Validation
Every build is checked against 96 reference calculations.
The WRC 537 engine behind the calculator is recomputed against the same geometry, loads and pressure run in an established commercial pressure-vessel design package (2026 edition). The comparison runs on every change to the code: a result that moves more than 0.3 % from the reference (or past a documented exception, below) fails the build. This page is generated from that comparison, not written by hand.
96
reference cases
86 / 96
within 0.3 % on both checks
0.005 %
median deviation, Pl + Pb + Q
0.68 %
largest deviation, Pl + Pb + Q
By attachment
| Attachment | Cases | Rm/T or Υ | Pl+Pb+Q median / max | Pl median / max |
|---|---|---|---|---|
| Rectangular clip on a cylinder | 9 | 5.0 – 150.5 | 0.005 % / 0.01 % | 0.003 % / 0.02 % |
| Round nozzle on a cylinder | 50 | 5.5 – 150.5 | 0.003 % / 0.09 % | 0.007 % / 1.48 % |
| Round nozzle on a cone | 14 | 11.8 – 41.8 | 0.005 % / 0.68 % | 0.010 % / 0.96 % |
| Round nozzle on a formed head | 23 | 5.5 – 11.3 | 0.041 % / 0.15 % | 0.009 % / 0.14 % |
Deviations are |engine − reference| / reference on the largest local primary membrane stress (Pl) and the largest combined stress (Pl + Pb + Q) of each table, the two values the acceptance checks use.
What the cases cover
- Rectangular clips on cylinders, with and without a reinforcing pad, including Rm/T below the chart floor.
- Round nozzles on cylinders: design pressure, MAWP, hot shut-down (P = 0) and pressure reversed; pad edges; offset (hillside) nozzles.
- Round nozzles on cones, axis normal to the surface and perpendicular to the vessel axis.
- Round nozzles on ellipsoidal, torispherical and hemispherical heads, radial, hillside and perpendicular.
Every deviation above 0.3 %, explained
All 25 load-only cases (P = 0) agree to within 0.15 %, so the WRC 537 load-stress core matches. The few larger differences sit in the pressure term, in the ASME VIII-2 Part 4.5 pressure stress intensity factor I:
- Cylinder pad edge: the reference applies I slightly above 1 at the pad edge; the engine uses I = 1 there (Pl up to 1.5 % lower).
- Padded offset nozzle: a 1.2 % difference in I (Pl up to 1.1 % lower).
- Cone nozzle with its axis perpendicular to the vessel axis: I is 1.1 % lower (Pl up to 1 % lower).
No combined-stress (Pl + Pb + Q) difference exceeds 0.68 %.
Checks against the bulletin itself
Beside the reference set, the engine's own test suite checks the parts of WRC 537 that have closed forms: shear V/(π·r₀·T) and torsion Mt/(2π·r₀²·T) at a round attachment, the hoop and longitudinal pressure terms, linearity in the loads, and the symmetry of the moment terms between opposite locations. Each intermediate value — γ, β, every figure read and every stress term — is printed in the calculation trace and the report, so any result can be checked by hand against the bulletin.
What is not validated yet
- Nozzles on cones use an equivalent cylinder at the local radius. It is an industry approximation, not a bulletin method, and every cone result says so.
- The diameter-ratio advisories (when WRC 537 stops applying and WRC 297 or FEA should be used) are under engineering review.
- Inclined nozzles and clips on cones are outside the engine's scope; it refuses them rather than guess.
- The shell-element FEA tool is in early access and under its own verification; nothing on this page covers it.
