Decrease In Outer Radius Of Inner Cylinder At Junction Of Compound Cylinder Calculator

Formula Used:

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

Radius at Junction (r*):

Modulus of Elasticity (E):

Hoop Stress (σ_θ):

Radial Pressure (P_v):

Pa/m²

Mass of Shell (M):

Decrease in Radius (Rd):

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1. What is Decrease in Outer Radius?

The decrease in outer radius of inner cylinder at junction of compound cylinder refers to the reduction in the outer radius of the inner cylinder when subjected to internal pressure and stress conditions in a compound cylinder configuration.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( Rd \) — Decrease in radius (m)
\( r^* \) — Radius at junction (m)
\( E \) — Modulus of elasticity (Pa)
\( \sigma_{\theta} \) — Hoop stress on thick shell (Pa)
\( P_v \) — Radial pressure (Pa/m²)
\( M \) — Mass of shell (kg)

Explanation: This formula calculates the reduction in outer radius of the inner cylinder at the junction point of compound cylinders, considering material properties and stress conditions.

3. Importance of Radius Decrease Calculation

Details: Accurate calculation of radius decrease is crucial for designing compound cylinders, ensuring proper fit and interference, and predicting deformation under pressure conditions in mechanical engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (meters for lengths, Pascals for stresses and pressures, kilograms for mass). Ensure all values are positive and non-zero for accurate calculations.

5. Frequently Asked Questions (FAQ)

Q1: What is a compound cylinder?
A: A compound cylinder consists of two or more concentric cylinders assembled with interference fits to withstand higher internal pressures than single cylinders.

Q2: Why is radius decrease important in compound cylinders?
A: Radius decrease calculations help determine the interference fit required and predict how the cylinders will behave under operational pressures.

Q3: What factors affect the decrease in radius?
A: Material properties (modulus of elasticity), geometric dimensions, applied pressures, and stress conditions all influence the radius decrease.

Q4: How accurate is this calculation?
A: The calculation provides theoretical values based on elastic deformation assumptions. Actual results may vary due to material imperfections and other factors.

Q5: Can this formula be used for other cylinder configurations?
A: This specific formula is designed for compound cylinders at their junction points. Different configurations may require modified formulas.