Outer radius of disc given Constant at boundary condition for circular disc Calculator

✖Constant at boundary condition is value obtained for stress in solid disc.ⓘ Constant at boundary condition [C₁]			+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 Disc [ρ]			+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%
✖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.ⓘ Poisson's Ratio [𝛎]			+10% -10%

✖Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.ⓘ Outer radius of disc given Constant at boundary condition for circular disc [r_outer]

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Formula

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Outer radius of disc given Constant at boundary condition for circular disc

Formula

`"r"_{"outer"} = sqrt((8*"C"_{"1"})/("ρ"*("ω"^2)*(3+"𝛎")))`

Example

`"1702.612mm"=sqrt((8*"300")/("2kg/m³"*(("11.2rad/s")^2)*(3+"0.3")))`

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Outer radius of disc given Constant at boundary condition for circular disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Outer Radius Disc = sqrt((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))
r_outer = sqrt((8*C₁)/(ρ*(ω^2)*(3+𝛎)))
This formula uses 1 Functions, 5 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Outer Radius Disc - (Measured in Meter) - Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.
Constant at boundary condition - Constant at boundary condition is value obtained for stress in solid disc.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Constant at boundary condition: 300 --> No Conversion Required
Density Of Disc: 2 Kilogram per Cubic Meter --> 2 Kilogram per Cubic Meter No Conversion Required
Angular Velocity: 11.2 Radian per Second --> 11.2 Radian per Second No Conversion Required
Poisson's Ratio: 0.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_outer = sqrt((8*C₁)/(ρ*(ω^2)*(3+𝛎))) --> sqrt((8*300)/(2*(11.2^2)*(3+0.3)))

Evaluating ... ...

r_outer = 1.70261176650999

STEP 3: Convert Result to Output's Unit

1.70261176650999 Meter -->1702.61176650999 Millimeter (Check conversion here)

FINAL ANSWER

1702.61176650999 ≈ 1702.612 Millimeter <-- Outer Radius Disc

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Rotating Disc And Cylinder » Expression for Stresses in Solid Disc » Radius of Disc » Outer radius of disc given Constant at boundary condition for circular disc

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< 9 Radius of Disc Calculators

Outer radius of disc given Circumferential stress

Go Outer Radius Disc = sqrt(((8*Circumferential Stress)/((Density Of Disc*(Angular Velocity^2))*((1+(3*Poisson's Ratio)*Radius of Element^2))))/(3+Poisson's Ratio))

Radius of disc given Circumferential stress in solid disc

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

Radius of Circular disc given Radial stress in solid disc

Go Disc Radius = sqrt((((Constant at boundary condition/2)-Radial Stress)*8)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))

Disc outer radius given Radial stress in solid disc

Go Outer Radius Disc = sqrt(((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2))

Outer radius of disc given Constant at boundary condition for circular disc

Go Outer Radius Disc = sqrt((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))

Outer Radius of disc given Circumferential stress at center of solid disc

Go Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))

Outer radius of disc given max circumferential stress in solid disc

Go Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))

Outer radius of disc given Radial stress at center of solid disc

Go Outer Radius Disc = sqrt((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))

Outer radius of disc given Maximum radial stress in solid disc

Go Outer Radius Disc = sqrt((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))

Outer radius of disc given Constant at boundary condition for circular disc Formula

Outer Radius Disc = sqrt((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))
r_outer = sqrt((8*C₁)/(ρ*(ω^2)*(3+𝛎)))

What is radial and tangential stress?

The “Hoop Stress” or “Tangential Stress” acts on a line perpendicular to the “longitudinal “and the “radial stress;” this stress attempts to separate the pipe wall in the circumferential direction. This stress is caused by internal pressure.

How to Calculate Outer radius of disc given Constant at boundary condition for circular disc?

Outer radius of disc given Constant at boundary condition for circular disc calculator uses Outer Radius Disc = sqrt((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio))) to calculate the Outer Radius Disc, The Outer radius of disc given Constant at boundary condition for circular disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Outer Radius Disc is denoted by r_outer symbol.

How to calculate Outer radius of disc given Constant at boundary condition for circular disc using this online calculator? To use this online calculator for Outer radius of disc given Constant at boundary condition for circular disc, enter Constant at boundary condition (C₁), Density Of Disc (ρ), Angular Velocity (ω) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Outer radius of disc given Constant at boundary condition for circular disc calculation can be explained with given input values -> 1.7E+6 = sqrt((8*300)/(2*(11.2^2)*(3+0.3))).

FAQ

What is Outer radius of disc given Constant at boundary condition for circular disc?

The Outer radius of disc given Constant at boundary condition for circular disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface and is represented as r_outer = sqrt((8*C₁)/(ρ*(ω^2)*(3+𝛎))) or Outer Radius Disc = sqrt((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio))). Constant at boundary condition is value obtained for stress in solid 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, 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 & 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.

How to calculate Outer radius of disc given Constant at boundary condition for circular disc?

The Outer radius of disc given Constant at boundary condition for circular disc formula is defined as a line segment extending from the center of a circle or sphere to the circumference or bounding surface is calculated using Outer Radius Disc = sqrt((8*Constant at boundary condition)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio))). To calculate Outer radius of disc given Constant at boundary condition for circular disc, you need Constant at boundary condition (C₁), Density Of Disc (ρ), Angular Velocity (ω) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Constant at boundary condition, Density Of Disc, Angular Velocity & Poisson's Ratio 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 Outer Radius Disc?

In this formula, Outer Radius Disc uses Constant at boundary condition, Density Of Disc, Angular Velocity & Poisson's Ratio. We can use 6 other way(s) to calculate the same, which is/are as follows -

Outer Radius Disc = sqrt(((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))+(Radius of Element^2))
Outer Radius Disc = sqrt(((8*Circumferential Stress)/((Density Of Disc*(Angular Velocity^2))*((1+(3*Poisson's Ratio)*Radius of Element^2))))/(3+Poisson's Ratio))
Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))
Outer Radius Disc = sqrt((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))
Outer Radius Disc = sqrt((8*Radial Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))
Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))

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