1. What Is The Constant 'b' For Outer Cylinder Given Outer Radius Of Cylinder?

The constant 'b' for outer cylinder is defined as the constant used in Lame's equation for thick-walled cylinders under pressure. It is calculated based on the constant 'a' and the outer radius of the cylinder.

2. How Does The Calculator Work?

The calculator uses the formula:

Where:

• \( b_1 \) — Constant 'b' for outer cylinder (unitless)
• \( a_1 \) — Constant 'a' for outer cylinder (unitless)
• \( r_2 \) — Outer radius of cylinder (m)

Explanation: This formula calculates the constant 'b' by multiplying constant 'a' with the square of the outer radius of the cylinder.

3. Importance Of Constant 'b' Calculation

Details: Accurate calculation of constant 'b' is crucial for solving Lame's equations in thick-walled cylinder analysis, which is essential for determining stress distributions in pressurized cylindrical structures.

4. Using The Calculator

Tips: Enter constant 'a' for outer cylinder (must be > 0) and outer radius of cylinder in meters (must be > 0). The calculator will compute constant 'b' for the outer cylinder.

5. Frequently Asked Questions (FAQ)

Q1: What is Lame's equation used for?
A: Lame's equation is used to calculate stresses in thick-walled cylinders subjected to internal and/or external pressure.

Q2: What are typical values for constant 'a'?
A: Constant 'a' values vary depending on the specific cylinder geometry and loading conditions, but are typically positive values.

Q3: Why is the outer radius squared in the formula?
A: The squaring of the radius comes from the mathematical derivation of Lame's equations for thick-walled cylinders under pressure.

Q4: Can this formula be used for thin-walled cylinders?
A: No, this formula is specifically for thick-walled cylinders where radial stress variations are significant.

Q5: What units should be used for the inputs?
A: Constant 'a' is unitless, while outer radius should be in meters (m) for consistent SI units.