Constant for outer cylinder given original difference of radii at junction Calculator

✖Original difference of radii is the original difference happened in the inner and outer radius of compound cylinder.ⓘ Original difference of radii [Δr_original]			+10% -10%
✖Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.ⓘ Modulus of Elasticity Of Thick Shell [E]			+10% -10%
✖The Radius at Junction is the radius value at the junction of compound cylinders.ⓘ Radius at Junction [r_*]			+10% -10%
✖Constant 'a' for inner cylinder is defined as the constant used in lame's equation.ⓘ Constant 'a' for inner cylinder [a₂]			+10% -10%

✖Constant 'a' for outer cylinder is defined as the constant used in lame's equation.ⓘ Constant for outer cylinder given original difference of radii at junction [a₁]

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Formula

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Constant for outer cylinder given original difference of radii at junction

Formula

`"a"_{"1"} = ("Δr"_{"original"}*"E"/(2*"r"_{"*"}))+"a"_{"2"}`

Example

`"9.5"=("0.02mm"*"2.6MPa"/(2*"4000mm"))+"3"`

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Constant for outer cylinder given original difference of radii at junction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Constant 'a' for outer cylinder = (Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))+Constant 'a' for inner cylinder
a₁ = (Δr_original*E/(2*r_*))+a₂
This formula uses 5 Variables

Variables Used

Constant 'a' for outer cylinder - Constant 'a' for outer cylinder is defined as the constant used in lame's equation.
Original difference of radii - (Measured in Meter) - Original difference of radii is the original difference happened in the inner and outer radius of compound cylinder.
Modulus of Elasticity Of Thick Shell - (Measured in Pascal) - Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it.
Radius at Junction - (Measured in Meter) - The Radius at Junction is the radius value at the junction of compound cylinders.
Constant 'a' for inner cylinder - Constant 'a' for inner cylinder is defined as the constant used in lame's equation.

STEP 1: Convert Input(s) to Base Unit

Original difference of radii: 0.02 Millimeter --> 2E-05 Meter (Check conversion here)
Modulus of Elasticity Of Thick Shell: 2.6 Megapascal --> 2600000 Pascal (Check conversion here)
Radius at Junction: 4000 Millimeter --> 4 Meter (Check conversion here)
Constant 'a' for inner cylinder: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a₁ = (Δr_original*E/(2*r_*))+a₂ --> (2E-05*2600000/(2*4))+3

Evaluating ... ...

a₁ = 9.5

STEP 3: Convert Result to Output's Unit

9.5 --> No Conversion Required

FINAL ANSWER

9.5 <-- Constant 'a' for outer cylinder

(Calculation completed in 00.004 seconds)

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< 21 Compound Cylinder Shrinkage Radii Change Calculators

Decrease in outer radius of inner cylinder at junction given constants of lame equation

Go Decrease in radius = -Radius at Junction*(((1/Modulus of Elasticity Of Thick Shell)*((Constant 'b' for inner cylinder/Radius at Junction)+Constant 'a' for inner cylinder))+((1/Modulus of Elasticity Of Thick Shell*Mass Of Shell)*((Constant 'b' for inner cylinder/Radius at Junction)-Constant 'a' for inner cylinder)))

Increase in inner radius of outer cylinder at junction given constants of lame equation

Go Increase in radius = Radius at Junction*(((1/Modulus of Elasticity Of Thick Shell)*((Constant 'b' for outer cylinder/Radius at Junction)+Constant 'a' for outer cylinder))+((1/Modulus of Elasticity Of Thick Shell*Mass Of Shell)*((Constant 'b' for outer cylinder/Radius at Junction)-Constant 'a' for outer cylinder)))

Modulus of elasticity given decrease in outer radius of inner cylinder and constants

Go Modulus of Elasticity Of Thick Shell = -Radius at Junction*(((1/Decrease in radius)*((Constant 'b' for inner cylinder/Radius at Junction)+Constant 'a' for inner cylinder))+((1/Decrease in radius*Mass Of Shell)*((Constant 'b' for inner cylinder/Radius at Junction)-Constant 'a' for inner cylinder)))

Modulus of elasticity given increase in inner radius of outer cylinder and constants

Go Modulus of Elasticity Of Thick Shell = Radius at Junction*(((1/Increase in radius)*((Constant 'b' for outer cylinder/Radius at Junction)+Constant 'a' for outer cylinder))+((1/Increase in radius*Mass Of Shell)*((Constant 'b' for outer cylinder/Radius at Junction)-Constant 'a' for outer cylinder)))

Radius at junction of compound cylinder given increase in inner radius of outer cylinder

Go Radius at Junction = (Increase in radius*Modulus of Elasticity Of Thick Shell)/(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Radius at junction of compound cylinder given decrease in outer radius of inner cylinder

Go Radius at Junction = (Decrease in radius*Modulus of Elasticity Of Thick Shell)/(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Increase in inner radius of outer cylinder at junction of compound cylinder