All 96 cases
| # | Attachment | Case | Pl+Pb+Q ref. | engine | Δ | Pl ref. | engine | Δ |
|---|---|---|---|---|---|---|---|---|
| V01 | Rectangular clip on a cylinder | Clip #1 lug edge P=3.712 | 234.3 | 234.3 | 0.002 % | 124.9 | 124.9 | -0.003 % |
| V02 | Rectangular clip on a cylinder | Clip #1 lug edge P=0.7789 | 189.6 | 189.6 | 0.006 % | 129.5 | 129.5 | 0.002 % |
| V03 | Rectangular clip on a cylinder | Clip #1 lug edge P=20.9464 | 522.0 | 522.1 | 0.001 % | 192.0 | 192.0 | 0.002 % |
| V04 | Rectangular clip on a cylinder | Clip #1 lug edge P=7.5192 | 133.2 | 133.2 | -0.006 % | 120.6 | 120.6 | 0.004 % |
| V05 | Rectangular clip on a cylinder | Clip #1 lug edge P=7.5192 | 132.5 | 132.5 | -0.005 % | 115.5 | 115.5 | -0.006 % |
| V06 | Rectangular clip on a cylinder | Clip #1 pad edge P=7.5192 | 133.5 | 133.5 | -0.006 % | 116.4 | 116.4 | -0.002 % |
| V07 | Rectangular clip on a cylinder | Clip #1 lug edge P=7.5192 | 132.5 | 132.5 | -0.005 % | 115.5 | 115.5 | -0.006 % |
| V08 | Rectangular clip on a cylinder | Clip #1 pad edge P=7.5192 | 133.5 | 133.5 | -0.006 % | 116.4 | 116.4 | -0.002 % |
| V09 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=1 | 238.3 | 238.3 | -0.001 % | 119.6 | 119.6 | 0.016 % |
| V10 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=2.0802 | 263.9 | 263.9 | 0.002 % | 207.0 | 207.0 | 0.010 % |
| V11 | Round nozzle on a cylinder | Nozzle #2 (N2) pad edge P=1 | 182.4 | 182.4 | -0.001 % | 53.57 | 53.34 | -0.422 % |
| V12 | Round nozzle on a cylinder | Nozzle #2 (N2) nozzle OD P=1 | 96.27 | 96.27 | 0.001 % | 65.49 | 65.49 | -0.001 % |
| V13 | Round nozzle on a cylinder | Nozzle #2 (N2) pad edge P=3.9243 | 248.0 | 248.0 | -0.002 % | 119.2 | 117.4 | -1.478 % |
| V14 | Round nozzle on a cylinder | Nozzle #2 (N2) nozzle OD P=3.9243 | 221.8 | 221.8 | 0.001 % | 207.0 | 207.0 | 0.004 % |
| V15 | Round nozzle on a cylinder | Nozzle #1 (N1) pad edge P=0.5 | 161.6 | 161.6 | 0.001 % | 93.58 | 93.57 | -0.009 % |
| V16 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=0.5 | 119.9 | 119.9 | -0.004 % | 78.49 | 78.49 | 0.001 % |
| V17 | Round nozzle on a cylinder | Nozzle #1 (N1) pad edge P=0.9163 | 224.0 | 224.0 | -0.002 % | 156.0 | 156.0 | -0.002 % |
| V18 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=0.9163 | 182.1 | 182.1 | -0.003 % | 140.4 | 140.4 | -0.003 % |
| V19 | Round nozzle on a cylinder | Nozzle #2 (N2) nozzle OD P=0.5 | 258.8 | 258.7 | -0.006 % | 135.9 | 135.9 | -0.002 % |
| V20 | Round nozzle on a cylinder | Nozzle #2 (N2) nozzle OD P=0.7789 | 320.6 | 320.6 | 0.002 % | 199.0 | 199.0 | 0.001 % |
