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Inner Diameter of Pressurized Cylinder from Bernie's Equation Formula

GoInner Diameter of Pressurized Cylinder from Clavarino's Equation Formula

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Inner diameter of pressurized cylinder is the diameter of the inner circle or the internal surface of a cylinder under pressure. Check FAQs

d i = \frac{2 \cdot t w}{({(\frac{σ t + ((1 - (𝛎) \cdot P i))}{σ t - ((1 + 𝛎) \cdot P i)})}^{0.5}) - 1}

d_i - Inner Diameter of Pressurized Cylinder?t_w - Thickness of Pressurized Cylinder Wall?σ_t - Permissible Tensile Stress in Pressurized Cylinder?𝛎 - Poisson's Ratio of Pressurized Cylinder?P_i - Internal Pressure on Cylinder?

Inner Diameter of Pressurized Cylinder from Bernie's Equation Example

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Here is how the Inner Diameter of Pressurized Cylinder from Bernie's Equation equation looks like with Values.

Here is how the Inner Diameter of Pressurized Cylinder from Bernie's Equation equation looks like with Units.

Here is how the Inner Diameter of Pressurized Cylinder from Bernie's Equation equation looks like.

755.2067 = \frac{2 \cdot 30}{({(\frac{75 + ((1 - (0.3) \cdot 10.2))}{75 - ((1 + 0.3) \cdot 10.2)})}^{0.5}) - 1}

755.2067mm = \frac{2 \cdot 30mm}{({(\frac{75N/mm² + ((1 - (0.3) \cdot 10.2MPa))}{75N/mm² - ((1 + 0.3) \cdot 10.2MPa)})}^{0.5}) - 1}

755.2067 = \frac{2 \cdot 30}{({(\frac{75 + ((1 - (0.3) \cdot 10.2))}{75 - ((1 + 0.3) \cdot 10.2)})}^{0.5}) - 1}

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Inner Diameter of Pressurized Cylinder from Bernie's Equation Solution

Follow our step by step solution on how to calculate Inner Diameter of Pressurized Cylinder from Bernie's Equation?

FIRST Step Consider the formula

d i = \frac{2 \cdot t w}{({(\frac{σ t + ((1 - (𝛎) \cdot P i))}{σ t - ((1 + 𝛎) \cdot P i)})}^{0.5}) - 1}

Next Step Substitute values of Variables

∴

d i = \frac{2 \cdot 30mm}{({(\frac{75N/mm² + ((1 - (0.3) \cdot 10.2MPa))}{75N/mm² - ((1 + 0.3) \cdot 10.2MPa)})}^{0.5}) - 1}

Next Step Convert Units

∴

d i = \frac{2 \cdot 0.03m}{({(\frac{7.5E+7Pa + ((1 - (0.3) \cdot 1E+7Pa))}{7.5E+7Pa - ((1 + 0.3) \cdot 1E+7Pa)})}^{0.5}) - 1}

Next Step Prepare to Evaluate

∴

d i = \frac{2 \cdot 0.03}{({(\frac{7.5E+7 + ((1 - (0.3) \cdot 1E+7))}{7.5E+7 - ((1 + 0.3) \cdot 1E+7)})}^{0.5}) - 1}

Next Step Evaluate

∴

d i = 0.755206674920526m

Next Step Convert to Output's Unit

∴

d i = 755.206674920526mm

LAST Step Rounding Answer

∴

d i = 755.2067mm

Inner Diameter of Pressurized Cylinder from Bernie's Equation Formula Elements

Variables

Inner Diameter of Pressurized Cylinder

Inner diameter of pressurized cylinder is the diameter of the inner circle or the internal surface of a cylinder under pressure.

Symbol: d_i

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Inner Diameter of Pressurized Cylinder

Thickness of Pressurized Cylinder Wall

Thickness of pressurized cylinder wall is the measure of the smallest dimension of a solid figure, here a cylindrical wall.

Symbol: t_w

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Thickness of Pressurized Cylinder Wall

Permissible Tensile Stress in Pressurized Cylinder

Permissible Tensile stress in pressurized cylinder is the tensile stress of the stretching force per unit area into the walls of the cylinder.

