Radial Pressure Given Increase In Inner Radius Of Outer Cylinder Calculator

Formula Used:

\[ P_v = \left( \frac{R_i}{r^*/E} - \sigma_\theta \right) \times M \]

Increase in Radius (Ri):

Radius at Junction (r*):

Modulus of Elasticity (E):

Hoop Stress (σθ):

Mass of Shell (M):

Radial Pressure (Pv):

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1. What is Radial Pressure?

Radial pressure is pressure towards or away from the central axis of a component. In the context of compound cylinders, it represents the pressure at the junction between inner and outer cylinders.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_v = \left( \frac{R_i}{r^*/E} - \sigma_\theta \right) \times M \]

Where:

\( P_v \) — Radial Pressure (Pa/m²)
\( R_i \) — Increase in radius (m)
\( r^* \) — Radius at junction (m)
\( E \) — Modulus of Elasticity (Pa)
\( \sigma_\theta \) — Hoop Stress (Pa)
\( M \) — Mass of Shell (kg)

Explanation: This formula calculates radial pressure based on the increase in inner radius of the outer cylinder, accounting for material properties and stress conditions.

3. Importance of Radial Pressure Calculation

Details: Accurate calculation of radial pressure is crucial for designing compound cylinders, ensuring structural integrity, and preventing failure at the junction between cylinders.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, Pascals for stress and modulus, kilograms for mass). Ensure all values are positive and valid for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of radial pressure in compound cylinders?
A: Radial pressure determines the interfacial pressure between concentric cylinders, which affects stress distribution and overall structural performance.

Q2: How does modulus of elasticity affect radial pressure?
A: Higher modulus of elasticity typically results in lower radial pressure for the same dimensional changes, as stiffer materials resist deformation more effectively.

Q3: What are typical applications of this calculation?
A: This calculation is used in pressure vessel design, hydraulic systems, and any application involving compound cylindrical structures.

Q4: How does hoop stress influence radial pressure?
A: Higher hoop stress generally increases radial pressure, as it represents the circumferential stress that contributes to the radial deformation.

Q5: What units should be used for accurate results?
A: Use consistent SI units: meters for lengths, Pascals for stress and modulus, and kilograms for mass to ensure dimensional consistency.