Internal fluid pressure in thin cylindrical vessel given change in diameter Solution

STEP 0: Pre-Calculation Summary
Formula Used
Internal Pressure in thin shell = (Change in Diameter*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/((((Inner Diameter of Cylinder^2)))*(1-(Poisson's Ratio/2)))
Pi = (∆d*(2*t*E))/((((Di^2)))*(1-(𝛎/2)))
This formula uses 6 Variables
Variables Used
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.
Change in Diameter - (Measured in Meter) - The Change in Diameter is the difference between the initial and final diameter.
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.
Inner Diameter of Cylinder - (Measured in Meter) - Inner Diameter of Cylinder is the diameter of the inside of the cylinder.
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
Change in Diameter: 50.5 Millimeter --> 0.0505 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)
Inner Diameter of Cylinder: 50 Millimeter --> 0.05 Meter (Check conversion here)
Poisson's Ratio: 0.3 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pi = (∆d*(2*t*E))/((((Di^2)))*(1-(𝛎/2))) --> (0.0505*(2*0.525*10000000))/((((0.05^2)))*(1-(0.3/2)))
Evaluating ... ...
Pi = 249529411.764706
STEP 3: Convert Result to Output's Unit
249529411.764706 Pascal -->249.529411764706 Megapascal (Check conversion here)
FINAL ANSWER
249.529411764706 249.5294 Megapascal <-- Internal Pressure in thin shell
(Calculation completed in 00.004 seconds)

Credits

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National Institute Of Technology (NIT), Hamirpur
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23 Effect of Internal Pressure on Dimension of Thin Cylindrical Shell Calculators

Diameter of cylindrical shell given change in length of cylindrical shell
Go Diameter of Shell = (Change in Length*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell*Length Of Cylindrical Shell))*((1/2)-Poisson's Ratio))
Length of cylindrical shell given change in length of cylindrical shell
Go Length Of Cylindrical Shell = (Change in Length*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell*Diameter of Shell))*((1/2)-Poisson's Ratio))
Internal fluid pressure given change in length of cylindrical shell
Go Internal Pressure in thin shell = (Change in Length*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Diameter of Shell*Length Of Cylindrical Shell))*((1/2)-Poisson's Ratio))
Internal diameter of thin cylindrical vessel given circumferential strain
Go Inner Diameter of Cylinder = (Circumferential strain Thin Shell*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell))*((1/2)-Poisson's Ratio))
Internal fluid pressure given circumferential strain
Go Internal Pressure in thin shell = (Circumferential strain Thin Shell*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Inner Diameter of Cylinder))*((1/2)-Poisson's Ratio))
Internal fluid pressure in thin cylindrical vessel given change in diameter
Go Internal Pressure in thin shell = (Change in Diameter*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/((((Inner Diameter of Cylinder^2)))*(1-(Poisson's Ratio/2)))
Internal fluid pressure in thin cylindrical vessel given longitudinal strain
Go Internal Pressure in thin shell = (Longitudinal Strain*2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell)/((Inner Diameter of Cylinder)*((1/2)-Poisson's Ratio))
Internal diameter of thin cylindrical vessel given longitudinal strain
Go Inner Diameter of Cylinder = (Longitudinal Strain*2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell)/((Internal Pressure in thin shell)*((1/2)-Poisson's Ratio))
Original diameter of vessel given change in diameter
Go Original Diameter = (Change in Diameter*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Internal Pressure in thin shell))*(1-(Poisson's Ratio/2)))^(1/2)
Length of cylindrical shell given change in volume of cylindrical shell
Go Length Of Cylindrical Shell = ((Change in Volume/(pi/4))-(Change in Length*(Diameter of Shell^2)))/(2*Diameter of Shell*Change in Diameter)
Diameter of thin cylindrical shell given volumetric strain
Go Diameter of Shell = (Volumetric Strain*2*Modulus of Elasticity Of Thin Shell*Thickness Of Thin Shell)/((Internal Pressure in thin shell)*((5/2)-Poisson's Ratio))
Internal fluid pressure in shell given volumetric strain
Go Internal Pressure in thin shell = (Volumetric Strain*2*Modulus of Elasticity Of Thin Shell*Thickness Of Thin Shell)/((Diameter of Shell)*((5/2)-Poisson's Ratio))
Longitudinal stress given circumferential strain
Go Longitudinal Stress Thick Shell = (Hoop Stress in Thin shell-(Circumferential strain Thin Shell*Modulus of Elasticity Of Thin Shell))/Poisson's Ratio
Hoop stress given circumferential strain
Go Hoop Stress in Thin shell = (Circumferential strain Thin Shell*Modulus of Elasticity Of Thin Shell)+(Poisson's Ratio*Longitudinal Stress Thick Shell)
Hoop stress in thin cylindrical vessel given Longitudinal strain
Go Hoop Stress in Thin shell = (-(Longitudinal Strain*Modulus of Elasticity Of Thin Shell)+Longitudinal Stress Thick Shell)/(Poisson's Ratio)
Longitudinal stress in thin cylindrical vessel given Longitudinal strain
Go Longitudinal Stress Thick Shell = ((Longitudinal Strain*Modulus of Elasticity Of Thin Shell))+(Poisson's Ratio*Hoop Stress in Thin shell)
Diameter of thin cylindrical strain given volumetric strain
Go Diameter of Shell = 2*Change in Distance/(Volumetric Strain-(Change in Length/Length Of Cylindrical Shell))
Length of thin cylindrical strain given volumetric strain
Go Length Of Cylindrical Shell = Change in Length/(Volumetric Strain-(2*Change in Diameter/Diameter of Shell))
Volume of thin cylindrical shell given circumferential and longitudinal strain
Go Volume of Thin Cylindrical Shell = Change in Volume/((2*Circumferential strain Thin Shell)+Longitudinal Strain)
Original circumference of thin cylindrical vessel given circumferential strain
Go Original Circumference = Change in circumference/Circumferential strain Thin Shell
Original diameter of thin cylindrical vessel given circumferential strain
Go Original Diameter = Change in Diameter/Circumferential strain Thin Shell
Original length of vessel given longitudinal strain
Go Initial Length = Change in Length/Longitudinal Strain
Original volume of cylindrical shell given volumetric strain
Go Original Volume = Change in Volume/Volumetric Strain

