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Change in diameter of thin spherical shell Formula

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

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

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

Change in diameter of thin spherical shell Example

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Here is how the Change in diameter of thin spherical shell equation looks like with Values.

Here is how the Change in diameter of thin spherical shell equation looks like with Units.

Here is how the Change in diameter of thin spherical shell equation looks like.

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

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

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

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Change in diameter of thin spherical shell Solution

Follow our step by step solution on how to calculate Change in diameter of thin spherical shell?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

∆d = (\frac{53000Pa \cdot ({1.5m}^{2})}{4 \cdot 0.012m \cdot 1E+7Pa}) \cdot (1 - 0.3)

Next Step Prepare to Evaluate

∴

∆d = (\frac{53000 \cdot ({1.5}^{2})}{4 \cdot 0.012 \cdot 1E+7}) \cdot (1 - 0.3)

Next Step Evaluate

∴

∆d = 0.17390625m

Next Step Convert to Output's Unit

∴

∆d = 173.90625mm

LAST Step Rounding Answer

∴

∆d = 173.9062mm

Change in diameter of thin spherical shell Formula Elements

Variables

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

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

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

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

Other formulas in Change in Dimension of Thin Spherical Shell due to Internal Pressure category

Go Strain in any one direction of thin spherical shell

ε = (\frac{σ θ}{E}) \cdot (1 - 𝛎)

Go Hoop stress induced in thin spherical shell given strain in any one direction

σ θ = (\frac{ε}{1 - 𝛎}) \cdot E

Go Hoop stress in thin spherical shell given strain in any one direction and Poisson's ratio

σ θ = (\frac{ε}{1 - 𝛎}) \cdot E

Go Modulus of elasticity of thin spherical shell given strain in any one direction

E = (\frac{σ θ}{ε}) \cdot (1 - 𝛎)

How to Evaluate Change in diameter of thin spherical shell?

Change in diameter of thin spherical shell evaluator uses Change in Diameter = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio) to evaluate the Change in Diameter, The Change in diameter of thin spherical shell formula is defined as a change that happened in diameter due to the strain in the thin spherical shell. Change in Diameter is denoted by ∆d symbol.

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

FAQs on Change in diameter of thin spherical shell

What is the formula to find Change in diameter of thin spherical shell?

The formula of Change in diameter of thin spherical shell is expressed as Change in Diameter = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio). Here is an example- 173906.2 = ((53000*(1.5^2))/(4*0.012*10000000))*(1-0.3).

How to calculate Change in diameter of thin spherical shell?

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

Can the Change in diameter of thin spherical shell be negative?

Yes, the Change in diameter of thin spherical shell, measured in Length can be negative.

Which unit is used to measure Change in diameter of thin spherical shell?

Change in diameter of thin spherical shell is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Change in diameter of thin spherical shell can be measured.

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Change in diameter of thin spherical shell Formula

Change in diameter of thin spherical shell Example

Change in diameter of thin spherical shell Solution

Change in diameter of thin spherical shell Formula Elements

Other formulas in Change in Dimension of Thin Spherical Shell due to Internal Pressure category

How to Evaluate Change in diameter of thin spherical shell?

FAQs on Change in diameter of thin spherical shell

Variable Name