Outer radius of disc given max circumferential stress in solid disc Solution

STEP 0: Pre-Calculation Summary
Formula Used
Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))
router = sqrt((8*σc)/(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 distance from the center of the disc to its outer edge or boundary.
Circumferential Stress - (Measured in Pascal) - Circumferential stress, also known as hoop stress, is a type of normal stress that acts tangentially to the circumference of a cylindrical or spherical object.
Density Of Disc - (Measured in Kilogram per Cubic Meter) - Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc.
Angular Velocity - (Measured in Radian per Second) - Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time.
Poisson's Ratio - Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.
STEP 1: Convert Input(s) to Base Unit
Circumferential Stress: 100 Newton per Square Meter --> 100 Pascal (Check conversion ​here)
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
router = sqrt((8*σc)/(ρ*(ω^2)*(3+𝛎))) --> sqrt((8*100)/(2*(11.2^2)*(3+0.3)))
Evaluating ... ...
router = 0.983003361719965
STEP 3: Convert Result to Output's Unit
0.983003361719965 Meter -->983.003361719965 Millimeter (Check conversion ​here)
FINAL ANSWER
983.003361719965 983.0034 Millimeter <-- Outer Radius Disc
(Calculation completed in 00.004 seconds)

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Radius of Disc Calculators

Outer radius of disc given Circumferential stress
​ LaTeX ​ 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))
Disc outer radius given Radial stress in solid disc
​ LaTeX ​ 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
​ LaTeX ​ 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 max circumferential stress in solid disc
​ LaTeX ​ 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 Formula

​LaTeX ​Go
Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))
router = sqrt((8*σc)/(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 max circumferential stress in solid disc?

Outer radius of disc given max circumferential stress in solid disc calculator uses Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio))) to calculate the Outer Radius Disc, The Outer radius of disc given max circumferential stress in solid 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 router symbol.

How to calculate Outer radius of disc given max circumferential stress in solid disc using this online calculator? To use this online calculator for Outer radius of disc given max circumferential stress in solid disc, enter Circumferential Stress c), 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 max circumferential stress in solid disc calculation can be explained with given input values -> 983003.4 = sqrt((8*100)/(2*(11.2^2)*(3+0.3))).

FAQ

What is Outer radius of disc given max circumferential stress in solid disc?
The Outer radius of disc given max circumferential stress in solid 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 router = sqrt((8*σc)/(ρ*(ω^2)*(3+𝛎))) or Outer Radius Disc = sqrt((8*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio))). Circumferential stress, also known as hoop stress, is a type of normal stress that acts tangentially to the circumference of a cylindrical or spherical object, Density of disc typically refers to the mass per unit volume of the disc material. It is a measure of how much mass is contained in a given volume of the disc, Angular velocity is a measure of how quickly an object rotates or revolves around a central point or axis, describes the rate of change of the angular position of the object with respect to time & Poisson's ratio is a measure of the deformation of a material in directions perpendicular to the direction of loading. It is defined as the negative ratio of transverse strain to axial strain.
How to calculate Outer radius of disc given max circumferential stress in solid disc?
The Outer radius of disc given max circumferential stress in solid 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*Circumferential Stress)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio))). To calculate Outer radius of disc given max circumferential stress in solid disc, you need Circumferential Stress c), Density Of Disc (ρ), Angular Velocity (ω) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Circumferential Stress, 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 Circumferential Stress, Density Of Disc, Angular Velocity & Poisson's Ratio. We can use 3 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*Constant at Boundary Condition)/(Density Of Disc*(Angular Velocity^2)*(3+Poisson's Ratio)))
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