Longitudinal strain in thin cylindrical vessel given internal fluid pressure Calculator

✖Internal Pressure in thin shell is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature.ⓘ Internal Pressure in thin shell [P_i]			+10% -10%
✖Inner Diameter of Cylinder is the diameter of the inside of the cylinder.ⓘ Inner Diameter of Cylinder [D_i]			+10% -10%
✖Thickness Of Thin Shell is the distance through an object.ⓘ Thickness Of Thin 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%

✖The Longitudinal Strain is ratio of change in length to original length.ⓘ Longitudinal strain in thin cylindrical vessel given internal fluid pressure [ε_longitudinal]

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Formula

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Longitudinal strain in thin cylindrical vessel given internal fluid pressure

Formula

`"ε"_{"longitudinal"} = (("P"_{"i"}*"D"_{"i"})/(2*"t"*"E"))*((1/2)-"𝛎")`

Example

`"0.013333"=(("14MPa"*"50mm")/(2*"525mm"*"10MPa"))*((1/2)-"0.3")`

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Longitudinal strain in thin cylindrical vessel given internal fluid pressure Solution

STEP 0: Pre-Calculation Summary

Formula Used

Longitudinal Strain = ((Internal Pressure in thin shell*Inner Diameter of Cylinder)/(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))*((1/2)-Poisson's Ratio)
ε_longitudinal = ((P_i*D_i)/(2*t*E))*((1/2)-𝛎)
This formula uses 6 Variables

Variables Used

Longitudinal Strain - The Longitudinal Strain is ratio of change in length to original length.
Internal Pressure in thin shell - (Measured in Pascal) - Internal Pressure in thin shell is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature.
Inner Diameter of Cylinder - (Measured in Meter) - Inner Diameter of Cylinder is the diameter of the inside of the cylinder.
Thickness Of Thin Shell - (Measured in Meter) - Thickness Of Thin 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.

STEP 1: Convert Input(s) to Base Unit

Internal Pressure in thin shell: 14 Megapascal --> 14000000 Pascal (Check conversion here)
Inner Diameter of Cylinder: 50 Millimeter --> 0.05 Meter (Check conversion here)
Thickness Of Thin Shell: 525 Millimeter --> 0.525 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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ε_longitudinal = ((P_i*D_i)/(2*t*E))*((1/2)-𝛎) --> ((14000000*0.05)/(2*0.525*10000000))*((1/2)-0.3)

Evaluating ... ...

ε_longitudinal = 0.0133333333333333

STEP 3: Convert Result to Output's Unit

0.0133333333333333 --> No Conversion Required

FINAL ANSWER

0.0133333333333333 ≈ 0.013333 <-- Longitudinal Strain

(Calculation completed in 00.004 seconds)

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Home » Physics » Strength of Materials » Thin Cylinders And Spheres » Effect of Internal Pressure on Dimension of Thin Cylindrical Shell » Strain » Longitudinal strain in thin cylindrical vessel given internal fluid pressure

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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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< 15 Strain Calculators

Circumferential strain given internal fluid pressure

Go Circumferential strain Thin Shell = ((Internal Pressure in thin shell*Inner Diameter of Cylinder)/(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))*((1/2)-Poisson's Ratio)

Longitudinal strain in thin cylindrical vessel given internal fluid pressure

Go Longitudinal Strain = ((Internal Pressure in thin shell*Inner Diameter of Cylinder)/(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))*((1/2)-Poisson's Ratio)

Volumetric strain given internal fluid pressure

Go Volumetric Strain = (Internal Pressure in thin shell*Diameter of Shell/(2*Modulus of Elasticity Of Thin Shell*Thickness Of Thin Shell))*((5/2)-Poisson's Ratio)

Circumferential strain given hoop stress

Go Circumferential strain Thin Shell = (Hoop Stress in Thin shell-(Poisson's Ratio*Longitudinal Stress Thick Shell))/Modulus of Elasticity Of Thin Shell

Longitudinal strain given hoop and longitudinal stress

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

Volumetric strain of thin cylindrical shell given changes in diameter and length

Go Volumetric Strain = (2*Change in Diameter/Diameter of Shell)+(Change in Length/Length Of Cylindrical Shell)

Circumferential strain given volume of thin cylindrical shell

Go Circumferential strain Thin Shell = ((Change in Volume/Volume of Thin Cylindrical Shell)-Longitudinal Strain)/2

Longitudinal strain given volume of thin cylindrical shell

Go Longitudinal Strain = (Change in Volume/Volume of Thin Cylindrical Shell)-(2*Circumferential strain Thin Shell)

Circumferential strain given circumference

Go Circumferential strain Thin Shell = Change in circumference/Original Circumference

