Inner Diameter of Pressurized Cylinder from Bernie's Equation Calculator

✖Thickness of pressurized cylinder wall is the measure of the smallest dimension of a solid figure, here a cylindrical wall.ⓘ Thickness of Pressurized Cylinder Wall [t_w]			+10% -10%
✖Permissible Tensile stress in pressurized cylinder is the tensile stress of the stretching force per unit area into the walls of the cylinder.ⓘ Permissible Tensile Stress in Pressurized Cylinder [σ_t]			+10% -10%
✖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.ⓘ Poisson's Ratio of Pressurized Cylinder [𝛎]			+10% -10%
✖Internal pressure on cylinder is the amount of pressure of force per unit area acting onto the internal surface of a cylinder.ⓘ Internal Pressure on Cylinder [P_i]			+10% -10%

✖Inner diameter of pressurized cylinder is the diameter of the inner circle or the internal surface of a cylinder under pressure.ⓘ Inner Diameter of Pressurized Cylinder from Bernie's Equation [d_i]

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Inner Diameter of Pressurized Cylinder from Bernie's Equation Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
d_i = (2*t_w)/((((σ_t+((1-(𝛎)*P_i)))/(σ_t-((1+𝛎)*P_i)))^0.5)-1)
This formula uses 5 Variables

Variables Used

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.
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.
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

Thickness of Pressurized Cylinder Wall: 30 Millimeter --> 0.03 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

d_i = (2*t_w)/((((σ_t+((1-(𝛎)*P_i)))/(σ_t-((1+𝛎)*P_i)))^0.5)-1) --> (2*0.03)/((((75000000+((1-(0.3)*10200000)))/(75000000-((1+0.3)*10200000)))^0.5)-1)

Evaluating ... ...

d_i = 0.755206674920526

STEP 3: Convert Result to Output's Unit

0.755206674920526 Meter -->755.206674920526 Millimeter (Check conversion here)

FINAL ANSWER

755.206674920526 ≈ 755.2067 Millimeter <-- Inner Diameter of Pressurized Cylinder

(Calculation completed in 00.016 seconds)

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Home » Engineering » Mechanical » Machine Design » Design of Pressure Vessels » Bernie's and Clavarino's Equation » Inner Diameter of Pressurized Cylinder from Bernie's Equation

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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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< Bernie's and Clavarino's Equation Calculators

Inner Diameter of Pressurized Cylinder from Clavarino's Equation

LaTeX 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

LaTeX 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

LaTeX 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

LaTeX 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)

Inner Diameter of Pressurized Cylinder from Bernie's Equation Formula

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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 Inner Diameter of Pressurized Cylinder from Bernie's Equation?

Inner Diameter of Pressurized Cylinder from Bernie's Equation calculator uses 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) to calculate the Inner Diameter of Pressurized Cylinder, Inner Diameter of Pressurized Cylinder from Bernie's Equation formula is defined as the diameter of the internal surface of a pressurized cylindrical vessel. Inner Diameter of Pressurized Cylinder is denoted by d_i symbol.

How to calculate Inner Diameter of Pressurized Cylinder from Bernie's Equation using this online calculator? To use this online calculator for Inner Diameter of Pressurized Cylinder from Bernie's Equation, enter Thickness of Pressurized Cylinder Wall (t_w), Permissible Tensile Stress in Pressurized Cylinder (σ_t), Poisson's Ratio of Pressurized Cylinder (𝛎) & Internal Pressure on Cylinder (P_i) and hit the calculate button. Here is how the Inner Diameter of Pressurized Cylinder from Bernie's Equation calculation can be explained with given input values -> 755206.7 = (2*0.03)/((((75000000+((1-(0.3)*10200000)))/(75000000-((1+0.3)*10200000)))^0.5)-1).

FAQ

What is Inner Diameter of Pressurized Cylinder from Bernie's Equation?

Inner Diameter of Pressurized Cylinder from Bernie's Equation formula is defined as the diameter of the internal surface of a pressurized cylindrical vessel and is represented as d_i = (2*t_w)/((((σ_t+((1-(𝛎)*P_i)))/(σ_t-((1+𝛎)*P_i)))^0.5)-1) or 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 wall is the measure of the smallest dimension of a solid figure, here a cylindrical wall, 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 Inner Diameter of Pressurized Cylinder from Bernie's Equation?

Inner Diameter of Pressurized Cylinder from Bernie's Equation formula is defined as the diameter of the internal surface of a pressurized cylindrical vessel is calculated using 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). To calculate Inner Diameter of Pressurized Cylinder from Bernie's Equation, you need Thickness of Pressurized Cylinder Wall (t_w), Permissible Tensile Stress in Pressurized Cylinder (σ_t), Poisson's Ratio of Pressurized Cylinder (𝛎) & Internal Pressure on Cylinder (P_i). With our tool, you need to enter the respective value for Thickness of Pressurized Cylinder Wall, 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 Inner Diameter of Pressurized Cylinder?

In this formula, Inner Diameter of Pressurized Cylinder uses Thickness of Pressurized Cylinder Wall, 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 -

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)

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