Pressure End-Thrust Reference

Concise reference for pressure end thrust at closures, bends, reducers and expansion joints.

Pressure & Containment3 min read

pressurereferenceend thrustpressure thrustbendreducer

End thrust formulae

Closed end / blind flange:  F = p * pi * r^2
90-degree bend:              F = p * A * sqrt(2)  (at 45 deg)
Reducer:                     F = p * (A_large - A_small)
Tee (branch):                F = p * A_branch  (on branch)

where:
  F = pressure thrust [N]
  p = internal pressure [MPa]
  r = internal radius [mm]
  A = internal cross-sectional area [mm^2]

Notes

Pressure thrust at bends is a static force from the pressure acting on the curved wall
Fluid momentum forces must be added separately if flow velocity is significant
Expansion joints and bellows cannot carry pressure thrust — external anchoring required
All thrust forces must be reacted by supports, anchors or the vessel structure