Thin-Wall Pressure Vessel Stress mechanism

Model scope

The stated equations are standard membrane-stress formulas: cylinder hoop stress pr/t, closed-end cylinder longitudinal stress pr/(2t), and spherical-vessel membrane stress pr/(2t). Review is required because pressure convention, radius-versus-diameter handling, and the closed-end assumption are not fully specified.

• The cylinder longitudinal-stress formula is valid for a closed-ended cylinder under internal pressure; the specification does not state the closed-end assumption.
• The inputs allow r or d, but the specification does not define the required conversion d=2r before applying the formulas.
• The pressure convention is unspecified; these membrane-stress formulas normally use internal gauge pressure, not absolute pressure.

Units and conventions

• p, r, d, and t must use mutually consistent units; stress has the same pressure units as p.
• If diameter d is supplied, use r=d/2 before calculation.
• p is assumed to be internal gauge pressure; signed pressure may represent external pressure if the sign convention is explicitly defined.
• The thin-wall validity condition is t/r<0.1, using the mean radius and uniform wall thickness.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "p": 200000,
    "r": 0.5,
    "t": 0.01,
    "vessel_type": "cylinder",
    "units": "p in Pa; r and t in m"
  },
  "expected_outputs": {
    "sigma_hoop": 10000000,
    "sigma_long": 5000000,
    "stress_units": "Pa"
  },
  "working": "t/r = 0.01/0.5 = 0.02, which is less than 0.1. σ_hoop = pr/t = (200000 Pa × 0.5 m)/0.01 m = 100000/0.01 = 10000000 Pa. σ_long = pr/(2t) = (200000 × 0.5)/(2 × 0.01) = 100000/0.02 = 5000000 Pa."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The instrument should reject t=0 because both formulas divide by zero, and it should flag or reject t/r=0.1 because the thin-wall assumption is valid only for t/r<0.1. Signed-versus-magnitude pressure conventions can also reverse the reported stress signs.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json