| V21 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=0.1 | 115.3 | 115.3 | 0.008 % | 29.68 | 29.67 | -0.028 % |
| V22 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=18.0634 | 246.2 | 245.9 | -0.091 % | 189.3 | 189.0 | -0.123 % |
| V23 | Round nozzle on a cylinder | Nozzle #1 (N1) pad edge P=1 | 43.93 | 43.93 | 0.000 % | 22.62 | 22.62 | 0.006 % |
| V24 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=1 | 42.38 | 42.38 | -0.003 % | 24.90 | 24.90 | 0.005 % |
| V25 | Round nozzle on a cylinder | Nozzle #1 (N1) pad edge P=7.855 | 146.5 | 146.5 | 0.003 % | 125.4 | 125.4 | 0.005 % |
| V26 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=7.855 | 182.2 | 182.2 | 0.002 % | 165.8 | 165.8 | 0.004 % |
| V27 | Round nozzle on a cylinder | Nozzle #10 (N10) nozzle OD P=1 | 202.6 | 202.7 | 0.033 % | 114.0 | 114.1 | 0.061 % |
| V28 | Round nozzle on a cylinder | Nozzle #10 (N10) nozzle OD P=2.0977 | 294.1 | 294.2 | 0.054 % | 207.0 | 207.1 | 0.075 % |
| V29 | Round nozzle on a cylinder | Nozzle #11 (N11) nozzle OD P=1 | 197.0 | 197.0 | 0.002 % | 107.8 | 107.8 | 0.007 % |
| V30 | Round nozzle on a cylinder | Nozzle #11 (N11) nozzle OD P=2.2622 | 294.1 | 294.1 | 0.002 % | 207.0 | 207.0 | 0.003 % |
| V31 | Round nozzle on a cylinder | Nozzle #12 (N12) nozzle OD P=1 | 189.2 | 189.2 | -0.003 % | 91.06 | 91.06 | 0.003 % |
| V32 | Round nozzle on a cylinder | Nozzle #12 (N12) nozzle OD P=2.7272 | 285.1 | 285.1 | -0.001 % | 197.8 | 197.8 | -0.001 % |
| V33 | Round nozzle on a cone | Nozzle #6 (N6) (cone) pad edge P=1 | 62.63 | 62.63 | 0.004 % | 36.77 | 36.77 | 0.004 % |
| V34 | Round nozzle on a cone | Nozzle #6 (N6) (cone) nozzle OD P=1 | 43.20 | 43.20 | -0.003 % | 34.27 | 34.27 | 0.004 % |
| V35 | Round nozzle on a cone | Nozzle #6 (N6) (cone) pad edge P=4.1826 | 154.8 | 154.8 | -0.003 % | 129.0 | 129.0 | -0.005 % |
| V36 | Round nozzle on a cone | Nozzle #6 (N6) (cone) nozzle OD P=4.1826 | 140.3 | 140.3 | -0.002 % | 132.5 | 132.5 | -0.002 % |
| V37 | Round nozzle on a cone | Nozzle #7 (N7) (cone) nozzle OD P=1 | 184.9 | 184.2 | -0.406 % | 101.4 | 100.6 | -0.823 % |
| V38 | Round nozzle on a cone | Nozzle #7 (N7) (cone) nozzle OD P=2.391 | 288.3 | 286.3 | -0.680 % | 207.0 | 205.0 | -0.956 % |
| V39 | Round nozzle on a cone | Nozzle #8 (N8) (cone) nozzle OD P=1 | 195.6 | 195.6 | -0.005 % | 117.7 | 117.6 | -0.009 % |
| V40 | Round nozzle on a cone | Nozzle #8 (N8) (cone) nozzle OD P=1.9582 | 284.0 | 284.0 | 0.001 % | 207.0 | 207.0 | 0.004 % |
| V41 | Round nozzle on a cone | Nozzle #9 (N9) (cone) nozzle OD P=1 | 187.5 | 186.7 | -0.417 % | 103.4 | 102.6 | -0.838 % |