Go Increase in radius = (Radius at Junction/Modulus of Elasticity Of Thick Shell)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Decrease in outer radius of inner cylinder at junction of compound cylinder

Go Decrease in radius = (Radius at Junction/Modulus of Elasticity Of Thick Shell)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Mass of compound cylinder given increase in inner radius of outer cylinder

Go Mass Of Shell = Radial Pressure/((Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)

Mass of compound cylinder given decrease in outer radius of inner cylinder

Go Mass Of Shell = Radial Pressure/((Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)

Modulus of elasticity given increase in inner radius of outer cylinder

Go Modulus of Elasticity Of Thick Shell = (Radius at Junction/Increase in radius)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Radial pressure given increase in inner radius of outer cylinder

Go Radial Pressure = ((Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)*Mass Of Shell

Radial pressure given decrease in outer radius of inner cylinder

Go Radial Pressure = ((Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-Hoop Stress on thick shell)*Mass Of Shell

Modulus of elasticity decrease in outer radius of inner cylinder

Go Modulus of Elasticity Of Thick Shell = (Radius at Junction/Decrease in radius)*(Hoop Stress on thick shell+(Radial Pressure/Mass Of Shell))

Hoop stress given increase in inner radius of outer cylinder

Go Hoop Stress on thick shell = (Increase in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)

Hoop stress given decrease in outer radius of inner cylinder

Go Hoop Stress on thick shell = (Decrease in radius/(Radius at Junction/Modulus of Elasticity Of Thick Shell))-(Radial Pressure/Mass Of Shell)

Radius at junction of compound cylinder given original difference of radii at junction

Go Radius at Junction = Original difference of radii/(2*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell)

Constant 'a' for inner cylinder given original difference of radii at junction

Go Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))

Constant for outer cylinder given original difference of radii at junction

Go Constant 'a' for outer cylinder = (Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))+Constant 'a' for inner cylinder

Modulus of elasticity given original difference of radii at junction

Go Modulus of Elasticity Of Thick Shell = 2*Radius at Junction*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Original difference of radii

Original difference of radii at junction

Go Original difference of radii = 2*Radius at Junction*(Constant 'a' for outer cylinder-Constant 'a' for inner cylinder)/Modulus of Elasticity Of Thick Shell

Constant for outer cylinder given original difference of radii at junction Formula

Constant 'a' for outer cylinder = (Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))+Constant 'a' for inner cylinder
a₁ = (Δr_original*E/(2*r_*))+a₂

What is meant by hoop stress?

The hoop stress is the force over the area exerted circumferentially (perpendicular to the axis and the radius of the object) in both directions on every particle in the cylinder wall.

How to Calculate Constant for outer cylinder given original difference of radii at junction?

Constant for outer cylinder given original difference of radii at junction calculator uses Constant 'a' for outer cylinder = (Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))+Constant 'a' for inner cylinder to calculate the Constant 'a' for outer cylinder, The Constant for outer cylinder given original difference of radii at junction formula is defined as the constant used in lame's equation for the compound cylinder. Constant 'a' for outer cylinder is denoted by a₁ symbol.

How to calculate Constant for outer cylinder given original difference of radii at junction using this online calculator? To use this online calculator for Constant for outer cylinder given original difference of radii at junction, enter Original difference of radii (Δr_original), Modulus of Elasticity Of Thick Shell (E), Radius at Junction (r_*) & Constant 'a' for inner cylinder (a₂) and hit the calculate button. Here is how the Constant for outer cylinder given original difference of radii at junction calculation can be explained with given input values -> 9.5 = (2E-05*2600000/(2*4))+3.

FAQ

What is Constant for outer cylinder given original difference of radii at junction?

The Constant for outer cylinder given original difference of radii at junction formula is defined as the constant used in lame's equation for the compound cylinder and is represented as a₁ = (Δr_original*E/(2*r_*))+a₂ or Constant 'a' for outer cylinder = (Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))+Constant 'a' for inner cylinder. Original difference of radii is the original difference happened in the inner and outer radius of compound cylinder, Modulus of Elasticity Of Thick Shell is a quantity that measures an object or substance's resistance to being deformed elastically when a stress is applied to it, The Radius at Junction is the radius value at the junction of compound cylinders & Constant 'a' for inner cylinder is defined as the constant used in lame's equation.

How to calculate Constant for outer cylinder given original difference of radii at junction?

The Constant for outer cylinder given original difference of radii at junction formula is defined as the constant used in lame's equation for the compound cylinder is calculated using Constant 'a' for outer cylinder = (Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction))+Constant 'a' for inner cylinder. To calculate Constant for outer cylinder given original difference of radii at junction, you need Original difference of radii (Δr_original), Modulus of Elasticity Of Thick Shell (E), Radius at Junction (r_*) & Constant 'a' for inner cylinder (a₂). With our tool, you need to enter the respective value for Original difference of radii, Modulus of Elasticity Of Thick Shell, Radius at Junction & Constant 'a' for inner cylinder and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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