Mass Of Compound Cylinder Given Decrease In Outer Radius Of Inner Cylinder Calculator

Formula Used:

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

Radial Pressure (P_v):

Pa/m²

Decrease in Radius (R_d):

Radius at Junction (r*):

Modulus of Elasticity (E):

Hoop Stress (σ_θ):

Mass Of Shell (M):

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1. What is Mass Of Compound Cylinder Given Decrease In Outer Radius Of Inner Cylinder?

This calculation determines the mass of a compound cylinder shell based on radial pressure, decrease in radius, radius at junction, modulus of elasticity, and hoop stress. It's essential for engineering applications involving compound cylindrical structures.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the mass of a compound cylinder shell by considering the relationship between radial pressure, elastic deformation, and material properties.

3. Importance of Mass Calculation

Details: Accurate mass calculation is crucial for structural design, material selection, and stress analysis in engineering applications involving compound cylindrical structures.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure radial pressure, decrease in radius, radius at junction, and modulus of elasticity are positive values. Hoop stress can be positive or negative depending on the stress state.

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 create residual stresses that improve strength and pressure resistance.

Q2: When is this calculation particularly useful?
A: This calculation is essential in pressure vessel design, piping systems, and mechanical engineering applications where compound cylinders are used to withstand high internal pressures.

Q3: What factors affect the mass calculation?
A: The mass depends on material properties (modulus of elasticity), geometric parameters (radii), and stress conditions (radial pressure and hoop stress).

Q4: Are there limitations to this formula?
A: This formula assumes linear elastic material behavior and may not accurately represent materials with non-linear elasticity or plastic deformation.

Q5: How does decrease in radius affect the mass calculation?
A: The decrease in radius represents the deformation of the inner cylinder and directly influences the stress distribution and resulting mass calculation.