Internal fluid pressure in thin cylindrical vessel given change in diameter Formula

Internal Pressure in thin shell = (Change in Diameter*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/((((Inner Diameter of Cylinder^2)))*(1-(Poisson's Ratio/2)))
Pi = (∆d*(2*t*E))/((((Di^2)))*(1-(𝛎/2)))

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 Internal fluid pressure in thin cylindrical vessel given change in diameter?

Internal fluid pressure in thin cylindrical vessel given change in diameter calculator uses Internal Pressure in thin shell = (Change in Diameter*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/((((Inner Diameter of Cylinder^2)))*(1-(Poisson's Ratio/2))) to calculate the Internal Pressure in thin shell, The Internal fluid pressure in thin cylindrical vessel given change in diameter 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 in thin shell is denoted by Pi symbol.

How to calculate Internal fluid pressure in thin cylindrical vessel given change in diameter using this online calculator? To use this online calculator for Internal fluid pressure in thin cylindrical vessel given change in diameter, enter Change in Diameter (∆d), Thickness Of Thin Shell (t), Modulus of Elasticity Of Thin Shell (E), Inner Diameter of Cylinder (Di) & Poisson's Ratio (𝛎) and hit the calculate button. Here is how the Internal fluid pressure in thin cylindrical vessel given change in diameter calculation can be explained with given input values -> 0.00025 = (0.0505*(2*0.525*10000000))/((((0.05^2)))*(1-(0.3/2))).

FAQ

What is Internal fluid pressure in thin cylindrical vessel given change in diameter?
The Internal fluid pressure in thin cylindrical vessel given change in diameter 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 Pi = (∆d*(2*t*E))/((((Di^2)))*(1-(𝛎/2))) or Internal Pressure in thin shell = (Change in Diameter*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/((((Inner Diameter of Cylinder^2)))*(1-(Poisson's Ratio/2))). The Change in Diameter is the difference between the initial and final diameter, 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, Inner Diameter of Cylinder is the diameter of the inside of the cylinder & 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 Internal fluid pressure in thin cylindrical vessel given change in diameter?
The Internal fluid pressure in thin cylindrical vessel given change in diameter 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 in thin shell = (Change in Diameter*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/((((Inner Diameter of Cylinder^2)))*(1-(Poisson's Ratio/2))). To calculate Internal fluid pressure in thin cylindrical vessel given change in diameter, you need Change in Diameter (∆d), Thickness Of Thin Shell (t), Modulus of Elasticity Of Thin Shell (E), Inner Diameter of Cylinder (Di) & Poisson's Ratio (𝛎). With our tool, you need to enter the respective value for Change in Diameter, Thickness Of Thin Shell, Modulus of Elasticity Of Thin Shell, Inner Diameter of Cylinder & 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 Internal Pressure in thin shell?
In this formula, Internal Pressure in thin shell uses Change in Diameter, Thickness Of Thin Shell, Modulus of Elasticity Of Thin Shell, Inner Diameter of Cylinder & Poisson's Ratio. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Internal Pressure in thin shell = (Circumferential strain Thin Shell*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Inner Diameter of Cylinder))*((1/2)-Poisson's Ratio))
  • Internal Pressure in thin shell = (Longitudinal Strain*2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell)/((Inner Diameter of Cylinder)*((1/2)-Poisson's Ratio))
  • Internal Pressure in thin shell = (Change in Length*(2*Thickness Of Thin Shell*Modulus of Elasticity Of Thin Shell))/(((Diameter of Shell*Length Of Cylindrical Shell))*((1/2)-Poisson's Ratio))
  • Internal Pressure in thin shell = (Volumetric Strain*2*Modulus of Elasticity Of Thin Shell*Thickness Of Thin Shell)/((Diameter of Shell)*((5/2)-Poisson's Ratio))
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