Steam Boiler Stress

Overview

Engineering reference data for Steam Boiler Stress in steam condensate.

Key Formulas

Steam Quality

$x = \frac{m_v}{m_{total}}$

Mass fraction of vapor in two-phase mixture.

Enthalpy of Wet Steam

$h = h_f + x \cdot h_{fg}$

Specific enthalpy of wet steam.

Flash Steam

$m_{flash} = m_{liquid} \frac{h_f - h_{f2}}{h_{fg2}}$

Steam generated when condensate flashes to lower pressure.

Condensate Load

$m_c = \frac{Q}{h_{fg}}$

Condensate generated by heat transfer.

Variables

Symbol	Description	Unit
$x$	Steam quality	—
$h_f$	Enthalpy of saturated liquid	kJ/kg
$h_{fg}$	Latent heat of vaporization	kJ/kg
$h$	Specific enthalpy	kJ/kg
$Q$	Heat transfer rate	kW

Hoop Stress Derivation & Application

The hoop stress (circumferential stress) formula for a thin-walled cylindrical pressure vessel like a steam boiler shell is a fundamental equation in mechanical engineering. It can be derived from a static equilibrium analysis of a half-cylinder section.

Derivation Principle: For a cylindrical shell of internal diameter $D$, thickness $t$, and internal pressure $P$:

1. The total force acting on the projected area (the rectangular section of the half-cylinder) is $F = P \times D \times L$ (where $L$ is the length of the cylinder segment).
2. This force is resisted by the tensile hoop stress $\sigma$ acting over the two rectangular cross-section areas of the shell wall: $A = 2 \times (t \times L)$.
3. Equating force to resistance: $P \cdot D \cdot L = \sigma \cdot (2 \cdot t \cdot L)$.
4. Simplifying yields the core formula: $\sigma = \frac{P \cdot D}{2t}$

Key Applications & Limitations:

• Design Criterion: This stress is the primary parameter used to size the shell thickness $t$ to ensure it remains below the material's allowable stress.
• Thin-Wall Assumption: The formula is valid for "thin-walled" vessels, typically defined as $D/t > 20$. For thicker vessels, more complex formulas (Lamé's equations) must be used to account for the stress variation across the wall thickness.
• Stress State: This is the principal (largest) stress in the boiler shell. Longitudinal (axial) stress is generally half this value ($\sigma_{long} = PD/4t$).

References

• Original Source