Source: https://guthlabs.ai/docs/instruments/cooling-tower-approach-range-calculator/

instrument / verified-clean

# Cooling Tower Approach/Range 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](<https://guthlabs.ai/docs/instruments/cooling-tower-approach-range-calculator/>)[02**Mechanism**Method and assumptions](<https://guthlabs.ai/docs/instruments/cooling-tower-approach-range-calculator/mechanism/>)[03**Implementation**Binding and validation](<https://guthlabs.ai/docs/instruments/cooling-tower-approach-range-calculator/implementation/>)[04**Qualification**Evidence and errata](<https://guthlabs.ai/docs/instruments/cooling-tower-approach-range-calculator/qualification/>)

## Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

**Area**: Thermodynamics, Fluids & Aero

**Tranche**: tranche-4

**Evidence ID**: t4-096

**Ledger rows**: 1

No ledger note is attached.

## Review findings

Range and approach are verifiable as specified. The instrument cannot be fully verified until the effectiveness formula and output-unit behavior are made explicit. Test-vector effectiveness values use the common provisional formula Effectiveness=Range/(Range+Approach)×100.

### Formula and scope findings

- Range=Twater,in−Twater,out is the standard cooling-tower range formula, provided both water temperatures use the same unit and temperature scale.

- Approach=Twater,out−Twb is the standard cooling-tower approach formula, provided outlet-water and wet-bulb temperatures use the same unit and temperature scale.

- The output list includes effectiveness %, but no effectiveness formula is specified. A common definition is Effectiveness=(Range/(Range+Approach))×100=(Twater,in−Twater,out)/(Twater,in−Twb)×100; this must be explicitly added before implementation can be verified.

- The effectiveness formula is undefined when Twater,in=Twb because its denominator is zero.

### Unit assumptions

- All three temperatures must be supplied in the same unit and scale, such as all °C or all °F; mixing Celsius and Fahrenheit directly is invalid.

- Temperature differences may be calculated in either °C or °F, but the resulting Range and Approach units follow the input unit.

- The effectiveness percentage is dimensionless, so its ratio is unchanged when all temperatures are consistently converted between °C and °F.

- No output temperature unit is specified; the interface should label Range and Approach with the input unit.

## Boundary hardening

**BREAK_CLAIMED** · SELF_FLAGGED

The effectiveness denominator can be zero, producing an undefined result, and negative approach or range values can produce mathematically finite but physically invalid outputs. Additionally, the specification lists effectiveness as an output but does not explicitly provide its formula; the calculations above assume the conventional formula Range/(Range+Approach) × 100.

## 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": {
    "water_in_temperature": 35,
    "water_out_temperature": 29,
    "wet_bulb_temperature": 25,
    "temperature_unit": "°C"
  },
  "expected_outputs": {
    "range": 6,
    "approach": 4,
    "effectiveness_percent": 60
  },
  "working": "Range = 35 − 29 = 6 °C. Approach = 29 − 25 = 4 °C. Effectiveness = [6 ÷ (6 + 4)] × 100 = (6 ÷ 10) × 100 = 60%."
}
````

## 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-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`