Longitudinal Stress In Thin Cylinder Given Internal Pressure Calculator

Formula Used:

\[ \sigma_l = \frac{P_i \times d_i}{4 \times t_w} \]

Internal Pressure On Cylinder (P_i):

Inner Diameter Of Pressurized Cylinder (d_i):

Thickness Of Pressurized Cylinder Wall (t_w):

Longitudinal Stress In Pressurized Cylinder (σ_l):

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1. What Is Longitudinal Stress In Pressurized Cylinder?

Longitudinal stress in pressurized cylinder is defined as the stress produced in curved surface of a cylinder parallel to central axis subjected to internal pressure. It represents the axial stress component in thin-walled pressure vessels.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ \sigma_l = \frac{P_i \times d_i}{4 \times t_w} \]

Where:

\( \sigma_l \) — Longitudinal stress in pressurized cylinder (Pa)
\( P_i \) — Internal pressure on cylinder (Pa)
\( d_i \) — Inner diameter of pressurized cylinder (m)
\( t_w \) — Thickness of pressurized cylinder wall (m)

Explanation: This formula calculates the axial stress component in thin-walled cylindrical pressure vessels subjected to internal pressure.

3. Importance Of Longitudinal Stress Calculation

Details: Calculating longitudinal stress is crucial for designing pressure vessels, piping systems, and cylindrical containers to ensure structural integrity and prevent failure under internal pressure.

4. Using The Calculator

Tips: Enter internal pressure in pascals (Pa), inner diameter in meters (m), and wall thickness in meters (m). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between longitudinal and hoop stress?
A: Longitudinal stress acts parallel to the cylinder axis, while hoop stress acts circumferentially around the cylinder. Hoop stress is typically twice the longitudinal stress.

Q2: When is this formula valid?
A: This formula is valid for thin-walled cylinders where the wall thickness is less than about 1/10 of the cylinder diameter.

Q3: What units should be used for input values?
A: Pressure should be in pascals (Pa), dimensions in meters (m). Consistent SI units must be used for accurate results.

Q4: How does wall thickness affect longitudinal stress?
A: Longitudinal stress decreases as wall thickness increases, following an inverse relationship as shown in the formula.

Q5: Can this formula be used for thick-walled cylinders?
A: No, this formula is specifically for thin-walled cylinders. Thick-walled cylinders require more complex formulas that account for radial stress variations.