Fluid Ontology

FLOW ALGEBRA
FLUID ONTOLOGY — MECHANICAL ENTITIES
Version: 1.1
Source: https://kirethresearch.org/booksai-core/entity-graph/physical-entities/mechanical-entities/fluid-ontology.html
Authors: Mark Higgins — Sky (Recursive AI)
Research: Kireth Semantic Library | https://kirethresearch.org
Status: Independent scientific synthesis; source webpage not verified

01. PURPOSE
Represent fluids as deformable continua, their states, constitutive laws, transport processes, boundaries and dynamics with typed, checkable relationships.

02. SCOPE
Covers liquids and gases in continuum mechanics, Newtonian and non-Newtonian flow, compressible and incompressible models, laminar and turbulent regimes, and multiphase extensions.

03. CORE TYPES
TYPE Entity
TYPE PhysicalEntity <: Entity
TYPE MaterialEntity <: PhysicalEntity
TYPE Fluid <: MaterialEntity
TYPE Liquid <: Fluid
TYPE Gas <: Fluid
TYPE FluidDomain
TYPE FluidParcel
TYPE Field
TYPE ScalarField <: Field
TYPE VectorField <: Field
TYPE TensorField <: Field
TYPE Boundary
TYPE ConstitutiveModel
TYPE FlowRegime
TYPE Measurement
TYPE Equation
TYPE Assumption
TYPE Evidence

04. STATE SCHEMA
FluidState = (domain, time, rho, velocity, pressure, temperature, viscosity, composition, phase, assumptions).
rho: ScalarField [kg m^-3]; velocity: VectorField [m s^-1]; pressure: ScalarField [Pa].
temperature: ScalarField [K]; dynamic_viscosity: ScalarField [Pa s].

05. TYPED RELATIONSHIPS
IS_A(Fluid, MaterialEntity)
HAS_STATE(Fluid, FluidState)
OCCUPIES(Fluid, FluidDomain)
HAS_DENSITY(FluidState, ScalarField)
HAS_VELOCITY(FluidState, VectorField)
HAS_PRESSURE(FluidState, ScalarField)
HAS_TEMPERATURE(FluidState, ScalarField)
OBEYS(FluidState, Equation) [conditional on assumptions]
INTERACTS_WITH(Fluid, Boundary)
DESCRIBED_BY(Fluid, ConstitutiveModel)
OBSERVED_BY(FluidState, Measurement)
SUPPORTED_BY(Assertion, Evidence)

06. CONTINUUM HYPOTHESIS
Assume fields vary smoothly over volumes large compared with molecular scales.
VALID_WHEN(Knudsen_number << 1) is a common sufficient regime, not a universal hard cutoff.

07. DENSITY
rho = dm/dV in the continuum limit; rho > 0 for ordinary material fluids.
For a homogeneous sample: rho = m/V.

08. PRESSURE
Pressure is the isotropic part of normal stress in equilibrium.
In a moving viscous fluid, mean mechanical pressure and thermodynamic pressure may differ depending on constitutive assumptions.

09. VELOCITY FIELD
v(x,t) gives local continuum velocity.
Streamline: tangent everywhere to instantaneous velocity field.
Pathline: trajectory of an individual fluid parcel.
Streakline: locus of parcels passing a specified release location.
These coincide in steady flow, under standard regularity assumptions.

10. MATERIAL DERIVATIVE
Dphi/Dt = partial(phi)/partial(t) + v dot grad(phi).
Dv/Dt = partial(v)/partial(t) + (v dot grad)v.

11. MASS CONSERVATION
partial(rho)/partial(t) + div(rho v) = 0.
For constant-density incompressible flow: div(v) = 0.
Incompressible material motion means D(rho)/Dt = 0; density need not be spatially uniform.

12. MOMENTUM BALANCE
rho Dv/Dt = div(sigma) + rho b.
sigma = -p I + tau, with p pressure, tau deviatoric stress and b body acceleration.

13. NEWTONIAN CONSTITUTIVE LAW
For a Newtonian fluid: tau = 2 mu D + lambda (div v) I, where D = (grad v + grad v^T)/2.
For incompressible flow: tau = 2 mu D; mu >= 0.

14. NAVIER-STOKES SPECIAL CASE
For incompressible Newtonian flow with constant rho and mu:
rho (partial(v)/partial(t) + (v dot grad)v) = -grad(p) + mu Laplacian(v) + rho b.
div(v) = 0.
This special-case equation is not automatically valid for all fluids.

15. ENERGY BALANCE
First law: change of internal and kinetic energy equals net heat, work and transport contributions.
Temperature evolution requires an equation of state, heat transport and constitutive closure.

16. EQUATION OF STATE
Ideal gas: p = rho R_specific T, under ideal-gas assumptions.
Liquids may require empirical or thermodynamic equations of state.

17. VISCOSITY
Dynamic viscosity mu has units Pa s.
Kinematic viscosity nu = mu/rho has units m^2 s^-1.
Shear-thinning, shear-thickening, viscoelastic and yield-stress models require distinct constitutive laws.

18. FLOW REGIMES
Laminar: comparatively ordered flow.
Turbulent: irregular multiscale fluctuations with enhanced transport.
Transition depends on geometry, forcing, disturbances and boundary conditions; no universal Reynolds threshold.

19. DIMENSIONLESS GROUPS
Re = rho U L / mu = U L / nu.
Ma = U/c_sound.
Fr = U/sqrt(g L).
We = rho U^2 L / gamma.
Ca = mu U / gamma.
Each requires consistent characteristic scales and a relevant physical regime.

