External Pressure Acting On Thick Cylinder Given Tangential Stress Calculator

Formula Used:

\[ P_o = \frac{\sigma_{tang}}{\left(\frac{d_o^2}{d_o^2 - d_i^2}\right) \times \left(\frac{d_i^2}{4 \times r^2} + 1\right)} \]

Tangential Stress In Pressurized Cylinder (σ_tang):

Pascal

Outer Diameter Of Pressurized Cylinder (d_o):

Meter

Inner Diameter Of Pressurized Cylinder (d_i):

Meter

Radius Of Pressurized Cylinder (r):

Meter

External Pressure On Cylinder (P_o):

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1. What Is The External Pressure On Cylinder Formula?

The formula calculates the external pressure acting on a thick-walled cylinder based on tangential stress and geometric parameters. It's derived from Lame's equations for thick-walled cylinders under pressure.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ P_o = \frac{\sigma_{tang}}{\left(\frac{d_o^2}{d_o^2 - d_i^2}\right) \times \left(\frac{d_i^2}{4 \times r^2} + 1\right)} \]

Where:

\( P_o \) — External pressure on cylinder (Pascal)
\( \sigma_{tang} \) — Tangential stress in pressurized cylinder (Pascal)
\( d_o \) — Outer diameter of pressurized cylinder (Meter)
\( d_i \) — Inner diameter of pressurized cylinder (Meter)
\( r \) — Radius of pressurized cylinder (Meter)

Explanation: The formula relates external pressure to the tangential stress developed in the cylinder wall, accounting for the cylinder's geometry.

3. Importance Of External Pressure Calculation

Details: Calculating external pressure is crucial for designing pressure vessels, pipelines, and cylindrical structures to ensure they can withstand external loading without failure.

4. Using The Calculator

Tips: Enter all values in consistent units (Pascal for stress, Meter for dimensions). Ensure outer diameter is greater than inner diameter, and all values are positive.

5. Frequently Asked Questions (FAQ)

Q1: What is tangential stress in a cylinder?
A: Tangential stress (hoop stress) is the stress acting circumferentially around the cylinder, perpendicular to the longitudinal axis.

Q2: When is this formula applicable?
A: This formula applies to thick-walled cylinders with uniform external pressure and homogeneous, isotropic material properties.

Q3: What are the limitations of this formula?
A: The formula assumes elastic behavior, constant material properties, and doesn't account for end effects or non-uniform pressure distribution.

Q4: How does cylinder thickness affect the result?
A: Thicker cylinders (larger difference between outer and inner diameters) generally require higher external pressure to produce the same tangential stress.

Q5: Can this be used for internal pressure calculations?
A: No, this specific formula is designed for external pressure calculations. Different formulas apply for internal pressure scenarios.