| V42 | Round nozzle on a cone | Nozzle #9 (N9) (cone) nozzle OD P=2.325 | 289.0 | 287.0 | -0.683 % | 207.0 | 205.0 | -0.961 % |
| V43 | Round nozzle on a formed head | Nozzle #1 (N1) (head) nozzle OD P=1 | 174.9 | 174.9 | 0.009 % | 90.05 | 90.05 | 0.002 % |
| V44 | Round nozzle on a formed head | Nozzle #1 (N1) (head) nozzle OD P=2.988 | 291.8 | 291.8 | 0.007 % | 207.0 | 207.0 | 0.008 % |
| V45 | Round nozzle on a formed head | Nozzle #1 (N1) (head) nozzle OD P=1 | 245.1 | 245.1 | -0.011 % | 122.5 | 122.5 | -0.002 % |
| V46 | Round nozzle on a formed head | Nozzle #1 (N1) (head) nozzle OD P=1.5619 | 303.9 | 303.9 | -0.008 % | 181.4 | 181.4 | 0.005 % |
| V47 | Round nozzle on a formed head | Nozzle #1 (N1) (head) nozzle OD P=1 | 127.2 | 127.0 | -0.086 % | 61.29 | 61.26 | -0.045 % |
| V48 | Round nozzle on a formed head | Nozzle #1 (N1) (head) nozzle OD P=2.4731 | 205.2 | 205.0 | -0.073 % | 139.3 | 139.2 | -0.049 % |
| V49 | Round nozzle on a formed head | Nozzle #2 (N2) (head) nozzle OD P=1 | 125.8 | 125.7 | -0.075 % | 59.90 | 59.90 | -0.004 % |
| V50 | Round nozzle on a formed head | Nozzle #2 (N2) (head) nozzle OD P=2.7427 | 215.6 | 215.5 | -0.039 % | 149.8 | 149.7 | -0.002 % |
| V51 | Round nozzle on a formed head | Nozzle #3 (N3) (head) nozzle OD P=1 | 147.2 | 147.1 | -0.064 % | 81.33 | 81.33 | -0.003 % |
| V52 | Round nozzle on a formed head | Nozzle #3 (N3) (head) nozzle OD P=2.2947 | 241.7 | 241.6 | -0.041 % | 175.8 | 175.8 | -0.009 % |
| V53 | Round nozzle on a formed head | Nozzle #4 (N4) (head) nozzle OD P=1 | 127.5 | 127.4 | -0.070 % | 61.60 | 61.60 | 0.004 % |
| V54 | Round nozzle on a formed head | Nozzle #4 (N4) (head) nozzle OD P=2.7145 | 218.8 | 218.7 | -0.041 % | 152.9 | 152.9 | -0.006 % |
| V55 | Round nozzle on a formed head | Nozzle #5 (N5) (head) pad edge P=1 | 43.87 | 43.85 | -0.045 % | 33.85 | 33.85 | -0.010 % |
| V56 | Round nozzle on a formed head | Nozzle #5 (N5) (head) nozzle OD P=1 | 46.99 | 47.01 | 0.034 % | 35.68 | 35.68 | -0.008 % |
| V57 | Round nozzle on a formed head | Nozzle #5 (N5) (head) pad edge P=4.5847 | 151.9 | 151.9 | -0.014 % | 141.9 | 141.9 | -0.010 % |
| V58 | Round nozzle on a formed head | Nozzle #5 (N5) (head) nozzle OD P=4.5847 | 169.6 | 169.6 | 0.006 % | 158.3 | 158.3 | -0.005 % |
| V59 | Round nozzle on a cylinder | Nozzle #1 (N1) Hot Shut Down P=0 (governing edge) | 215.3 | 215.3 | -0.003 % | 56.13 | 56.13 | 0.003 % |
| V60 | Round nozzle on a cylinder | Nozzle #2 (N2) Hot Shut Down P=0 (governing edge) | 160.0 | 160.0 | -0.000 % | 42.09 | 42.09 | 0.005 % |
| V61 | Round nozzle on a cylinder | Nozzle #1 (N1) Hot Shut Down P=0 (governing edge) | 86.83 | 86.83 | -0.002 % | 18.57 | 18.57 | -0.014 % |
