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Poisson's ratio given change in diameter of thin spherical shells Formula

GoPoisson's ratio for thin spherical shell given strain and internal fluid pressure Formula

GoPoisson's ratio for thin spherical shell given strain in any one direction Formula

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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. Check FAQs

𝛎 = 1 - (∆d \cdot \frac{4 \cdot t \cdot E}{P i \cdot (D^{2})})

𝛎 - Poisson's Ratio?∆d - Change in Diameter?t - Thickness Of Thin Spherical Shell?E - Modulus of Elasticity Of Thin Shell?P_i - Internal Pressure?D - Diameter of Sphere?

Poisson's ratio given change in diameter of thin spherical shells Example

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Here is how the Poisson's ratio given change in diameter of thin spherical shells equation looks like with Values.

Here is how the Poisson's ratio given change in diameter of thin spherical shells equation looks like with Units.

Here is how the Poisson's ratio given change in diameter of thin spherical shells equation looks like.

0.3 = 1 - (173.9062 \cdot \frac{4 \cdot 12 \cdot 10}{0.053 \cdot (1500^{2})})

0.3 = 1 - (173.9062mm \cdot \frac{4 \cdot 12mm \cdot 10MPa}{0.053MPa \cdot ({1500mm}^{2})})

0.3 = 1 - (173.9062 \cdot \frac{4 \cdot 12 \cdot 10}{0.053 \cdot (1500^{2})})

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Poisson's ratio given change in diameter of thin spherical shells Solution

Follow our step by step solution on how to calculate Poisson's ratio given change in diameter of thin spherical shells?

FIRST Step Consider the formula

𝛎 = 1 - (∆d \cdot \frac{4 \cdot t \cdot E}{P i \cdot (D^{2})})

Next Step Substitute values of Variables

∴

𝛎 = 1 - (173.9062mm \cdot \frac{4 \cdot 12mm \cdot 10MPa}{0.053MPa \cdot ({1500mm}^{2})})

Next Step Convert Units

∴

𝛎 = 1 - (0.1739m \cdot \frac{4 \cdot 0.012m \cdot 1E+7Pa}{53000Pa \cdot ({1.5m}^{2})})

Next Step Prepare to Evaluate

∴

𝛎 = 1 - (0.1739 \cdot \frac{4 \cdot 0.012 \cdot 1E+7}{53000 \cdot ({1.5}^{2})})

Next Step Evaluate

∴

𝛎 = 0.300000201257862

LAST Step Rounding Answer

∴

𝛎 = 0.3

Poisson's ratio given change in diameter of thin spherical shells Formula Elements

Variables

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.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Poisson's Ratio

Change in Diameter

The Change in Diameter is the difference between the initial and final diameter.

Symbol: ∆d

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Change in Diameter

Thickness Of Thin Spherical Shell

Thickness Of Thin Spherical Shell is the distance through an object.

Symbol: t

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness Of Thin Spherical Shell

Modulus of Elasticity Of Thin Shell

Modulus of Elasticity Of Thin 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 Thin Shell

Internal Pressure

Internal Pressure is a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature.

Symbol: P_i

Measurement: PressureUnit: MPa

Note: Value can be positive or negative.

Formulas to find Internal Pressure

Diameter of Sphere

Diameter of Sphere, is a chord that runs through the center point of the circle. It is the longest possible chord of any circle. The center of a circle is the midpoint of its diameter.

Symbol: D

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Sphere

Other Formulas to find Poisson's Ratio

Go Poisson's ratio for thin spherical shell given strain and internal fluid pressure

𝛎 = 1 - (ε \cdot \frac{4 \cdot t \cdot E}{P i \cdot D})

Go Poisson's ratio for thin spherical shell given strain in any one direction

𝛎 = 1 - (E \cdot \frac{ε}{σ θ})

Go Poisson's ratio for thin cylindrical vessel given change in diameter

𝛎 = 2 \cdot (1 - \frac{∆d \cdot (2 \cdot t \cdot E)}{((P i \cdot ({D i}^{2})))})

Go Poisson's ratio given change in length of cylindrical shell

𝛎 = (\frac{1}{2}) - (\frac{ΔL \cdot (2 \cdot t \cdot E)}{(P i \cdot D \cdot L cylinder)})

How to Evaluate Poisson's ratio given change in diameter of thin spherical shells?

Poisson's ratio given change in diameter of thin spherical shells evaluator uses Poisson's Ratio = 1-(Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(Internal Pressure*(Diameter of Sphere^2))) to evaluate the Poisson's Ratio, The Poisson's ratio given change in diameter of thin spherical shells formula is defined as the ratio of the change in the width per unit width of a material, to the change in its length per unit length, as a result of strain. Poisson's Ratio is denoted by 𝛎 symbol.

How to evaluate Poisson's ratio given change in diameter of thin spherical shells using this online evaluator? To use this online evaluator for Poisson's ratio given change in diameter of thin spherical shells, enter Change in Diameter (∆d), Thickness Of Thin Spherical Shell (t), Modulus of Elasticity Of Thin Shell (E), Internal Pressure (P_i) & Diameter of Sphere (D) and hit the calculate button.

FAQs on Poisson's ratio given change in diameter of thin spherical shells

What is the formula to find Poisson's ratio given change in diameter of thin spherical shells?

The formula of Poisson's ratio given change in diameter of thin spherical shells is expressed as Poisson's Ratio = 1-(Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(Internal Pressure*(Diameter of Sphere^2))). Here is an example- 0.79673 = 1-(0.1739062*(4*0.012*10000000)/(53000*(1.5^2))).

How to calculate Poisson's ratio given change in diameter of thin spherical shells?

With Change in Diameter (∆d), Thickness Of Thin Spherical Shell (t), Modulus of Elasticity Of Thin Shell (E), Internal Pressure (P_i) & Diameter of Sphere (D) we can find Poisson's ratio given change in diameter of thin spherical shells using the formula - Poisson's Ratio = 1-(Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(Internal Pressure*(Diameter of Sphere^2))).

What are the other ways to Calculate Poisson's Ratio?

Here are the different ways to Calculate Poisson's Ratio-

Poisson's Ratio=1-(Strain in thin shell*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(Internal Pressure*Diameter of Sphere))
Poisson's Ratio=1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell)
Poisson's Ratio=2*(1-(Change in Diameter*(2*Thickness of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell*(Inner Diameter of Cylinder^2)))))

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Poisson's ratio given change in diameter of thin spherical shells Formula

​GoPoisson's ratio for thin spherical shell given strain and internal fluid pressure Formula

​GoPoisson's ratio for thin spherical shell given strain in any one direction Formula

Poisson's ratio given change in diameter of thin spherical shells Example

Poisson's ratio given change in diameter of thin spherical shells Solution

Poisson's ratio given change in diameter of thin spherical shells Formula Elements

Other Formulas to find Poisson's Ratio

How to Evaluate Poisson's ratio given change in diameter of thin spherical shells?

FAQs on Poisson's ratio given change in diameter of thin spherical shells

Variable Name

GoPoisson's ratio for thin spherical shell given strain and internal fluid pressure Formula

GoPoisson's ratio for thin spherical shell given strain in any one direction Formula