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Radial Stress in Rotating Flywheel at given Radius Calculator

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✖Mass Density of Flywheel is the mass of the flywheel material per unit volume.ⓘ Mass Density of Flywheel [ρ]			+10% -10%
✖Peripheral Speed of Flywheel is the speed of the periphery of the flywheel.ⓘ Peripheral Speed of Flywheel [V_peripheral]			+10% -10%
✖Poisson Ratio for Flywheel is defined as the deformation of the material in directions perpendicular to the direction of loading.ⓘ Poisson Ratio for Flywheel [u]			+10% -10%
✖Distance from Flywheel Centre is the radial line from the centre to any point of the flywheel.ⓘ Distance from Flywheel Centre [r]			+10% -10%
✖Outer Radius of Flywheel is the distance of the flywheel's outer surface from its centre.ⓘ Outer Radius of Flywheel [R]			+10% -10%

✖Radial Stress in Flywheel is the stress induced in the flywheel along its radial direction.ⓘ Radial Stress in Rotating Flywheel at given Radius [σ_r]

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Formula

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Radial Stress in Rotating Flywheel at given Radius

Formula

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

Example

0.228837 N/mm² = 7800 kg/m³ \cdot {10.35 m/s}^{2} \cdot (\frac{3 + 0.3}{8}) \cdot (1 - {(\frac{200 mm}{345 mm})}^{2})

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Radial Stress in Rotating Flywheel at given Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
σ_r = ρ*V_peripheral^2*((3+u)/8)*(1-(r/R)^2)
This formula uses 6 Variables

Variables Used

Radial Stress in Flywheel - (Measured in Pascal) - Radial Stress in Flywheel is the stress induced in the flywheel along its radial direction.
Mass Density of Flywheel - (Measured in Kilogram per Cubic Meter) - Mass Density of Flywheel is the mass of the flywheel material per unit volume.
Peripheral Speed of Flywheel - (Measured in Meter per Second) - Peripheral Speed of Flywheel is the speed of the periphery of the flywheel.
Poisson Ratio for Flywheel - Poisson Ratio for Flywheel is defined as the deformation of the material in directions perpendicular to the direction of loading.
Distance from Flywheel Centre - (Measured in Meter) - Distance from Flywheel Centre is the radial line from the centre to any point of the flywheel.
Outer Radius of Flywheel - (Measured in Meter) - Outer Radius of Flywheel is the distance of the flywheel's outer surface from its centre.

STEP 1: Convert Input(s) to Base Unit

Mass Density of Flywheel: 7800 Kilogram per Cubic Meter --> 7800 Kilogram per Cubic Meter No Conversion Required
Peripheral Speed of Flywheel: 10.35 Meter per Second --> 10.35 Meter per Second No Conversion Required
Poisson Ratio for Flywheel: 0.3 --> No Conversion Required
Distance from Flywheel Centre: 200 Millimeter --> 0.2 Meter (Check conversion here)
Outer Radius of Flywheel: 345 Millimeter --> 0.345 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_r = ρ*V_peripheral^2*((3+u)/8)*(1-(r/R)^2) --> 7800*10.35^2*((3+0.3)/8)*(1-(0.2/0.345)^2)

Evaluating ... ...

σ_r = 228836.64375

STEP 3: Convert Result to Output's Unit

228836.64375 Pascal -->0.22883664375 Newton per Square Millimeter (Check conversion here)

FINAL ANSWER

0.22883664375 ≈ 0.228837 Newton per Square Millimeter <-- Radial Stress in Flywheel

(Calculation completed in 00.004 seconds)

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< Design of Flywheel Calculators

Coefficient of Fluctuation of Flywheel Speed given Mean Speed

Go Coefficient of Fluctuation of Flywheel Speed = (Maximum Angular Speed of Flywheel-Minimum Angular Speed of Flywheel)/Mean Angular Speed of Flywheel

Energy Output from Flywheel

Go Energy Output From Flywheel = Moment of Inertia of Flywheel*Mean Angular Speed of Flywheel^2*Coefficient of Fluctuation of Flywheel Speed

Moment of Inertia of Flywheel

Go Moment of Inertia of Flywheel = (Driving Input Torque of Flywheel-Load Output Torque of Flywheel)/Angular Acceleration of Flywheel

Mean Angular Velocity of Flywheel

Go Mean Angular Speed of Flywheel = (Maximum Angular Speed of Flywheel+Minimum Angular Speed of Flywheel)/2

Radial Stress in Rotating Flywheel at given Radius Formula

What is flywheel ?

A flywheel is a heavy rotating body that acts as a reservoir of energy. The energy is stored in the flywheel in the form of kinetic energy. The flywheel acts as an energy bank between the source of power and the driven machinery.

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

Radial Stress in Rotating Flywheel at given Radius calculator 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 calculate the Radial Stress in Flywheel, Radial Stress in Rotating Flywheel at given Radius is the value of stress in the flywheel along the radial direction. Radial Stress in Flywheel is denoted by σ_r symbol.

How to calculate Radial Stress in Rotating Flywheel at given Radius using this online calculator? To use this online calculator for Radial Stress in Rotating Flywheel at given Radius, enter Mass Density of Flywheel (ρ), Peripheral Speed of Flywheel (V_peripheral), Poisson Ratio for Flywheel (u), Distance from Flywheel Centre (r) & Outer Radius of Flywheel (R) and hit the calculate button. Here is how the Radial Stress in Rotating Flywheel at given Radius calculation can be explained with given input values -> 2.3E-7 = 7800*10.35^2*((3+0.3)/8)*(1-(0.2/0.345)^2).

FAQ

What is Radial Stress in Rotating Flywheel at given Radius?

Radial Stress in Rotating Flywheel at given Radius is the value of stress in the flywheel along the radial direction and is represented as σ_r = ρ*V_peripheral^2*((3+u)/8)*(1-(r/R)^2) or 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). Mass Density of Flywheel is the mass of the flywheel material per unit volume, Peripheral Speed of Flywheel is the speed of the periphery of the flywheel, Poisson Ratio for Flywheel is defined as the deformation of the material in directions perpendicular to the direction of loading, Distance from Flywheel Centre is the radial line from the centre to any point of the flywheel & Outer Radius of Flywheel is the distance of the flywheel's outer surface from its centre.

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

Radial Stress in Rotating Flywheel at given Radius is the value of stress in the flywheel along the radial direction is calculated using 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 calculate Radial Stress in Rotating Flywheel at given Radius, you need Mass Density of Flywheel (ρ), Peripheral Speed of Flywheel (V_peripheral), Poisson Ratio for Flywheel (u), Distance from Flywheel Centre (r) & Outer Radius of Flywheel (R). With our tool, you need to enter the respective value for Mass Density of Flywheel, Peripheral Speed of Flywheel, Poisson Ratio for Flywheel, Distance from Flywheel Centre & Outer Radius of Flywheel and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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