Inner Radius Of Compound Cylinder Given Internal Fluid Pressure Calculator

Formula Used:

\[ \text{Inner Radius of Cylinder} = \sqrt{\frac{\text{Constant B for Single Thick Shell}}{\text{Internal Pressure} + \text{Constant A for single thick shell}}} \] \[ r_1 = \sqrt{\frac{B}{P_i + A}} \]

Inner Radius of Cylinder:

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1. What is the Inner Radius Calculation?

The inner radius calculation for a compound cylinder under internal fluid pressure determines the internal dimension of the cylinder based on material constants and applied pressure. This is crucial for designing pressure vessels and cylindrical containers.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r_1 = \sqrt{\frac{B}{P_i + A}} \]

Where:

\( r_1 \) — Inner radius of cylinder (m)
\( B \) — Constant B for single thick shell
\( P_i \) — Internal pressure (Pa)
\( A \) — Constant A for single thick shell

Explanation: The formula calculates the inner radius by considering the material properties (constants A and B) and the internal pressure applied to the cylinder.

3. Importance of Inner Radius Calculation

Details: Accurate calculation of inner radius is essential for pressure vessel design, ensuring structural integrity under internal pressure, and determining appropriate wall thickness for safety and efficiency.

4. Using the Calculator

Tips: Enter Constant B, Internal Pressure in Pascals, and Constant A. All values must be valid (Constant B > 0, Internal Pressure ≥ 0).

5. Frequently Asked Questions (FAQ)

Q1: What are constants A and B in the formula?
A: Constants A and B are material-specific parameters derived from Lame's equations that account for the mechanical properties and behavior of the cylinder material under pressure.

Q2: Why is the inner radius important in cylinder design?
A: The inner radius determines the internal volume capacity and affects stress distribution within the cylinder walls under internal pressure.

Q3: What units should be used for input values?
A: Internal pressure should be in Pascals (Pa), while constants A and B are dimensionless but must be consistent with the pressure units used.

Q4: Can this formula be used for thin-walled cylinders?
A: This formula is specifically derived for thick-walled cylinders. For thin-walled cylinders, different simplified formulas are typically used.

Q5: What factors affect the accuracy of this calculation?
A: Material homogeneity, temperature effects, and accurate determination of constants A and B are critical factors affecting calculation accuracy.