Constant at boundary condition for circular disc Calculator

✖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%
✖Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.ⓘ Outer Radius Disc [r_outer]			+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%

✖Constant at boundary condition is value obtained for stress in solid disc.ⓘ Constant at boundary condition for circular disc [C₁]

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Formula

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Constant at boundary condition for circular disc

Formula

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

Example

`"83.82528"=("2kg/m³"*(("11.2rad/s")^2)*(("900mm")^2)*(3+"0.3"))/8`

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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 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.
Outer Radius Disc - (Measured in Meter) - Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary.
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

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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< 19 Expression for Stresses in Solid Disc Calculators

Circumferential stress in solid disc given Outer radius

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

Poisson's ratio given Circumferential stress in solid disc

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

Constant at boundary condition given Circumferential stress in solid disc

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

Circumferential stress in solid disc

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

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

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 and outer radius

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

Radial stress in solid disc given Outer radius

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

Poisson's ratio given Radial stress in solid disc

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

Poisson's ratio given constant at boundary condition for circular disc

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

Constant at boundary condition for circular disc

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

Poisson's ratio given Circumferential stress at center of solid disc

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

Poisson's Ratio given max circumferential stress in solid disc

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

Circumferential stress at center of solid disc

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

Maximum circumferential stress in solid disc

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

Poisson's ratio given Radial stress at center of solid disc

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

Poisson's ratio given maximum radial stress in solid disc

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

Maximum Radial Stress in solid disc

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

Radial stress at center of solid disc

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

Constant at boundary condition for circular disc Formula

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 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, Outer Radius Disc is the radius of the larger of the two concentric circles that form its boundary & 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 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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