Source: https://guthlabs.ai/docs/instruments/pipe-system-pressure-drop-series-network-calculator/mechanism/

instrument mechanism / verified-clean

# Pipe System Pressure Drop (Series Network) Calculator mechanism

The inspectable method record for Pipe System Pressure Drop (Series Network) Calculator, kept separate from implementation and qualification.

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

## Model scope

The loss formulas are standard Darcy-Weisbach plus minor-loss relations under the stated SI assumptions, but the spec is not fully implementable without defining local velocity calculation, segment-specific K reference conditions, elevation sign convention, and the pump-head equation. The honest-label restriction to a single-path series run is appropriate and should remain explicit.

- The friction and minor-loss terms are standard only when V is the local mean velocity for each segment: V_i=Q/(πD_i²/4). A single shared V is incorrect when segment diameters differ.

- The specification accepts flow rate Q but does not define how velocity V is derived from Q and each segment diameter.

- The required pump-head formula is not stated. Under the stated pressure-drop model it should be H_pump=ΔP_total/(ρg), subject to a clearly defined pressure and elevation sign convention.

- The elevation term ρgΔz is standard for static pressure change when Δz is outlet elevation minus inlet elevation; the sign convention is not specified.

- For fittings in segments with different diameters, each K must be multiplied by that fitting's local dynamic pressure ρV_i²/2, not by one common dynamic-pressure term.

## Units and conventions

- Use SI units: Q in m³/s, L and D in m, ρ in kg/m³, g=9.81 m/s², Δz in m, pressure in Pa, and pump head in m of the specified fluid.

- f and K are dimensionless Darcy friction factors and minor-loss coefficients.

- For each segment, V_i=Q/(πD_i²/4).

- Δz means outlet elevation minus inlet elevation; positive Δz increases the reported total pressure drop.

- Pump head is computed as H_pump=ΔP_total/(ρg), with no pump, motor, or efficiency losses included.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "flow_rate_m3_s": 0.01,
    "rho_kg_m3": 1000,
    "elevation_change_m": 2,
    "g_m_s2": 9.81,
    "segments": [
      {
        "length_m": 20,
        "diameter_m": 0.1,
        "friction_factor": 0.02,
        "minor_loss_K": 1.5
      }
    ]
  },
  "expected_outputs": {
    "total_pressure_drop_Pa": 24078.13,
    "required_pump_head_m": 2.45445
  },
  "working": "Area=π(0.1²)/4=0.00785398 m². V=0.01/0.00785398=1.27324 m/s. Dynamic pressure=ρV²/2=1000(1.27324²)/2=810.569 Pa. Friction coefficient=fL/D=0.02(20/0.1)=4. Minor coefficient=1.5. Friction plus minor loss=(4+1.5)(810.569)=4458.13 Pa. Elevation term=1000(9.81)(2)=19620 Pa. Total=4458.13+19620=24078.13 Pa. Pump head=24078.13/(1000·9.81)=2.45445 m."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

A zero-diameter segment creates undefined area, velocity, and L/D terms. The calculator must reject it; accepting it without validation is a concrete failure mode. The branch test also exposes reliance on an unstated Reynolds-number friction-factor regime and threshold.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/pipe-system-pressure-drop-series-network-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/pipe-system-pressure-drop-series-network-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/pipe-system-pressure-drop-series-network-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-tranche4/tranche4-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`