Bernoulli Equation Solver mechanism

Model scope

The core ideal Bernoulli relation is correct, but the specification needs an explicit loss-inclusive equation and documented required inputs and constraints before it can receive PASS. The honest label should state that the loss-inclusive version is a steady incompressible energy equation with modeled head loss, not an inviscid equation.

• The ideal Bernoulli equation shown is standard for steady, incompressible, inviscid flow along a streamline, assuming no pump or turbine head.
• The phrase "(+ head loss term)" is ambiguous unless the equation explicitly states P1/(rho*g)+V1^2/(2*g)+z1 = P2/(rho*g)+V2^2/(2*g)+z2+h_L. A positive loss head must be added on the downstream side, or equivalently subtracted when solving for an upstream-to-downstream pressure.
• The claim "Any 5 of 6 terms at two points" is incomplete unless density, gravitational acceleration, and any head loss are known inputs. Some missing-term choices also require a physical-domain constraint, such as a nonnegative velocity magnitude.
• The formula does not include pump head or turbine-extraction head, so it cannot represent systems containing pumps or turbines without additional terms.

Units and conventions

• Use a single consistent unit system; the test vectors use SI units with pressure in Pa, density in kg/m^3, velocity in m/s, elevation and head loss in m, and g in m/s^2.
• rho is fluid density and is assumed constant between the two points.
• g is gravitational acceleration, taken as 9.81 m/s^2.
• P1 and P2 must use the same pressure reference, either both absolute or both gauge; only pressure differences affect the basic equation.
• For the loss-inclusive form, h_L is a nonnegative head loss in metres of the same fluid.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "rho_kg_per_m3": 1000,
    "g_m_per_s2": 9.81,
    "P1_Pa": 200000,
    "V1_m_per_s": 3,
    "z1_m": 5,
    "V2_m_per_s": 5,
    "z2_m": 2,
    "hL_m": 0
  },
  "expected_outputs": {
    "P2_Pa": 221430
  },
  "working": "Use P1/(rho*g)+V1^2/(2*g)+z1 = P2/(rho*g)+V2^2/(2*g)+z2+hL. Rearrange: P2 = P1 + 0.5*rho*(V1^2-V2^2) + rho*g*(z1-z2) - rho*g*hL. Compute: P2 = 200000 + 0.5*1000*(3^2-5^2) + 1000*9.81*(5-2) - 1000*9.81*0 = 200000 + 500*(9-25) + 9810*3 = 200000 - 8000 + 29430 = 221430 Pa."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero-density input causes division by zero in the pressure-head terms, so the solver must reject the input or return undefined rather than a numeric pressure.

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-tranche4/tranche4-results.json
• BOUNDARY_HAZARD_CATALOG.json