| V62 | Round nozzle on a cylinder | Nozzle #2 (N2) Hot Shut Down P=0 (governing edge) | 194.1 | 194.1 | -0.003 % | 22.69 | 22.69 | -0.010 % |
| V63 | Round nozzle on a cylinder | Nozzle #1 (N1) Hot Shut Down P=0 (governing edge) | 114.8 | 114.8 | 0.010 % | 28.78 | 28.78 | 0.020 % |
| V64 | Round nozzle on a cylinder | Nozzle #1 (N1) Hot Shut Down P=0 (governing edge) | 29.14 | 29.14 | 0.010 % | 7.62 | 7.62 | 0.030 % |
| V65 | Round nozzle on a formed head | Nozzle #1 (N1) Hot Shut Down P=0 (governing edge) | 116.0 | 116.0 | 0.011 % | 31.21 | 31.22 | 0.027 % |
| V66 | Round nozzle on a formed head | Nozzle #1 (N1) Hot Shut Down P=0 (governing edge) | 140.4 | 140.4 | -0.022 % | 17.84 | 17.85 | 0.010 % |
| V67 | Round nozzle on a formed head | Nozzle #1 (N1) Hot Shut Down P=0 (governing edge) | 74.21 | 74.12 | -0.121 % | 8.34 | 8.34 | -0.035 % |
| V68 | Round nozzle on a formed head | Nozzle #2 (N2) Hot Shut Down P=0 (governing edge) | 74.21 | 74.12 | -0.121 % | 8.34 | 8.34 | -0.035 % |
| V69 | Round nozzle on a formed head | Nozzle #3 (N3) Hot Shut Down P=0 (governing edge) | 74.21 | 74.12 | -0.121 % | 8.34 | 8.34 | -0.035 % |
| V70 | Round nozzle on a formed head | Nozzle #4 (N4) Hot Shut Down P=0 (governing edge) | 74.21 | 74.12 | -0.121 % | 8.34 | 8.34 | -0.035 % |
| V71 | Round nozzle on a formed head | Nozzle #5 (N5) Hot Shut Down P=0 (governing edge) | 13.72 | 13.70 | -0.153 % | 3.70 | 3.70 | -0.145 % |
| V72 | Round nozzle on a cylinder | Nozzle #10 (N10) Hot Shut Down P=0 (governing edge) | 147.2 | 147.2 | 0.005 % | 29.27 | 29.28 | 0.009 % |
| V73 | Round nozzle on a cylinder | Nozzle #11 (N11) Hot Shut Down P=0 (governing edge) | 147.2 | 147.2 | 0.005 % | 29.27 | 29.28 | 0.009 % |
| V74 | Round nozzle on a cylinder | Nozzle #12 (N12) Hot Shut Down P=0 (governing edge) | 147.2 | 147.2 | 0.005 % | 29.27 | 29.28 | 0.009 % |
| V75 | Round nozzle on a cone | Nozzle #6 (N6) Hot Shut Down P=0 (governing edge) | 33.83 | 33.83 | -0.007 % | 8.29 | 8.29 | -0.026 % |
| V76 | Round nozzle on a cone | Nozzle #7 (N7) Hot Shut Down P=0 (governing edge) | 140.7 | 140.7 | -0.005 % | 25.55 | 25.55 | 0.011 % |
| V77 | Round nozzle on a cone | Nozzle #8 (N8) Hot Shut Down P=0 (governing edge) | 132.2 | 132.2 | 0.000 % | 24.39 | 24.38 | -0.024 % |
| V78 | Round nozzle on a cone | Nozzle #9 (N9) Hot Shut Down P=0 (governing edge) | 141.9 | 141.9 | 0.001 % | 25.27 | 25.27 | 0.002 % |
| V79 | Rectangular clip on a cylinder | Clip #1 lug edge P=2.167 (Rm/t 4.5 < 5) | 25.23 | 25.24 | 0.004 % | 11.51 | 11.51 | 0.023 % |
