Internal Pressure In Thick Cylinder Given Tangential Stress Calculator

Formula Used:

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

Tangential Stress (σ_tang):

Inner Diameter (d_i):

Outer Diameter (d_o):

Radius (r):

Internal Pressure (P_i):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Internal Pressure in Thick Cylinder?

Internal pressure in a thick cylinder refers to the pressure exerted by a fluid or gas on the inner surface of a cylindrical vessel with significant wall thickness. This calculation is crucial for designing pressure vessels, pipes, and other cylindrical containers that must withstand internal pressure forces.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( P_i \) — Internal pressure on cylinder (Pa)
\( \sigma_{tang} \) — Tangential stress in pressurized cylinder (Pa)
\( d_i \) — Inner diameter of pressurized cylinder (m)
\( d_o \) — Outer diameter of pressurized cylinder (m)
\( r \) — Radius of pressurized cylinder (m)

Explanation: This formula calculates the internal pressure that would produce a given tangential stress in a thick-walled cylinder, accounting for the geometry and material properties.

3. Importance of Internal Pressure Calculation

Details: Accurate calculation of internal pressure is essential for designing safe and efficient pressure vessels, ensuring structural integrity, preventing failures, and meeting industry standards and regulations.

4. Using the Calculator

Tips: Enter tangential stress in Pascals, inner and outer diameters in meters, and radius in meters. All values must be positive and the outer diameter must be greater than the inner diameter.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between thick and thin wall cylinders?
A: Thick wall cylinders have a wall thickness greater than 1/10 of the inner radius, requiring more complex stress analysis than thin wall cylinders.

Q2: Why is tangential stress important in cylinder design?
A: Tangential stress (hoop stress) is typically the highest stress in pressurized cylinders and often determines the failure point of the vessel.

Q3: What safety factors should be considered?
A: Engineering designs typically include safety factors of 2-4 times the calculated stress values to account for material variations and unexpected loads.

Q4: Can this formula be used for all materials?
A: This formula assumes isotropic, homogeneous material behavior and is most accurate for materials with linear elastic properties.

Q5: How does temperature affect the calculation?
A: Temperature changes can affect material properties and induce thermal stresses, which should be considered separately in comprehensive designs.