Isentropic Flow Relations Calculator mechanism

Model scope

The exact ambiguity requiring review is that the specification claims four outputs and says 'standard isentropic flow relations incl.' but provides only the A/A* equation, not explicit formulas for T/T0, P/P0, or ρ/ρ0. Add the three missing equations, input-domain validation, and an honest label stating the ideal-gas, constant-γ, isentropic-flow assumptions.

• The supplied formula explicitly defines only A/A*; the formulas for T/T0, P/P0, and ρ/ρ0 are not written, so the claimed complete output set is ambiguous.
• The standard relations should explicitly be T/T0 = [1 + ((γ−1)/2)M²]⁻¹, P/P0 = [1 + ((γ−1)/2)M²]⁻(γ/(γ−1)), and ρ/ρ0 = [1 + ((γ−1)/2)M²]⁻(1/(γ−1)).
• The stated A/A* formula is correct for steady, one-dimensional, isentropic, quasi-area-varying flow with A* denoting the sonic throat area; those validity conditions are not stated.
• A/A* is a geometric area ratio and does not by itself select the subsonic or supersonic branch; for a given area ratio greater than one, both branches may exist.

Units and conventions

• Mach number M is dimensionless and must be positive.
• γ is dimensionless, equals cp/cv, and is constant; the standard formulas require γ > 1 and a calorically perfect ideal gas.
• T, P, and ρ must use consistent units in numerator and denominator; because these are ratios, the specific temperature, pressure, and density units cancel.
• A and A* must use the same area units; the area ratio is dimensionless.
• The stagnation quantities T0, P0, and ρ0 refer to the same isentropic reference state as the local quantities.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "Mach": 1,
    "gamma": 1.4
  },
  "expected_outputs": {
    "T_over_T0": 0.8333333333,
    "P_over_P0": 0.5282817877,
    "rho_over_rho0": 0.6339381452,
    "A_over_Astar": 1
  },
  "working": "For γ=1.4, (γ−1)/2=0.2, γ/(γ−1)=3.5, 1/(γ−1)=2.5, and (γ+1)/(2(γ−1))=3. First q=1+0.2(1²)=1.2. T/T0=1/1.2=0.8333333333. P/P0=1.2^(-3.5)=0.5282817877. ρ/ρ0=1.2^(-2.5)=0.6339381452. A/A*=(1/1)[(2/2.4)(1.2)]^3=1[(5/6)(1.2)]^3=1^3=1. This is the sonic throat boundary case M=1."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

M=0 causes division by zero in A/A*, and a signed negative Mach produces a nonphysical negative area ratio unless the instrument explicitly uses Mach magnitude or rejects signed inputs.

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-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json