อัปเดต 2026-09-07

Thermal / Hydraulic Expansion Relief

API STD 521 §4.4.13

Sizes relief for a blocked-in, liquid-full line or vessel heated by an external source (solar, a leaking blocked heat exchanger, or fire/ambient exposure). The required relief flow is tiny, but a rigid full liquid line generates enormous pressure per °C of rise without a relief path — the canonical API 521 teaching point is that the smallest standard orifice (letter D) is still the correct spec.

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Computes heat input H from whichever source applies (solar / exchanger cross-heat / fire), then converts H to a required volumetric relief rate via the closed-form liquid thermal-expansion equation, then hands that flow to the SAME liquid-orifice sizing function reliefValve.ts uses (no re-derivation — thermal expansion is just a liquid relief case with a different flow source).

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Thermal-expansion relief rate, API 521 §4.4.13

Q = \frac{β H}{ρ _{w a t er} G C _{p}}

β = volumetric thermal-expansion coefficient (1/K), H = heat input (W), G = specific gravity, ρ_water = 1000 kg/m³ (SI form of the US Q[gpm]=(B·H)/(500·G·Cp)).

Ambient/fire heat input, API 521 §4.4.13.2.5.2

Q = C \cdot F \cdot A_{w}^{0.82}

C = 43,200 (adequate drainage + firefighting) or 70,900 (conservative default); F = environmental/insulation factor (1.0 bare); A_w = wetted area, m². Imported verbatim from reliefValve.ts's fireCaseHeatInput().

Solar heat input

H = α \cdot I \cdot A_{p r o j}

α = surface absorptivity (clamped to (0,1], ≈0.9 bare steel), I = incident solar flux (design default 1000 W/m²), A_proj = sun-facing projected area.

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