| V80 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=0.6895 [I as radial as the reference does] | 151.4 | 151.4 | 0.002 % | 64.56 | 64.57 | 0.005 % |
| V81 | Round nozzle on a cylinder | Nozzle #1 (N1) nozzle OD P=3.6464 (MAWP) [I as radial as the reference does] | 264.4 | 264.4 | 0.004 % | 193.5 | 193.5 | 0.005 % |
| V82 | Round nozzle on a cylinder | Nozzle #1 (N1) Hot Shut Down P=0 | 135.9 | 135.9 | -0.000 % | 34.50 | 34.50 | 0.001 % |
| V83 | Round nozzle on a cylinder | Nozzle #1 (N1) Pr reversed P=0.6895 [I as radial as the reference does] | 132.9 | 132.9 | -0.001 % | 58.00 | 58.00 | 0.008 % |
| V84 | Round nozzle on a cylinder | Nozzle #1 (N1) Pr reversed Hot Shut Down P=0 | 134.4 | 134.4 | 0.003 % | 34.50 | 34.50 | 0.001 % |
| V85 | Round nozzle on a cylinder | Nozzle #1 (N1) Pr reversed P=3.6464 (MAWP) [I as radial as the reference does] | 238.9 | 238.9 | 0.008 % | 186.9 | 186.9 | 0.006 % |
| V86 | Round nozzle on a cylinder | Nozzle #2 (N2) pad edge P=0.6895 | 41.54 | 41.54 | 0.000 % | 20.84 | 20.84 | 0.007 % |
| V87 | Round nozzle on a cylinder | Nozzle #2 (N2) nozzle OD P=0.6895 | 56.85 | 56.84 | -0.011 % | 26.62 | 26.43 | -0.719 % |
| V88 | Round nozzle on a cylinder | Nozzle #2 (N2) pad edge P=5.5844 (MAWP) | 151.6 | 151.6 | 0.002 % | 131.0 | 131.0 | -0.003 % |
| V89 | Round nozzle on a cylinder | Nozzle #2 (N2) nozzle OD P=5.5844 (MAWP) | 166.0 | 166.0 | -0.005 % | 141.5 | 140.0 | -1.094 % |
| V90 | Round nozzle on a cylinder | Nozzle #2 (N2) Hot Shut Down P=0 | 41.88 | 41.88 | -0.005 % | 10.44 | 10.44 | -0.023 % |
| V91 | Round nozzle on a cylinder | Nozzle #2 (N2) Pr reversed P=0.6895 | 49.35 | 49.34 | -0.003 % | 24.51 | 24.33 | -0.753 % |
| V92 | Round nozzle on a cylinder | Nozzle #2 (N2) Pr reversed Hot Shut Down P=0 | 40.87 | 40.86 | -0.006 % | 10.44 | 10.44 | -0.023 % |
| V93 | Round nozzle on a cylinder | Nozzle #2 (N2) Pr reversed P=5.5844 (MAWP) | 159.0 | 159.0 | -0.004 % | 139.4 | 137.9 | -1.105 % |
| V94 | Round nozzle on a cylinder | Nozzle #3 (N3) nozzle OD P=0.6895 [I as radial as the reference does] | 173.9 | 173.9 | 0.002 % | 72.22 | 72.23 | 0.006 % |
| V95 | Round nozzle on a cylinder | Nozzle #3 (N3) nozzle OD P=2.3022 (MAWP) [I as radial as the reference does] | 260.3 | 260.3 | -0.001 % | 172.7 | 172.7 | -0.001 % |
| V96 | Round nozzle on a cylinder | Nozzle #3 (N3) Hot Shut Down P=0 | 147.2 | 147.2 | 0.005 % | 29.27 | 29.28 | 0.009 % |
Stresses in MPa. P in each case label is the internal pressure in MPa.
Have a reference calculation of your own? Send it and we will run it through the engine and send you the comparison.