Normal Shock Relations Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified with errata that must be applied at binding time.

Area

Thermodynamics, Fluids & Aero

Tranche

tranche-5

Evidence ID

t5-086

Ledger rows

1

No ledger note is attached.

Review findings

The supplied M2 and static-pressure formulas are standard for a perfect-gas normal shock. The specification fails because three claimed outputs lack formulas and the stagnation-pressure-loss label is undefined. The implementation should add the missing standard relations, define the loss convention, validate gamma>1 and M1>1, and clearly identify the perfect-gas normal-shock assumptions.

Formula and scope findings

• The supplied formulas correctly define M2² and P2/P1 for a perfect-gas normal shock, assuming M1 and gamma are dimensionless and M1 is in the supersonic regime.
• Formulas are missing for the claimed outputs T2/T1 and rho2/rho1. Standard formulas are rho2/rho1=((gamma+1)M1²)/((gamma-1)M1²+2) and T2/T1=(P2/P1)/(rho2/rho1).
• The formula for stagnation pressure loss is missing. If the intended output is the stagnation-pressure ratio P02/P01, the standard formula is [((gamma+1)M1²)/((gamma-1)M1²+2)]^(gamma/(gamma-1))*[((gamma+1))/(2gamma M1²-(gamma-1))]^(1/(gamma-1)).
• The phrase 'stagnation pressure loss' is ambiguous: it must specify whether the output is the ratio P02/P01, fractional loss 1-P02/P01, or percentage loss 100(1-P02/P01).

Unit assumptions

• M1 is dimensionless Mach number.
• gamma is dimensionless ratio of specific heats, normally constant with gamma>1; air is commonly modeled with gamma=1.4.
• All pressure, temperature, and density outputs are dimensionless ratios, so the upstream and downstream quantities must use matching units.
• The supplied relations assume a perfect gas and an adiabatic, one-dimensional normal shock with negligible body-force effects.
• The honest-label restriction M1>1 must be enforced for a physical compressive normal shock; M1=1 is the zero-strength limiting case, not a finite shock.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The calculator breaks or must reject several edge inputs: the exact M1=1 boundary violates the strict validity condition, gamma=1 and M1=0 causes a zero denominator and undefined results, and a subsonic input produces formal algebraic values despite being outside the normal-shock branch. Signed Mach-number handling is also convention-dependent.

Errata and corrections

Tranche errata

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "M1": 2,
    "gamma": 1.4
  },
  "expected_outputs": {
    "M2": 0.5773502692,
    "P2_P1": 4.5,
    "T2_T1": 1.6875,
    "rho2_rho1": 2.6666666667,
    "P02_P01": 0.7208738615
  },
  "working": "M1²=2²=4. M2²=(1+((1.4-1)/2)×4)/(1.4×4-(1.4-1)/2)=(1+0.2×4)/(5.6-0.2)=1.8/5.4=1/3, so M2=√(1/3)=0.5773502692. P2/P1=1+[2×1.4/(1.4+1)]×(4-1)=1+(2.8/2.4)×3=1+3.5=4.5. rho2/rho1=((1.4+1)×4)/((1.4-1)×4+2)=9.6/3.6=2.6666666667. T2/T1=4.5/2.6666666667=1.6875. P02/P01=(2.6666666667)^3.5×(2.4/10.8)^2.5=0.7208738615."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

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

• VERIFIED_LEDGER.json · VERIFIED_WITH_ERRATA
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json