API 526 standard orifices
Effective areas for preliminary sizing. The final valve uses the maker's actual (certified) area and coefficient, which can differ.
Equations used
P1 = set pressure × (1 + overpressure) + atmospheric (absolute)
Gas, critical (P2/P1 ≤ (2/(k+1))^(k/(k−1))): A = W/(C·Kd·P1·Kb·Kc)·√(T·Z/M), C = 520·√(k·(2/(k+1))^((k+1)/(k−1)))
Gas, subcritical: A = W/(735·F2·Kd·Kc)·√(Z·T/(M·P1·(P1 − P2))), F2 = √[(k/(k−1))·r^(2/k)·(1 − r^((k−1)/k))/(1 − r)], r = P2/P1
Steam: gas equation with real-steam k, Z and M from IAPWS-IF97 at P1 and T
Liquid: A = Q/(38·Kd·Kw·Kc·Kv)·√(G/(P1 − P2)), Kv = 1/(0.9935 + 2.878/Re^0.5 + 342.75/Re^1.5), Re = 2800·Q·G/(μ·√A)
(USCS inside: W lb/h, Q US gpm, A in², P psia, T °R)
Public form of the API 520 Part I sizing equations, for a first-pass check only. Relief valve sizing is a safety decision: the final design must follow the current API 520 / ASME code, the relief load study and the valve maker's certified data, and be checked by a competent engineer.