Internal Pressure In Thick Cylinder Given Radial Stress Calculator

Formula Used:

\[ P_i = \frac{\sigma_r}{\left(\frac{d_i^2}{d_o^2 - d_i^2}\right) \times \left(\frac{d_o^2}{4 \times r^2} + 1\right)} \]

Radial Stress in Pressurized Cylinder (σr):

Inner Diameter of Pressurized Cylinder (di):

Outer Diameter of Pressurized Cylinder (do):

Radius of Pressurized Cylinder (r):

Internal Pressure on Cylinder (Pi):

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1. What is the Internal Pressure in Thick Cylinder Formula?

The formula calculates the internal pressure on a thick-walled cylinder based on radial stress, inner and outer diameters, and radius. It's derived from Lame's equations for thick-walled cylinders under internal pressure.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_i = \frac{\sigma_r}{\left(\frac{d_i^2}{d_o^2 - d_i^2}\right) \times \left(\frac{d_o^2}{4 \times r^2} + 1\right)} \]

Where:

\( P_i \) — Internal pressure on cylinder (Pa)
\( \sigma_r \) — Radial stress in pressurized cylinder (Pa)
\( d_i \) — Inner diameter of pressurized cylinder (m)
\( d_o \) — Outer diameter of pressurized cylinder (m)
\( r \) — Radius of pressurized cylinder (m)

Explanation: The formula relates internal pressure to radial stress through geometric parameters of the cylinder, accounting for the stress distribution in thick-walled pressure vessels.

3. Importance of Internal Pressure Calculation

Details: Accurate calculation of internal pressure is crucial for designing pressure vessels, piping systems, and cylindrical containers to ensure structural integrity and prevent failure under operational conditions.

4. Using the Calculator

Tips: Enter radial stress in Pascals, diameters and radius in meters. All values must be positive and valid (outer diameter > inner diameter > 0, radius > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between thin and thick-walled cylinders?
A: Thin-walled cylinders have wall thickness less than 1/10 of the diameter, while thick-walled cylinders have greater wall thickness requiring different stress analysis approaches.

Q2: When is this formula applicable?
A: This formula applies to thick-walled cylinders with closed ends subjected to internal pressure, assuming homogeneous, isotropic material and elastic behavior.

Q3: What are the limitations of this formula?
A: The formula assumes constant material properties, no external pressures, and may not account for temperature effects or plastic deformation.

Q4: How does radial stress relate to other stresses in cylinders?
A: In pressurized cylinders, three principal stresses exist: radial stress, hoop (circumferential) stress, and longitudinal (axial) stress, each with different distributions.

Q5: Can this formula be used for composite cylinders?
A: For composite or multilayer cylinders, more complex analysis is needed as the formula assumes homogeneous material properties throughout the cylinder wall.