Source: https://guthlabs.ai/docs/instruments/isentropic-flow-relations-calculator/mechanism/

instrument mechanism / verified-clean

# Isentropic Flow Relations Calculator mechanism

The inspectable method record for Isentropic Flow Relations Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## 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

[01**Overview**](<https://guthlabs.ai/docs/instruments/isentropic-flow-relations-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/isentropic-flow-relations-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/isentropic-flow-relations-calculator/qualification/>)

## 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`