1. What is the Radius Calculation Formula?

The formula calculates the radius of a cylindrical shell using Lame's equation constants and radial pressure. It provides the radius value 'x' for an inner cylinder given the radial pressure at that radius.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( r_{cylindrical\ shell} \) — Radius of cylindrical shell (m)
• \( b_2 \) — Constant 'b' for inner cylinder
• \( P_v \) — Radial pressure (Pascal/m²)
• \( a_2 \) — Constant 'a' for inner cylinder

Explanation: The formula calculates the radius where the radial pressure equals the given value, using the material constants from Lame's equation.

3. Importance of Radius Calculation

Details: Accurate radius calculation is crucial for pressure vessel design, stress analysis, and ensuring structural integrity in cylindrical components under internal or external pressure.

4. Using the Calculator

Tips: Enter the constant 'b' for inner cylinder, radial pressure value, and constant 'a' for inner cylinder. All values must be valid (b₂ > 0, Pᵥ ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What are Lame's constants?
A: Lame's constants (a and b) are material-specific parameters used in the analysis of thick-walled cylinders under pressure.

Q2: When is this formula applicable?
A: This formula applies to thick-walled cylindrical pressure vessels where the radial pressure distribution follows Lame's theory.

Q3: What units should be used?
A: Use consistent units - meters for radius, Pascal per square meter for pressure, and appropriate units for the constants.

Q4: Are there limitations to this equation?
A: The formula assumes homogeneous, isotropic material and applies to cylindrical shells with uniform wall thickness.

Q5: How are the constants determined?
A: The constants are typically determined from boundary conditions and material properties of the specific cylindrical component.