Longitudinal strain given volumetric strain for thin cylindrical shell

Go Longitudinal Strain = (Volumetric Strain-(2*Circumferential strain Thin Shell))

Circumferential strain given volumetric strain for thin cylindrical shell

Go Circumferential strain Thin Shell = (Volumetric Strain-Longitudinal Strain)/2

Volumetric strain given circumferential strain and longitudinal strain

Go Volumetric Strain = 2*Circumferential strain Thin Shell+(Longitudinal Strain)

Circumferential strain of vessel given diameter

Go Circumferential strain Thin Shell = Change in Diameter/Original Diameter

Longitudinal strain for vessel given change in length formula

Go Longitudinal Strain = Change in Length/Initial Length

Volumetric strain of thin cylindrical shell

Go Volumetric Strain = Change in Volume/Original Volume

Longitudinal strain in thin cylindrical vessel given internal fluid pressure Formula

What is meant by hoop stress?

The hoop stress, or tangential stress, is the stress around the circumference of the pipe due to a pressure gradient. The maximum hoop stress always occurs at the inner radius or the outer radius depending on the direction of the pressure gradient.

How to Calculate Longitudinal strain in thin cylindrical vessel given internal fluid pressure?

Longitudinal strain in thin cylindrical vessel given internal fluid pressure calculator uses Longitudinal Strain = ((Internal Pressure in thin shell*Inner Diameter of Cylinder)/(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))*((1/2)-Poisson's Ratio) to calculate the Longitudinal Strain, The Longitudinal strain in thin cylindrical vessel given internal fluid pressure formula is defined as the change in the length to the original length of an object. It is caused due to longitudinal stress and is denoted by the Greek letter epsilon 𝜺. Longitudinal Strain is denoted by ε_longitudinal symbol.

How to calculate Longitudinal strain in thin cylindrical vessel given internal fluid pressure using this online calculator? To use this online calculator for Longitudinal strain in thin cylindrical vessel given internal fluid pressure, enter Internal Pressure in thin shell (P_i), Inner Diameter of Cylinder (D_i), Thickness Of Thin Shell (t), Modulus of Elasticity Of Thin Shell (E) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Longitudinal strain in thin cylindrical vessel given internal fluid pressure calculation can be explained with given input values -> 0.013333 = ((14000000*0.05)/(2*0.525*10000000))*((1/2)-0.3).

FAQ

What is Longitudinal strain in thin cylindrical vessel given internal fluid pressure?

The Longitudinal strain in thin cylindrical vessel given internal fluid pressure formula is defined as the change in the length to the original length of an object. It is caused due to longitudinal stress and is denoted by the Greek letter epsilon 𝜺 and is represented as ε_longitudinal = ((P_i*D_i)/(2*t*E))*((1/2)-𝛎) or Longitudinal Strain = ((Internal Pressure in thin shell*Inner Diameter of Cylinder)/(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))*((1/2)-Poisson's Ratio). Internal Pressure in thin shell is a measure of how the internal energy of a system changes when it expands or contracts at constant temperature, Inner Diameter of Cylinder is the diameter of the inside of the cylinder, Thickness Of Thin 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.

How to calculate Longitudinal strain in thin cylindrical vessel given internal fluid pressure?

The Longitudinal strain in thin cylindrical vessel given internal fluid pressure formula is defined as the change in the length to the original length of an object. It is caused due to longitudinal stress and is denoted by the Greek letter epsilon 𝜺 is calculated using Longitudinal Strain = ((Internal Pressure in thin shell*Inner Diameter of Cylinder)/(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))*((1/2)-Poisson's Ratio). To calculate Longitudinal strain in thin cylindrical vessel given internal fluid pressure, you need Internal Pressure in thin shell (P_i), Inner Diameter of Cylinder (D_i), Thickness Of Thin Shell (t), Modulus of Elasticity Of Thin Shell (E) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Internal Pressure in thin shell, Inner Diameter of Cylinder, Thickness Of Thin Shell, Modulus of Elasticity Of Thin Shell & Poisson's Ratio 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 Longitudinal Strain?

In this formula, Longitudinal Strain uses Internal Pressure in thin shell, Inner Diameter of Cylinder, Thickness Of Thin Shell, Modulus of Elasticity Of Thin Shell & Poisson's Ratio. We can use 4 other way(s) to calculate the same, which is/are as follows -

Longitudinal Strain = Change in Length/Initial Length
Longitudinal Strain = (Longitudinal Stress Thick Shell-(Poisson's Ratio*Hoop Stress in Thin shell))/Modulus of Elasticity Of Thin Shell
Longitudinal Strain = (Change in Volume/Volume of Thin Cylindrical Shell)-(2*Circumferential strain Thin Shell)
Longitudinal Strain = (Volumetric Strain-(2*Circumferential strain Thin Shell))

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