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Tangential Stress in Rotating Flywheel at given Radius Formula

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Tangential Stress in Flywheel is the stress developed on the rim of a flywheel due to the centrifugal force of the rotating wheel. Check FAQs

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

σ_t - Tangential 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?

Tangential Stress in Rotating Flywheel at given Radius Example

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

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

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

0.278 = 7800 \cdot {10.35}^{2} \cdot \frac{0.3 + 3}{8} \cdot (1 - (\frac{3 \cdot 0.3 + 1}{0.3 + 3}) \cdot {(\frac{200}{345})}^{2})

0.278N/mm² = 7800kg/m³ \cdot {10.35m/s}^{2} \cdot \frac{0.3 + 3}{8} \cdot (1 - (\frac{3 \cdot 0.3 + 1}{0.3 + 3}) \cdot {(\frac{200mm}{345mm})}^{2})

0.278 = 7800 \cdot {10.35}^{2} \cdot \frac{0.3 + 3}{8} \cdot (1 - (\frac{3 \cdot 0.3 + 1}{0.3 + 3}) \cdot {(\frac{200}{345})}^{2})

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Tangential Stress in Rotating Flywheel at given Radius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

σ t = 277976.64375Pa

Next Step Convert to Output's Unit

∴

σ t = 0.27797664375N/mm²

LAST Step Rounding Answer

∴

σ t = 0.278N/mm²

Tangential Stress in Rotating Flywheel at given Radius Formula Elements

Variables

Tangential Stress in Flywheel

Tangential Stress in Flywheel is the stress developed on the rim of a flywheel due to the centrifugal force of the rotating wheel.

Symbol: σ_t

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Tangential 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 Tangential Stress in Rotating Flywheel at given Radius?

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

How to evaluate Tangential Stress in Rotating Flywheel at given Radius using this online evaluator? To use this online evaluator for Tangential 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 Tangential Stress in Rotating Flywheel at given Radius

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

The formula of Tangential Stress in Rotating Flywheel at given Radius is expressed as Tangential Stress in Flywheel = Mass Density of Flywheel*Peripheral Speed of Flywheel^2*(Poisson Ratio for Flywheel+3)/8*(1-((3*Poisson Ratio for Flywheel+1)/(Poisson Ratio for Flywheel+3))*(Distance from Flywheel Centre/Outer Radius of Flywheel)^2). Here is an example- 2.8E-7 = 7800*10.35^2*(0.3+3)/8*(1-((3*0.3+1)/(0.3+3))*(0.2/0.345)^2).

How to calculate Tangential 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 Tangential Stress in Rotating Flywheel at given Radius using the formula - Tangential Stress in Flywheel = Mass Density of Flywheel*Peripheral Speed of Flywheel^2*(Poisson Ratio for Flywheel+3)/8*(1-((3*Poisson Ratio for Flywheel+1)/(Poisson Ratio for Flywheel+3))*(Distance from Flywheel Centre/Outer Radius of Flywheel)^2).

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

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

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

Tangential 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 Tangential Stress in Rotating Flywheel at given Radius can be measured.

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Tangential Stress in Rotating Flywheel at given Radius Formula

Tangential Stress in Rotating Flywheel at given Radius Example

Tangential Stress in Rotating Flywheel at given Radius Solution

Tangential Stress in Rotating Flywheel at given Radius Formula Elements

Other formulas in Design of Flywheel category

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

FAQs on Tangential Stress in Rotating Flywheel at given Radius

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