Internal fluid pressure given change in diameter of thin spherical shells Calculator

✖The Change in Diameter is the difference between the initial and final diameter.ⓘ Change in Diameter [∆d]			+10% -10%
✖Thickness Of Thin Spherical Shell is the distance through an object.ⓘ Thickness Of Thin Spherical Shell [t]			+10% -10%
✖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.ⓘ Modulus of Elasticity Of Thin Shell [E]			+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%
✖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.ⓘ Diameter of Sphere [D]			+10% -10%

✖Internal Pressure is a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature.ⓘ Internal fluid pressure given change in diameter of thin spherical shells [P_i]

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Formula

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Internal fluid pressure given change in diameter of thin spherical shells

Formula

`"P"_{"i"} = ("∆d"*(4*"t"*"E")/(1-"𝛎"))/("D"^2)`

Example

`"0.01539MPa"=("50.5mm"*(4*"12mm"*"10MPa")/(1-"0.3"))/(("1500mm")^2)`

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Internal fluid pressure given change in diameter of thin spherical shells Solution

STEP 0: Pre-Calculation Summary

Formula Used

Internal Pressure = (Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Diameter of Sphere^2)
P_i = (∆d*(4*t*E)/(1-𝛎))/(D^2)
This formula uses 6 Variables

Variables Used

Internal Pressure - (Measured in Pascal) - Internal Pressure is a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature.
Change in Diameter - (Measured in Meter) - The Change in Diameter is the difference between the initial and final diameter.
Thickness Of Thin Spherical Shell - (Measured in Meter) - Thickness Of Thin Spherical Shell is the distance through an object.
Modulus of Elasticity Of Thin Shell - (Measured in Pascal) - 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.
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.
Diameter of Sphere - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Change in Diameter: 50.5 Millimeter --> 0.0505 Meter (Check conversion here)
Thickness Of Thin Spherical Shell: 12 Millimeter --> 0.012 Meter (Check conversion here)
Modulus of Elasticity Of Thin Shell: 10 Megapascal --> 10000000 Pascal (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required
Diameter of Sphere: 1500 Millimeter --> 1.5 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_i = (∆d*(4*t*E)/(1-𝛎))/(D^2) --> (0.0505*(4*0.012*10000000)/(1-0.3))/(1.5^2)

Evaluating ... ...

P_i = 15390.4761904762

STEP 3: Convert Result to Output's Unit

15390.4761904762 Pascal -->0.0153904761904762 Megapascal (Check conversion here)

FINAL ANSWER

0.0153904761904762 ≈ 0.01539 Megapascal <-- Internal Pressure

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Thin Cylinders And Spheres » Change in Dimension of Thin Spherical Shell due to Internal Pressure » Internal fluid pressure given change in diameter of thin spherical shells

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Birsa Institute of Technology (BIT), Sindri

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< 17 Change in Dimension of Thin Spherical Shell due to Internal Pressure Calculators

Diameter of spherical shell given change in diameter of thin spherical shells

Go Diameter of Sphere = sqrt((Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Internal Pressure))

Thickness of spherical shell given change in diameter of thin spherical shells

Go Thickness Of Thin Spherical Shell = ((Internal Pressure*(Diameter of Sphere^2))/(4*Change in Diameter*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio)

Modulus of elasticity given change in diameter of thin spherical shells

Go Modulus of Elasticity Of Thin Shell = ((Internal Pressure*(Diameter of Sphere^2))/(4*Thickness Of Thin Spherical Shell*Change in Diameter))*(1-Poisson's Ratio)

Change in diameter of thin spherical shell

Go 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)

Modulus of elasticity for thin spherical shell given strain and internal fluid pressure

Go Modulus of Elasticity Of Thin Shell = ((Internal Pressure*Diameter of Sphere)/(4*Thickness Of Thin Spherical Shell*Strain in thin shell))*(1-Poisson's Ratio)

Internal fluid pressure in thin spherical shell given strain in any one direction

Go Internal Pressure = (Strain in thin shell*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Diameter of Sphere)

Internal fluid pressure given change in diameter of thin spherical shells

Go Internal Pressure = (Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Diameter of Sphere^2)

