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

Formula Used:

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

Radial Pressure (P_v):

Pa/m²

Increase in Radius (R_i):

Radius at Junction (r*):

Modulus of Elasticity (E):

Hoop Stress (σ_θ):

Mass Of Shell (M):

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1. What is the Mass Of Compound Cylinder Formula?

The formula calculates the mass of a compound cylinder shell based on radial pressure, increase in radius, radius at junction, modulus of elasticity, and hoop stress. It provides a mechanical engineering approach to determine mass in compound cylinder systems.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: The formula accounts for the relationship between mechanical stresses, material properties, and geometric parameters in compound cylinder systems.

3. Importance of Mass Calculation

Details: Accurate mass calculation is crucial for structural design, material selection, and performance analysis of compound cylinder systems in mechanical engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate units. Ensure radial pressure, increase in radius, radius at junction, and modulus of elasticity are positive values. The denominator must not be zero for a valid result.

5. Frequently Asked Questions (FAQ)

Q1: What is a compound cylinder?
A: A compound cylinder consists of two or more concentric cylinders that are shrink-fitted together to create a system with improved strength and pressure resistance.

Q2: Why is mass calculation important in cylinder design?
A: Mass calculation helps in determining material requirements, structural integrity, and overall system performance in engineering applications.

Q3: What units should be used for input values?
A: Use Pascals per square meter for radial pressure, meters for radius measurements, Pascals for modulus of elasticity and hoop stress.

Q4: What causes division by zero in this calculation?
A: Division by zero occurs when the denominator \(\left(\frac{R_i}{\frac{r^*}{E}}\right) - \sigma_\theta\) equals zero, which indicates a specific mechanical condition in the system.

Q5: Can this formula be used for single cylinders?
A: This specific formula is designed for compound cylinder systems where junction radius and related parameters are relevant.