Density of cylinder material given hoop stress (for thin cylinder) Calculator

✖Hoop Stress in Disc is the circumferential stress in a cylinder.ⓘ Hoop Stress in Disc [σ_θ]			+10% -10%
✖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.ⓘ Angular Velocity [ω]			+10% -10%
✖Disc Radius is a radial line from the focus to any point of a curve.ⓘ Disc Radius [r_disc]			+10% -10%

✖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.ⓘ Density of cylinder material given hoop stress (for thin cylinder) [ρ]

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Formula

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Density of cylinder material given hoop stress (for thin cylinder)

Formula

`"ρ" = "σ"_{"θ"}/("ω"*"r"_{"disc"})`

Example

`"1.607143kg/m³"="18N/m²"/("11.2rad/s"*"1000mm")`

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Density of cylinder material given hoop stress (for thin cylinder) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Density Of Disc = Hoop Stress in Disc/(Angular Velocity*Disc Radius)
ρ = σ_θ/(ω*r_disc)
This formula uses 4 Variables

Variables Used

Density Of Disc - (Measured in Kilogram per Cubic Meter) - 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.
Hoop Stress in Disc - (Measured in Pascal) - Hoop Stress in Disc is the circumferential stress in a cylinder.
Angular Velocity - (Measured in Radian per Second) - 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.
Disc Radius - (Measured in Meter) - Disc Radius is a radial line from the focus to any point of a curve.

STEP 1: Convert Input(s) to Base Unit

Hoop Stress in Disc: 18 Newton per Square Meter --> 18 Pascal (Check conversion here)
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Disc Radius: 1000 Millimeter --> 1 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ρ = σ_θ/(ω*r_disc) --> 18/(11.2*1)

Evaluating ... ...

ρ = 1.60714285714286

STEP 3: Convert Result to Output's Unit

1.60714285714286 Kilogram per Cubic Meter --> No Conversion Required

FINAL ANSWER

1.60714285714286 ≈ 1.607143 Kilogram per Cubic Meter <-- Density Of Disc

(Calculation completed in 00.004 seconds)

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National Institute Of Technology (NIT), Hamirpur

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< 21 Expression for Stresses in Rotating Thin Disc Calculators

Poisson's ratio given initial radial width of disc

Go Poisson's Ratio = (Radial Stress-((Increase in Radial Width/Initial Radial Width)*Modulus Of Elasticity Of Disc))/(Circumferential Stress)

Modulus of elasticity given initial radial width of disc

Go Modulus Of Elasticity Of Disc = (Radial Stress-(Poisson's Ratio*Circumferential Stress))/(Increase in Radial Width/Initial Radial Width)

Modulus of elasticity given radius of disc

Go Modulus Of Elasticity Of Disc = ((Circumferential Stress-(Poisson's Ratio*Radial Stress))/(Increase in radius/Disc Radius))

Increase in radius of disc given stresses

Go Increase in radius = ((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc)*Disc Radius

Radius of disc given stresses on disc

Go Disc Radius = Increase in radius/((Circumferential Stress-(Poisson's Ratio*Radial Stress))/Modulus Of Elasticity Of Disc)

Poisson's ratio given radius of disc

Go Poisson's Ratio = (Circumferential Stress-((Increase in radius/Disc Radius)*Modulus Of Elasticity Of Disc))/Radial Stress

Poisson's ratio given circumferential strain on disc

Go Poisson's Ratio = (Circumferential Stress-(Circumferential strain*Modulus Of Elasticity Of Disc))/(Radial Stress)

Modulus of elasticity given circumferential strain on disc

Go Modulus Of Elasticity Of Disc = (Circumferential Stress-(Poisson's Ratio*Radial Stress))/Circumferential strain

Poisson's ratio given radial strain on disc

Go Poisson's Ratio = (Radial Stress-(Radial strain*Modulus Of Elasticity Of Disc))/(Circumferential Stress)

Modulus of elasticity given radial strain on disc

Go Modulus Of Elasticity Of Disc = (Radial Stress-(Poisson's Ratio*Circumferential Stress))/Radial strain

