Thickness of Pressurized Cylinder from Bernie's Equation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Thickness of pressurized cylinder wall = (Inner diameter of pressurized cylinder/2)*((((Permissible Tensile stress in pressurized cylinder+((1-(Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1)
tw = (di/2)*((((σt+((1-(𝛎)*Pi)))/(σt-((1+𝛎)*Pi)))^0.5)-1)
This formula uses 5 Variables
Variables Used
Thickness of pressurized cylinder wall - (Measured in Meter) - Thickness of pressurized cylinder wall is the measure of the smallest dimension of a solid figure, here a cylindrical wall.
Inner diameter of pressurized cylinder - (Measured in Meter) - Inner diameter of pressurized cylinder is the diameter of the inner circle or the internal surface of a cylinder under pressure.
Permissible Tensile stress in pressurized cylinder - (Measured in Pascal) - Permissible Tensile stress in pressurized cylinder is the tensile stress of the stretching force per unit area into the walls of the cylinder.
Poisson's Ratio of pressurized cylinder - Poisson's Ratio of pressurized cylinder 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.
Internal pressure on cylinder - (Measured in Pascal) - Internal pressure on cylinder is the amount of pressure of force per unit area acting onto the internal surface of a cylinder.
STEP 1: Convert Input(s) to Base Unit
Inner diameter of pressurized cylinder: 465 Millimeter --> 0.465 Meter (Check conversion here)
Permissible Tensile stress in pressurized cylinder: 75 Newton per Square Millimeter --> 75000000 Pascal (Check conversion here)
Poisson's Ratio of pressurized cylinder: 0.3 --> No Conversion Required
Internal pressure on cylinder: 10.2 Megapascal --> 10200000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
tw = (di/2)*((((σt+((1-(𝛎)*Pi)))/(σt-((1+𝛎)*Pi)))^0.5)-1) --> (0.465/2)*((((75000000+((1-(0.3)*10200000)))/(75000000-((1+0.3)*10200000)))^0.5)-1)
Evaluating ... ...
tw = 0.0184717647013224
STEP 3: Convert Result to Output's Unit
0.0184717647013224 Meter -->18.4717647013224 Millimeter (Check conversion here)
FINAL ANSWER
18.4717647013224 18.47176 Millimeter <-- Thickness of pressurized cylinder wall
(Calculation completed in 00.004 seconds)

Credits

Created by Vaibhav Malani
National Institute of Technology (NIT), Tiruchirapalli
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Verified by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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4 Bernie's and Clavarino's Equation Calculators

Inner Diameter of Pressurized Cylinder from Clavarino's Equation
Go Inner diameter of pressurized cylinder = (2*Thickness of pressurized cylinder wall)/((((Permissible Tensile stress in pressurized cylinder+((1-(2*Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1)
Thickness of Pressurized Cylinder from Clavarino's Equation
Go Thickness of pressurized cylinder wall = (Inner diameter of pressurized cylinder/2)*((((Permissible Tensile stress in pressurized cylinder+((1-(2*Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1)
Inner Diameter of Pressurized Cylinder from Bernie's Equation
Go Inner diameter of pressurized cylinder = (2*Thickness of pressurized cylinder wall)/((((Permissible Tensile stress in pressurized cylinder+((1-(Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1)
Thickness of Pressurized Cylinder from Bernie's Equation
Go Thickness of pressurized cylinder wall = (Inner diameter of pressurized cylinder/2)*((((Permissible Tensile stress in pressurized cylinder+((1-(Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1)

Thickness of Pressurized Cylinder from Bernie's Equation Formula

Thickness of pressurized cylinder wall = (Inner diameter of pressurized cylinder/2)*((((Permissible Tensile stress in pressurized cylinder+((1-(Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1)
tw = (di/2)*((((σt+((1-(𝛎)*Pi)))/(σt-((1+𝛎)*Pi)))^0.5)-1)

What is a Pressure Vessel?

A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure.

How to Calculate Thickness of Pressurized Cylinder from Bernie's Equation?

Thickness of Pressurized Cylinder from Bernie's Equation calculator uses Thickness of pressurized cylinder wall = (Inner diameter of pressurized cylinder/2)*((((Permissible Tensile stress in pressurized cylinder+((1-(Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1) to calculate the Thickness of pressurized cylinder wall, Thickness of Pressurized Cylinder from Bernie's Equation formula is defined as the wall thickness of a pressurized cylindrical vessel. Thickness of pressurized cylinder wall is denoted by tw symbol.

How to calculate Thickness of Pressurized Cylinder from Bernie's Equation using this online calculator? To use this online calculator for Thickness of Pressurized Cylinder from Bernie's Equation, enter Inner diameter of pressurized cylinder (di), Permissible Tensile stress in pressurized cylinder t), Poisson's Ratio of pressurized cylinder (𝛎) & Internal pressure on cylinder (Pi) and hit the calculate button. Here is how the Thickness of Pressurized Cylinder from Bernie's Equation calculation can be explained with given input values -> 18471.76 = (0.465/2)*((((75000000+((1-(0.3)*10200000)))/(75000000-((1+0.3)*10200000)))^0.5)-1).

FAQ

What is Thickness of Pressurized Cylinder from Bernie's Equation?
Thickness of Pressurized Cylinder from Bernie's Equation formula is defined as the wall thickness of a pressurized cylindrical vessel and is represented as tw = (di/2)*((((σt+((1-(𝛎)*Pi)))/(σt-((1+𝛎)*Pi)))^0.5)-1) or Thickness of pressurized cylinder wall = (Inner diameter of pressurized cylinder/2)*((((Permissible Tensile stress in pressurized cylinder+((1-(Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1). Inner diameter of pressurized cylinder is the diameter of the inner circle or the internal surface of a cylinder under pressure, Permissible Tensile stress in pressurized cylinder is the tensile stress of the stretching force per unit area into the walls of the cylinder, Poisson's Ratio of pressurized cylinder 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 & Internal pressure on cylinder is the amount of pressure of force per unit area acting onto the internal surface of a cylinder.
How to calculate Thickness of Pressurized Cylinder from Bernie's Equation?
Thickness of Pressurized Cylinder from Bernie's Equation formula is defined as the wall thickness of a pressurized cylindrical vessel is calculated using Thickness of pressurized cylinder wall = (Inner diameter of pressurized cylinder/2)*((((Permissible Tensile stress in pressurized cylinder+((1-(Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1). To calculate Thickness of Pressurized Cylinder from Bernie's Equation, you need Inner diameter of pressurized cylinder (di), Permissible Tensile stress in pressurized cylinder t), Poisson's Ratio of pressurized cylinder (𝛎) & Internal pressure on cylinder (Pi). With our tool, you need to enter the respective value for Inner diameter of pressurized cylinder, Permissible Tensile stress in pressurized cylinder, Poisson's Ratio of pressurized cylinder & Internal pressure on cylinder 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 Thickness of pressurized cylinder wall?
In this formula, Thickness of pressurized cylinder wall uses Inner diameter of pressurized cylinder, Permissible Tensile stress in pressurized cylinder, Poisson's Ratio of pressurized cylinder & Internal pressure on cylinder. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Thickness of pressurized cylinder wall = (Inner diameter of pressurized cylinder/2)*((((Permissible Tensile stress in pressurized cylinder+((1-(2*Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))/(Permissible Tensile stress in pressurized cylinder-((1+Poisson's Ratio of pressurized cylinder)*Internal pressure on cylinder)))^0.5)-1)
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