Steam PRV Orifice Area for a Required Capacity (Napier)
The inverse of the steam-PRV tile: the orifice / seat area a required relief capacity needs, A = W / (51.43 x Cd x P1) from the choked Napier form. A 5,000 lb/hr relief at 100 psia and Cd 0.9 wants about 1.08 in^2 - round up to a standard API 526 orifice letter. Assumes choked flow (P2 < 0.58 x P1); saturated steam. A sizing aid, not a relief-valve certification; ASME/API and the valve maker govern.
Formula and source
required_area_in2 = required_capacity_lb_hr / (51.43 x discharge_coeff x upstream_p_psia), the inverse of the choked Napier capacity W = 51.43 x Cd x A x P1; choke_threshold = 0.58 x upstream_p_psia.
Napier's formula / ASME/API 520 choked steam capacity, solved for the orifice area, by name.
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