1 · Design inputs

NPS 6 discharge nozzle on an API 610 centrifugal pump. The flexibility model delivers Fx 100, Fy 200, Fz 200 lbf and Mx 300, My 400, Mz 0 ft·lb. The allowables read from the governing standard's table for that nozzle size are 400 lbf on each force component and 600 ft·lb on each moment component.

2 · Method

The check is a per-component unity ratio. Every component is tested independently against its own allowable, and the largest ratio governs the result:

r_i = |applied_i| / allowable_i   for i = F_x, F_y, F_z, M_x, M_y, M_z

r_max = max(r_i)     governing = the i that produced r_max

F_R = √(F_x² + F_y² + F_z²)     M_R = √(M_x² + M_y² + M_z²)

status = PASS if r_max ≤ 1, otherwise FAIL

where applied_i is the load component transmitted by the piping to the nozzle, taken from the flexibility model in the axis system the equipment standard defines, and allowable_i is the limit for that component at that nozzle size, read from the governing standard's table or the vendor datasheet. The absolute value is taken, so a sign convention error in the model will not be caught here. F_R and M_R are the vector resultants of the applied loads, reported for the record — they are not compared against any allowable, because most standards limit components (and combinations), not the bare resultant. Ratios are reported to five decimals, resultants to two. A zero or negative allowable is rejected rather than silently divided by.

3 · Calculation

1. Resultant force: F_R = √(100² + 200² + 200²) = √(10,000 + 40,000 + 40,000) = √90,000 = 300 lbf.
2. Resultant moment: M_R = √(300² + 400² + 0²) = √(90,000 + 160,000 + 0) = √250,000 = 500 ft·lb.
3. Force ratios: F_x 100/400 = 0.25; F_y 200/400 = 0.50; F_z 200/400 = 0.50.
4. Moment ratios: M_x 300/600 = 0.50; M_y 400/600 = 0.66667; M_z 0/600 = 0.
5. Largest of the six: 0.66667 at M_y. Since r_max ≤ 1, every component is inside its allowable and the check returns PASS.
6. Note what was not compared: F_R = 300 lbf and M_R = 500 ft·lb are reported for the record only — no resultant allowable is applied, and the API 610 combined criteria are a separate check.

4 · Results PASS

5 · Verification statement

The result values above are locked as fixture nozzle-load-check.json, case “API 610 style, all components within allowables -> pass”, tolerance 0.00001, in the calc-core continuous verification gate (see https://pipingtoolset.com/trust/validation.html). Allowable-stress and factor data are user-supplied inputs; citations: API 610 / ISO 13709, Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries — §5.4 nozzle loadings and Annex F allowable-load criteria; table values user-supplied, not embedded. · NEMA SM 23, Steam Turbines for Mechanical Drive Service — §8.4 nozzle load limits, including the combined-resultant criterion evaluated by the separate combined-index calculator. · API 650, Welded Tanks for Oil Storage — Annex P, loads on shell openings; API 620 for low-pressure storage tanks. · API 560 (fired heaters), API 660 (shell-and-tube heat exchangers) and API 661 (air-cooled heat exchangers) — nozzle loading clauses; allowables per the standard or the purchased datasheet. · ASME B31.3, Process Piping — ¶319.4.4, flexibility analysis. Reactions on connected equipment are judged against the equipment standard's limits, not against B31.3 stress allowables.