Internal Fluid Pressure In Vessel Given Hoop Stress And Efficiency Of Longitudinal Joint Calculator

Formula Used:

\[ P_i = \frac{\sigma_\theta \times 2 \times t \times \eta_l}{D_i} \]

Hoop Stress in Thin shell (σθ):

Pascal

Thickness Of Thin Shell (t):

Meter

Efficiency of Longitudinal Joint (ηl):

Inner Diameter of Cylinderical Vessel (Di):

Meter

Internal Pressure in thin shell (Pi):

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1. What is the Internal Fluid Pressure Formula?

The formula calculates the internal pressure in a thin-walled cylindrical vessel based on hoop stress, thickness, joint efficiency, and inner diameter. It's essential for pressure vessel design and safety analysis.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_i = \frac{\sigma_\theta \times 2 \times t \times \eta_l}{D_i} \]

Where:

\( P_i \) — Internal Pressure in thin shell (Pascal)
\( \sigma_\theta \) — Hoop Stress in Thin shell (Pascal)
\( t \) — Thickness Of Thin Shell (Meter)
\( \eta_l \) — Efficiency of Longitudinal Joint
\( D_i \) — Inner Diameter of Cylinderical Vessel (Meter)

Explanation: This formula calculates the internal pressure that a thin-walled cylindrical vessel can withstand based on material properties and geometric dimensions.

3. Importance of Internal Pressure Calculation

Details: Accurate pressure calculation is crucial for designing safe pressure vessels, ensuring structural integrity, and preventing catastrophic failures in industrial applications.

4. Using the Calculator

Tips: Enter all values in appropriate units. Hoop stress and thickness must be positive values. Joint efficiency should be between 0 and 1. Inner diameter must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is hoop stress in a cylindrical vessel?
A: Hoop stress is the circumferential stress that develops in the walls of a cylindrical pressure vessel when it's subjected to internal pressure.

Q2: What does joint efficiency represent?
A: Joint efficiency accounts for the strength reduction due to welded joints, typically ranging from 0.6 to 1.0 depending on joint type and inspection.

Q3: When is this formula applicable?
A: This formula is valid for thin-walled pressure vessels where the wall thickness is less than about 1/10 of the radius.

Q4: What are the limitations of this formula?
A: The formula assumes uniform stress distribution and doesn't account for end effects, corrosion allowances, or temperature variations.

Q5: How does wall thickness affect internal pressure capacity?
A: Increasing wall thickness directly increases the vessel's ability to withstand higher internal pressures, as shown in the formula.