel at given Radius

What is the formula to find Radial Stress in Rotating Flywheel at given Radius?

The formula of Radial Stress in Rotating Flywheel at given Radius is expressed as Radial Stress in Flywheel = Mass Density of Flywheel*Peripheral Speed of Flywheel^2*((3+Poisson Ratio for Flywheel)/8)*(1-(Distance from Flywheel Centre/Outer Radius of Flywheel)^2). Here is an example- 2.3E-7 = 7800*10.35^2*((3+0.3)/8)*(1-(0.2/0.345)^2).

How to calculate Radial Stress in Rotating Flywheel at given Radius?

With Mass Density of Flywheel (ρ), Peripheral Speed of Flywheel (V_p), Poisson Ratio for Flywheel (u), Distance from Flywheel Centre (r) & Outer Radius of Flywheel (R) we can find Radial Stress in Rotating Flywheel at given Radius using the formula - Radial Stress in Flywheel = Mass Density of Flywheel*Peripheral Speed of Flywheel^2*((3+Poisson Ratio for Flywheel)/8)*(1-(Distance from Flywheel Centre/Outer Radius of Flywheel)^2).

Can the Radial Stress in Rotating Flywheel at given Radius be negative?

No, the Radial Stress in Rotating Flywheel at given Radius, measured in Stress cannot be negative.

Which unit is used to measure Radial Stress in Rotating Flywheel at given Radius?

Radial Stress in Rotating Flywheel at given Radius is usually measured using the Newton per Square Millimeter[N/mm²] for Stress. Pascal[N/mm²], Newton per Square Meter[N/mm²], Kilonewton per Square Meter[N/mm²] are the few other units in which Radial Stress in Rotating Flywheel at given Radius can be measured.

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Radial Stress in Rotating Flywheel at given Radius Formula

Radial Stress in Rotating Flywheel at given Radius Example

Radial Stress in Rotating Flywheel at given Radius Solution

Radial Stress in Rotating Flywheel at given Radius Formula Elements

Other formulas in Design of Flywheel category

How to Evaluate Radial Stress in Rotating Flywheel at given Radius?

FAQs on Radial Stress in Rotating Flywheel at given Radius

Variable Name