Source: https://guthlabs.ai/docs/instruments/isentropic-flow-relations-calculator/
instrument / verified-clean
# Isentropic Flow Relations Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Thermodynamics, Fluids & Aero
**Tranche**: tranche-5
**Evidence ID**: t5-076
**Ledger rows**: 1
No ledger note is attached.
## Review findings
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.
### Formula and scope findings
- 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.
### Unit assumptions
- 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.
## Boundary hardening
**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.
## Errata and corrections
No applied erratum is attached to this unique-name record.
## Inspectable example
4 review vectors are recorded. One source-bound sample is shown below.
````
{
"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."
}
````
## 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_CLEAN`
- `evidence-tranche5/tranche5-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`