Thickness of thin spherical shell given strain in any one direction

Go Thickness Of Thin Spherical Shell = ((Internal Pressure*Diameter of Sphere)/(4*Strain in thin shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio)

Diameter of thin spherical shell given strain in any one direction

Go Diameter of Sphere = (Strain in thin shell*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Internal Pressure)

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

Go 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)))

Strain in thin spherical shell given internal fluid pressure

Go Strain in thin shell = ((Internal Pressure*Diameter of Sphere)/(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell))*(1-Poisson's Ratio)

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

Go 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))

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

Go Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell

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

Go Modulus of Elasticity Of Thin Shell = (Hoop Stress in Thin shell/Strain in thin shell)*(1-Poisson's Ratio)

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

Go Hoop Stress in Thin shell = (Strain in thin shell/(1-Poisson's Ratio))*Modulus of Elasticity Of Thin Shell

Strain in any one direction of thin spherical shell

Go Strain in thin shell = (Hoop Stress in Thin shell/Modulus of Elasticity Of Thin Shell)*(1-Poisson's Ratio)

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

Go Poisson's Ratio = 1-(Modulus of Elasticity Of Thin Shell*Strain in thin shell/Hoop Stress in Thin shell)

Internal fluid pressure given change in diameter of thin spherical shells Formula

Internal Pressure = (Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Diameter of Sphere^2)
P_i = (∆d*(4*t*E)/(1-𝛎))/(D^2)

How do you reduce stress hoop?

We can suggest that the most efficient method is to apply double cold expansion with high interferences along with axial compression with strain equal to 0.5%. This technique helps to reduce the absolute value of hoop residual stresses by 58%, and decrease radial stresses by 75%.

How to Calculate Internal fluid pressure given change in diameter of thin spherical shells?

Internal fluid pressure given change in diameter of thin spherical shells calculator uses Internal Pressure = (Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Diameter of Sphere^2) to calculate the Internal Pressure, Internal fluid pressure given change in diameter of thin spherical shells formula is defined as a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature. Internal Pressure is denoted by P_i symbol.

How to calculate Internal fluid pressure given change in diameter of thin spherical shells using this online calculator? To use this online calculator for Internal fluid pressure 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), Poisson's Ratio (𝛎) & Diameter of Sphere (D) and hit the calculate button. Here is how the Internal fluid pressure given change in diameter of thin spherical shells calculation can be explained with given input values -> 1.5E-8 = (0.0505*(4*0.012*10000000)/(1-0.3))/(1.5^2).

FAQ

What is Internal fluid pressure given change in diameter of thin spherical shells?

Internal fluid pressure given change in diameter of thin spherical shells formula is defined as a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature and is represented as P_i = (∆d*(4*t*E)/(1-𝛎))/(D^2) or Internal Pressure = (Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Diameter of Sphere^2). The Change in Diameter is the difference between the initial and final diameter, Thickness Of Thin Spherical Shell is the distance through an object, 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, 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 & 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.

How to calculate Internal fluid pressure given change in diameter of thin spherical shells?

Internal fluid pressure given change in diameter of thin spherical shells formula is defined as a measure of how the internal energy of a system changes when it expands or contracts at a constant temperature is calculated using Internal Pressure = (Change in Diameter*(4*Thickness Of Thin Spherical Shell*Modulus of Elasticity Of Thin Shell)/(1-Poisson's Ratio))/(Diameter of Sphere^2). To calculate Internal fluid pressure given change in diameter of thin spherical shells, you need Change in Diameter (∆d), Thickness Of Thin Spherical Shell (t), Modulus of Elasticity Of Thin Shell (E), Poisson's Ratio (𝛎) & Diameter of Sphere (D). With our tool, you need to enter the respective value for Change in Diameter, Thickness Of Thin Spherical Shell, Modulus of Elasticity Of Thin Shell, Poisson's Ratio & Diameter of Sphere 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 Internal Pressure?

In this formula, Internal Pressure uses Change in Diameter, Thickness Of Thin Spherical Shell, Modulus of Elasticity Of Thin Shell, Poisson's Ratio & Diameter of Sphere. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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