Constant at boundary condition for circular disc Calculator

✖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%
✖Outer radius disc is the distance from the center of the disc to its outer edge or boundary.ⓘ Outer Radius Disc [r_outer]			+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%

✖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 for circular disc [C₁]

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Constant at boundary condition for circular disc Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

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.
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.
Outer Radius Disc - (Measured in Meter) - Outer radius disc is the distance from the center of the disc to its outer edge or boundary.
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

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
Outer Radius Disc: 900 Millimeter --> 0.9 Meter (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

C₁ = (ρ*(ω^2)*(r_outer^2)*(3+𝛎))/8 --> (2*(11.2^2)*(0.9^2)*(3+0.3))/8

Evaluating ... ...

C₁ = 83.82528

STEP 3: Convert Result to Output's Unit

83.82528 --> No Conversion Required

FINAL ANSWER

83.82528 <-- Constant at Boundary Condition

(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 » Stresses in Disc » Constant at boundary condition for circular disc

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< Stresses in Disc Calculators

Circumferential stress in solid disc

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

Constant at boundary condition given Radial stress in solid disc

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

Radial stress in solid disc

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

Poisson's ratio given Radial stress in solid disc

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

Constant at boundary condition for circular disc Formula

LaTeX Go

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

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 Constant at boundary condition for circular disc?

Constant at boundary condition for circular disc calculator uses Constant at Boundary Condition = (Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8 to calculate the Constant at Boundary Condition, The Constant at boundary condition for circular disc formula is defined as the value obtained at boundary condition for the equation of stresses in the solid disc. Constant at Boundary Condition is denoted by C₁ symbol.

How to calculate Constant at boundary condition for circular disc using this online calculator? To use this online calculator for Constant at boundary condition for circular disc, enter Density Of Disc (ρ), Angular Velocity (ω), Outer Radius Disc (r_outer) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Constant at boundary condition for circular disc calculation can be explained with given input values -> 83.82528 = (2*(11.2^2)*(0.9^2)*(3+0.3))/8.

FAQ

What is Constant at boundary condition for circular disc?

The Constant at boundary condition for circular disc formula is defined as the value obtained at boundary condition for the equation of stresses in the solid disc and is represented as C₁ = (ρ*(ω^2)*(r_outer^2)*(3+𝛎))/8 or Constant at Boundary Condition = (Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8. 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, Outer radius disc is the distance from the center of the disc to its outer edge or boundary & 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 Constant at boundary condition for circular disc?

The Constant at boundary condition for circular disc formula is defined as the value obtained at boundary condition for the equation of stresses in the solid disc is calculated using Constant at Boundary Condition = (Density Of Disc*(Angular Velocity^2)*(Outer Radius Disc^2)*(3+Poisson's Ratio))/8. To calculate Constant at boundary condition for circular disc, you need Density Of Disc (ρ), Angular Velocity (ω), Outer Radius Disc (r_outer) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Density Of Disc, Angular Velocity, Outer Radius Disc & 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 Constant at Boundary Condition?

In this formula, Constant at Boundary Condition uses Density Of Disc, Angular Velocity, Outer Radius Disc & Poisson's Ratio. We can use 2 other way(s) to calculate the same, which is/are as follows -

Constant at Boundary Condition = 2*(Radial Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*(3+Poisson's Ratio))/8))
Constant at Boundary Condition = 2*(Circumferential Stress+((Density Of Disc*(Angular Velocity^2)*(Disc Radius^2)*((3*Poisson's Ratio)+1))/8))

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