Radius of disc given Circumferential stress in solid disc Calculator

✖Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.ⓘ Constant at Boundary Condition [C₁]			+10% -10%
✖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.ⓘ Circumferential Stress [σ_c]			+10% -10%
✖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.ⓘ Density Of Disc [ρ]			+10% -10%
✖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.ⓘ Angular Velocity [ω]			+10% -10%
✖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.ⓘ Poisson's Ratio [𝛎]			+10% -10%

✖Disc radius is the distance from the center of the disc to any point on its circumference.ⓘ Radius of disc given Circumferential stress in solid disc [r_disc]

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Radius of disc given Circumferential stress in solid disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

Disc Radius = sqrt((((Constant at Boundary Condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*((3*Poisson's Ratio)+1)))
r_disc = sqrt((((C₁/2)-σ_c)*8)/(ρ*(ω^2)*((3*𝛎)+1)))
This formula uses 1 Functions, 6 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

Disc Radius - (Measured in Meter) - Disc radius is the distance from the center of the disc to any point on its circumference.
Constant at Boundary Condition - Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain.
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

Constant at Boundary Condition: 300 --> No Conversion Required
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

r_disc = sqrt((((C₁/2)-σ_c)*8)/(ρ*(ω^2)*((3*𝛎)+1))) --> sqrt((((300/2)-100)*8)/(2*(11.2^2)*((3*0.3)+1)))

Evaluating ... ...

r_disc = 0.916052100076031

STEP 3: Convert Result to Output's Unit

0.916052100076031 Meter -->916.052100076031 Millimeter (Check conversion here)

FINAL ANSWER

916.052100076031 ≈ 916.0521 Millimeter <-- Disc Radius

(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 » Mechanical » Radius of Disc » Radius of disc given Circumferential stress in solid disc

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National Institute Of Technology (NIT), Hamirpur

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< 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))

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 max circumferential stress in solid disc

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

Radius of disc given Circumferential stress in solid disc Formula

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 Radius of disc given Circumferential stress in solid disc?

Radius of disc given Circumferential stress in solid disc calculator uses Disc Radius = sqrt((((Constant at Boundary Condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*((3*Poisson's Ratio)+1))) to calculate the Disc Radius, The Radius of disc given 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. Disc Radius is denoted by r_disc symbol.

How to calculate Radius of disc given Circumferential stress in solid disc using this online calculator? To use this online calculator for Radius of disc given Circumferential stress in solid disc, enter Constant at Boundary Condition (C₁), Circumferential Stress (σ_c), Density Of Disc (ρ), Angular Velocity (ω) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Radius of disc given Circumferential stress in solid disc calculation can be explained with given input values -> 916052.1 = sqrt((((300/2)-100)*8)/(2*(11.2^2)*((3*0.3)+1))).

FAQ

What is Radius of disc given Circumferential stress in solid disc?

The Radius of disc given 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 r_disc = sqrt((((C₁/2)-σ_c)*8)/(ρ*(ω^2)*((3*𝛎)+1))) or Disc Radius = sqrt((((Constant at Boundary Condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*((3*Poisson's Ratio)+1))). Constant at boundary condition is a type of boundary condition used in mathematical and physical problems where a specific variable is held constant along the boundary of the domain, 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 Radius of disc given Circumferential stress in solid disc?

The Radius of disc given 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 Disc Radius = sqrt((((Constant at Boundary Condition/2)-Circumferential Stress)*8)/(Density Of Disc*(Angular Velocity^2)*((3*Poisson's Ratio)+1))). To calculate Radius of disc given Circumferential stress in solid disc, you need Constant at Boundary Condition (C₁), Circumferential Stress (σ_c), 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, 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 Disc Radius?

In this formula, Disc Radius uses Constant at Boundary Condition, Circumferential Stress, Density Of Disc, Angular Velocity & Poisson's Ratio. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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