Pipes Temperature Stress

Overview

Engineering reference data for Pipes Temperature Stress in piping systems.

Key Formulas

Continuity

$A_1 v_1 = A_2 v_2$

Mass conservation in pipe flow.

Pressure Drop

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Darcy-Weisbach equation.

Pipe Area

$A = \frac{\pi D^2}{4}$

Cross-sectional area of a pipe.

Variables

Example Calculation

For a carbon steel pipe with linear expansion coefficient $\alpha = 11.7 \times 10^{-6} \, \text{m/m}^\circ\text{C}$ and modulus of elasticity $E = 203 \, \text{GPa}$ (or $203 \times 10^9 \, \text{Pa}$), heated from $0^\circ\text{C}$ to $50^\circ\text{C}$, the thermal stress is calculated as:

$$\sigma = \alpha E \Delta T = (11.7 \times 10^{-6} \, \text{m/m}^\circ\text{C}) \times (203 \times 10^9 \, \text{Pa}) \times (50^\circ\text{C}) = 119 \times 10^6 \, \text{Pa} = 119 \, \text{MPa}$$

This result indicates the stress introduced in the fixed pipe due to thermal expansion. Depending on the material grade and applicable engineering codes (e.g., ASME B31.3), this stress may be within the maximum allowable limit.

Design Considerations

• Maximum Allowable Stress: The computed stress $\sigma$ must not exceed the material's maximum allowable stress specified by relevant design codes and standards.
• Fatigue Risk: Repeated temperature cycles, even with stresses below the allowable limit, can lead to fatigue failure over time. For applications with frequent thermal cycling, a fatigue analysis is recommended to ensure long-term integrity.

References

• Original Source