Internal Pressure In Thick Cylinder Given Longitudinal Stress Calculator

Formula Used:

\[ P_i = \sigma_l \times \frac{(d_o^2 - d_i^2)}{d_i^2} \]

Internal Pressure (Pi):

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The formula calculates the internal pressure in a thick-walled cylinder based on longitudinal stress and cylinder dimensions. It's derived from the relationship between stress and pressure in cylindrical pressure vessels.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_i = \sigma_l \times \frac{(d_o^2 - d_i^2)}{d_i^2} \]

Where:

\( P_i \) — Internal pressure on cylinder (Pa)
\( \sigma_l \) — Longitudinal stress in pressurized cylinder (Pa)
\( d_o \) — Outer diameter of pressurized cylinder (m)
\( d_i \) — Inner diameter of pressurized cylinder (m)

Explanation: The formula relates the internal pressure to the longitudinal stress and the geometric properties of the cylinder, specifically the difference between outer and inner diameters squared.

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 safety under operating conditions.

4. Using the Calculator

Tips: Enter longitudinal stress in Pascals, outer and inner diameters in meters. All values must be positive and inner diameter must be smaller than outer diameter.

5. Frequently Asked Questions (FAQ)

Q1: What is a thick-walled cylinder?
A: A thick-walled cylinder is one where the wall thickness is significant compared to the diameter, requiring different stress analysis than thin-walled cylinders.

Q2: When is this formula applicable?
A: This formula is applicable for thick-walled cylinders subjected to internal pressure where longitudinal stress is known or can be calculated.

Q3: What are typical units for these calculations?
A: Stress and pressure are typically measured in Pascals (Pa) or MPa, while diameters are measured in meters (m) or millimeters (mm).

Q4: Are there limitations to this formula?
A: This formula assumes homogeneous material properties, uniform wall thickness, and elastic behavior under loading conditions.

Q5: How does this differ from thin-walled cylinder formulas?
A: Thin-walled cylinder formulas assume uniform stress distribution through the wall thickness, while thick-walled formulas account for stress variation across the wall.