Angular speed of rotation for thin cylinder given hoop stress in thin cylinder

Go Angular Velocity = Hoop Stress in Disc/(Density Of Disc*Disc Radius)

Density of cylinder material given hoop stress (for thin cylinder)

Go Density Of Disc = Hoop Stress in Disc/(Angular Velocity*Disc Radius)

Mean radius of cylinder given hoop stress in thin cylinder

Go Disc Radius = Hoop Stress in Disc/(Density Of Disc*Angular Velocity)

Hoop stress in thin cylinder

Go Hoop Stress in Disc = Density Of Disc*Angular Velocity*Disc Radius

Initial circumference given circumferential strain for rotating thin disc

Go Initial circumference = Final Circumference/(Circumferential strain+1)

Final circumference given circumferential strain for rotating thin disc

Go Final Circumference = (Circumferential strain+1)*Initial circumference

Tangential velocity of cylinder given hoop stress in thin cylinder

Go Tangential Velocity = Hoop Stress in Disc/(Density Of Disc)

Density of material of cylinder given hoop stress and tangential velocity

Go Density Of Disc = Hoop Stress in Disc/Tangential Velocity

Hoop stress in thin cylinder given tangential velocity of cylinder

Go Hoop Stress in Disc = Tangential Velocity*Density Of Disc

Increase in radius given circumferential strain for rotating thin disc

Go Increase in radius = Circumferential strain*Disc Radius

Radius of disc given circumferential strain for rotating thin disc

Go Disc Radius = Increase in radius/Circumferential strain

Density of cylinder material given hoop stress (for thin cylinder) Formula

Density Of Disc = Hoop Stress in Disc/(Angular Velocity*Disc Radius)
ρ = σ_θ/(ω*r_disc)

What is the allowable stress?

Allowable stress, or allowable strength, is the maximum stress that can be safely applied to a structure. Allowable stress is the stress at which a member is not expected to fail under the given loading conditions.

How to Calculate Density of cylinder material given hoop stress (for thin cylinder)?

Density of cylinder material given hoop stress (for thin cylinder) calculator uses Density Of Disc = Hoop Stress in Disc/(Angular Velocity*Disc Radius) to calculate the Density Of Disc, The Density of cylinder material given hoop stress (for thin cylinder) formula is defined as a measure of mass per volume. The average density of an object equals its total mass divided by its total volume. Density Of Disc is denoted by ρ symbol.

How to calculate Density of cylinder material given hoop stress (for thin cylinder) using this online calculator? To use this online calculator for Density of cylinder material given hoop stress (for thin cylinder), enter Hoop Stress in Disc (σ_θ), Angular Velocity (ω) & Disc Radius (r_disc) and hit the calculate button. Here is how the Density of cylinder material given hoop stress (for thin cylinder) calculation can be explained with given input values -> 1.267606 = 18/(11.2*1).

FAQ

What is Density of cylinder material given hoop stress (for thin cylinder)?

The Density of cylinder material given hoop stress (for thin cylinder) formula is defined as a measure of mass per volume. The average density of an object equals its total mass divided by its total volume and is represented as ρ = σ_θ/(ω*r_disc) or Density Of Disc = Hoop Stress in Disc/(Angular Velocity*Disc Radius). Hoop Stress in Disc is the circumferential stress in a cylinder, 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 & Disc Radius is a radial line from the focus to any point of a curve.

How to calculate Density of cylinder material given hoop stress (for thin cylinder)?

The Density of cylinder material given hoop stress (for thin cylinder) formula is defined as a measure of mass per volume. The average density of an object equals its total mass divided by its total volume is calculated using Density Of Disc = Hoop Stress in Disc/(Angular Velocity*Disc Radius). To calculate Density of cylinder material given hoop stress (for thin cylinder), you need Hoop Stress in Disc (σ_θ), Angular Velocity (ω) & Disc Radius (r_disc). With our tool, you need to enter the respective value for Hoop Stress in Disc, Angular Velocity & Disc Radius and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Density Of Disc?

In this formula, Density Of Disc uses Hoop Stress in Disc, Angular Velocity & Disc Radius. We can use 1 other way(s) to calculate the same, which is/are as follows -

Density Of Disc = Hoop Stress in Disc/Tangential Velocity

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