PSV Reaction Force Calculator

Formula overview

US customary throughout, as above. Convert to SI for the support design after the force is found: 1 lbf = 4.448 N.

API 520 Part II, para 4.4 — open discharge:

  F = (W/366) · √( k·T / ((k+1)·M) )  +  A·P
  F_design = F · DLF

US units as the equation is defined: W in lb/hr, T in °R, A in in²,
P in psig, F in lbf. The first term is momentum, the second is the
pressure acting on the outlet area.

Worked example

Steam relief to atmosphere: W = 5 000 lb/hr, k = 1.3, T = 800 °R,
M = 18, outlet area A = 0.785 in², outlet pressure P = 20 psig,
dynamic load factor 2.0

F_momentum = (5 000/366) × √(1.3 × 800 / (2.3 × 18))
           = 13.66 × √25.1 = 13.66 × 5.01 = 68.5 lbf
F_pressure = 0.785 × 20 = 15.7 lbf
F          = 84.2 lbf  (375 N)
F_design   = 84.2 × 2.0 = 168 lbf  (750 N)

Common mistakes

• Omitting the dynamic load factor. The valve opens in milliseconds, so the load is a step input on the support. A factor of 2 is the classical bound for a suddenly applied load, and using the steady force alone under-designs the support.
• Forgetting the moment as well as the force. On an elbowed tailpipe the reaction acts at the outlet, some distance from the valve, so it applies a bending moment to the valve body and the inlet nozzle — which is often the governing check rather than the force itself.
• Applying open-discharge equations to a closed system. A valve piped into a closed relief header has a different load path; the reaction is reacted internally, and the header's own transient response is the concern instead.

FAQ