Symbol: σ_t

Measurement: StressUnit: N/mm²

Note: Value should be greater than 0.

Formulas to find Permissible Tensile Stress in Pressurized 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.

Symbol: 𝛎

Measurement: NAUnit: Unitless

Note: Value should be between -1 to 0.5.

Formulas to find Poisson's Ratio of Pressurized Cylinder

Internal Pressure on Cylinder

Internal pressure on cylinder is the amount of pressure of force per unit area acting onto the internal surface of a cylinder.

Symbol: P_i

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Internal Pressure on Cylinder

Other Formulas to find Inner Diameter of Pressurized Cylinder

Go Inner Diameter of Pressurized Cylinder from Clavarino's Equation

d i = \frac{2 \cdot t w}{({(\frac{σ t + ((1 - (2 \cdot 𝛎) \cdot P i))}{σ t - ((1 + 𝛎) \cdot P i)})}^{0.5}) - 1}

Other formulas in Bernie's and Clavarino's Equation category

Go Thickness of Pressurized Cylinder from Clavarino's Equation

t w = (\frac{d i}{2}) \cdot (({(\frac{σ t + ((1 - (2 \cdot 𝛎) \cdot P i))}{σ t - ((1 + 𝛎) \cdot P i)})}^{0.5}) - 1)

Go Thickness of Pressurized Cylinder from Bernie's Equation

t w = (\frac{d i}{2}) \cdot (({(\frac{σ t + ((1 - (𝛎) \cdot P i))}{σ t - ((1 + 𝛎) \cdot P i)})}^{0.5}) - 1)

How to Evaluate Inner Diameter of Pressurized Cylinder from Bernie's Equation?

Inner Diameter of Pressurized Cylinder from Bernie's Equation evaluator 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 evaluate 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 evaluate Inner Diameter of Pressurized Cylinder from Bernie's Equation using this online evaluator? To use this online evaluator 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.

FAQs on Inner Diameter of Pressurized Cylinder from Bernie's Equation

What is the formula to find Inner Diameter of Pressurized Cylinder from Bernie's Equation?

The formula of Inner Diameter of Pressurized Cylinder from Bernie's Equation is expressed as 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). Here is an example- 755206.7 = (2*0.03)/((((75000000+((1-(0.3)*10200000)))/(75000000-((1+0.3)*10200000)))^0.5)-1).

How to calculate Inner Diameter of Pressurized Cylinder from Bernie's Equation?

With 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) we can find Inner Diameter of Pressurized Cylinder from Bernie's Equation using the formula - 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).

What are the other ways to Calculate Inner Diameter of Pressurized Cylinder?

Here are the different ways to Calculate Inner Diameter of Pressurized Cylinder-

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)

Can the Inner Diameter of Pressurized Cylinder from Bernie's Equation be negative?

No, the Inner Diameter of Pressurized Cylinder from Bernie's Equation, measured in Length cannot be negative.

Which unit is used to measure Inner Diameter of Pressurized Cylinder from Bernie's Equation?

Inner Diameter of Pressurized Cylinder from Bernie's Equation is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Inner Diameter of Pressurized Cylinder from Bernie's Equation can be measured.

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Inner Diameter of Pressurized Cylinder from Bernie's Equation Formula

​GoInner Diameter of Pressurized Cylinder from Clavarino's Equation Formula

Inner Diameter of Pressurized Cylinder from Bernie's Equation Example

Inner Diameter of Pressurized Cylinder from Bernie's Equation Solution

Inner Diameter of Pressurized Cylinder from Bernie's Equation Formula Elements

Other Formulas to find Inner Diameter of Pressurized Cylinder

Other formulas in Bernie's and Clavarino's Equation category

How to Evaluate Inner Diameter of Pressurized Cylinder from Bernie's Equation?

FAQs on Inner Diameter of Pressurized Cylinder from Bernie's Equation

Variable Name

GoInner Diameter of Pressurized Cylinder from Clavarino's Equation Formula