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

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Constant 'a' for inner cylinder is defined as the constant used in lame's equation. Check FAQs

a 2 = a 1 - (Δr original \cdot \frac{E}{2 \cdot r *})

a₂ - Constant 'a' for inner cylinder?a₁ - Constant 'a' for outer cylinder?Δr_original - Original difference of radii?E - Modulus of Elasticity Of Thick Shell?r_* - Radius at Junction?

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

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Here is how the Constant 'a' for inner cylinder given original difference of radii at junction equation looks like with Values.

Here is how the Constant 'a' for inner cylinder given original difference of radii at junction equation looks like with Units.

Here is how the Constant 'a' for inner cylinder given original difference of radii at junction equation looks like.

-2.5 = 4 - (0.02 \cdot \frac{2.6}{2 \cdot 4000})

-2.5 = 4 - (0.02mm \cdot \frac{2.6MPa}{2 \cdot 4000mm})

-2.5 = 4 - (0.02 \cdot \frac{2.6}{2 \cdot 4000})

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

Follow our step by step solution on how to calculate Constant 'a' for inner cylinder given original difference of radii at junction?

FIRST Step Consider the formula

a 2 = a 1 - (Δr original \cdot \frac{E}{2 \cdot r *})

Next Step Substitute values of Variables

∴

a 2 = 4 - (0.02mm \cdot \frac{2.6MPa}{2 \cdot 4000mm})

Next Step Convert Units

∴

a 2 = 4 - (2E-5m \cdot \frac{2.6E+6Pa}{2 \cdot 4m})

Next Step Prepare to Evaluate

∴

a 2 = 4 - (2E-5 \cdot \frac{2.6E+6}{2 \cdot 4})

LAST Step Evaluate

∴

a 2 = -2.5

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

Variables

Constant 'a' for inner cylinder

Constant 'a' for inner cylinder is defined as the constant used in lame's equation.

Symbol: a₂

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant 'a' for inner cylinder

Constant 'a' for outer cylinder

Constant 'a' for outer cylinder is defined as the constant used in lame's equation.

Symbol: a₁

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Constant 'a' for outer cylinder

Original difference of radii

Original difference of radii is the original difference happened in the inner and outer radius of compound cylinder.

Symbol: Δr_original

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Original difference of radii

Modulus of Elasticity Of Thick Shell

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.

Symbol: E

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Modulus of Elasticity Of Thick Shell

Radius at Junction

The Radius at Junction is the radius value at the junction of compound cylinders.

Symbol: r_*

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius at Junction

Other formulas in Compound Cylinder Shrinkage Radii Change category

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

R i = (\frac{r *}{E}) \cdot (σ θ + (\frac{P v}{M}))

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

r * = \frac{R i \cdot E}{σ θ + (\frac{P v}{M})}

Go Radial pressure given increase in inner radius of outer cylinder

P v = ((\frac{R i}{\frac{r *}{E}}) - σ θ) \cdot M

Go Hoop stress given increase in inner radius of outer cylinder

σ θ = (\frac{R i}{\frac{r *}{E}}) - (\frac{P v}{M})

How to Evaluate Constant 'a' for inner cylinder given original difference of radii at junction?

Constant 'a' for inner cylinder given original difference of radii at junction evaluator uses Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction)) to evaluate the Constant 'a' for inner cylinder, The Constant 'a' for inner 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 inner cylinder is denoted by a₂ symbol.

How to evaluate Constant 'a' for inner cylinder given original difference of radii at junction using this online evaluator? To use this online evaluator for Constant 'a' for inner cylinder given original difference of radii at junction, enter Constant 'a' for outer cylinder (a₁), Original difference of radii (Δr_original), Modulus of Elasticity Of Thick Shell (E) & Radius at Junction (r_*) and hit the calculate button.

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

What is the formula to find Constant 'a' for inner cylinder given original difference of radii at junction?

The formula of Constant 'a' for inner cylinder given original difference of radii at junction is expressed as Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction)). Here is an example- -2.5 = 4-(2E-05*2600000/(2*4)).

How to calculate Constant 'a' for inner cylinder given original difference of radii at junction?

With Constant 'a' for outer cylinder (a₁), Original difference of radii (Δr_original), Modulus of Elasticity Of Thick Shell (E) & Radius at Junction (r_*) we can find Constant 'a' for inner cylinder given original difference of radii at junction using the formula - Constant 'a' for inner cylinder = Constant 'a' for outer cylinder-(Original difference of radii*Modulus of Elasticity Of Thick Shell/(2*Radius at Junction)).

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

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

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

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

Other formulas in Compound Cylinder Shrinkage Radii Change category

How to Evaluate Constant 'a' for inner cylinder given original difference of radii at junction?

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

Variable Name