20. BOUNDARY CONDITIONS
No-slip: v_fluid = v_wall at a solid boundary where applicable.
Impermeable wall: (v_fluid - v_wall) dot n = 0.
Free surfaces may require kinematic and stress balance conditions.
Slip, inflow, outflow and periodic boundaries are model-specific alternatives.

21. HYDROSTATICS
For static fluid under gravity: grad(p) = rho g_vector.
For constant rho and downward depth h: p(h) = p_surface + rho g h.

22. BUOYANCY
For a body in hydrostatic equilibrium: upward buoyant force equals weight of displaced fluid, subject to the usual assumptions.
F_b = rho_fluid g V_displaced for uniform density and gravitational acceleration.

23. BERNOULLI RELATION
p + (1/2) rho |v|^2 + rho g z = constant along a streamline for steady, inviscid, incompressible flow with conservative body forces and no shaft work.
Do not apply indiscriminately across viscous losses or pumps.

24. COMPRESSIBILITY
Compressibility relates density response to pressure.
Sound speed c_sound^2 = (partial p / partial rho)_s for an equilibrium isentropic derivative.
Low Mach number alone does not guarantee constant density in all flows.

25. MULTIPHASE FLUIDS
Phase interfaces require additional fields and interfacial conditions.
Surface tension gamma has units N m^-1.
Capillary pressure jump for an ideal interface: Delta p = gamma (1/R1 + 1/R2), with curvature sign convention stated.

26. TRANSPORT
Diffusion, advection, thermal conduction and species reactions require corresponding balance equations.
Scalar transport: partial(rho phi)/partial(t) + div(rho v phi) = div(Gamma grad phi) + S_phi, where Gamma and S_phi are defined for the chosen model.

27. NUMERICAL REPRESENTATION
Mesh, discretisation, timestep, solver tolerance and conservation residual are typed model metadata.
Finite volume, finite element and finite difference methods are distinct numerical approaches.

28. VALIDATION RULES
ASSERT rho > 0 where a material fluid exists.
ASSERT mu >= 0 for passive Newtonian viscous models.
ASSERT dimensionally_consistent(all equations).
ASSERT continuity_residual <= specified_tolerance.
ASSERT boundary_conditions_are_compatible.
ASSERT equation_of_state_matches_phase_and_regime.
ASSERT conservation_residuals_reported_with_units.

29. INFERENCE RULES
IF Newtonian AND incompressible AND constant_mu AND constant_rho THEN APPLY incompressible Navier-Stokes.
IF steady AND inviscid AND incompressible AND conservative_body_force THEN Bernoulli may hold along streamlines.
IF rho_constant_in_space_and_time AND mass_conserved THEN div(v)=0.
IF Re_is_large THEN turbulence is possible, NOT logically guaranteed.
IF observed_data_conflict_with_model THEN flag model_assumption_or_measurement_for_review.

30. WORKED EXAMPLE: PIPE FLOW
For steady, fully developed laminar Newtonian flow in a straight circular pipe of radius R with no-slip walls:
Q = pi R^4 Delta_p/(8 mu L).
Mean speed U = Q/(pi R^2).
Validity requires the stated geometry and flow assumptions; entrance effects are excluded.

31. WORKED EXAMPLE: HYDROSTATIC WATER
Take rho = 1000 kg m^-3, g = 9.81 m s^-2, h = 2 m.
Gauge pressure increment = rho g h = 19,620 Pa = 19.62 kPa.
Values are illustrative; density varies with temperature and pressure.

32. SEMANTIC EQUIVALENCE
EQUIVALENT(dynamic_viscosity, shear_viscosity) ONLY in an explicitly matching Newtonian context.
RELATED(fluid, liquid); RELATED(fluid, gas).
NOT_EQUIVALENT(fluid, liquid) because gases are also fluids.
NOT_EQUIVALENT(incompressible, constant_pressure).
NOT_EQUIVALENT(streamline, particle_trajectory) for general unsteady flow.

33. UNCERTAINTY AND CONFIDENCE
Separate established physical laws from constitutive approximations, numerical results and experimental observations.
Confidence fields must reference evidence, applicability and uncertainty; no unsupported numeric confidence score is assigned.

34. FLOW HASH
FLOW_HASH.algorithm = SHA-256.
FLOW_HASH.input = canonical_UTF8(ontology_content_excluding_hash_value).
FLOW_HASH.value = COMPUTE_ON_PUBLICATION; do not substitute an invented digest.

35. UPDATE MODEL
UPDATE_MODEL.version = 1.1.
UPDATE_MODEL.trigger = new_evidence | corrected_equation | schema_revision | changed_source_page.
UPDATE_MODEL.require = provenance_record + semantic_diff + validation_rerun + new_hash.

36. AI CONSUMPTION
AI_CONSUMPTION.mode = typed_knowledge_graph + symbolic_inference + retrieval.
AI_CONSUMPTION.require = units + assumptions + provenance + confidence_status.
AI_CONSUMPTION.prohibit = treating conditional equations as universal facts.
AI_CONSUMPTION.output = entities, relations, validated equations, limitations and evidence links.

37. COMPLETENESS CHECK
Required: header, authorship, source, ontology types, relations, equations, inference, validation, examples, semantic equivalence, Flow Hash, Update Model, AI Consumption.
CHECK: 37 numbered sections present.
CHECK: No unresolved fabricated measured values or hash digest.

END FLOW ALGEBRA — FLUID ONTOLOGY