09 / CHAPTER 12
Continuum studio: choose a model
Select assumptions for a fountain component and state what evidence would falsify them.
ANCHOR EQUATION
Model choice
In symbols: model = balances + constitutive law
Choose assumptions that make predictions testable against evidence.
A continuum model must face evidence
A fountain component is not ‘a fluid problem’ until geometry, scale, material behavior, and boundaries are stated. The model should make a prediction that measurements could contradict.
Choose assumptions by consequence
For a nozzle, begin with mass balance ρQ = constant, momentum balance for reaction force, and a constitutive model for viscosity. Add incompressibility if pressure changes are small relative to bulk modulus, no-slip if viscous wall gradients are observed, and steady flow only if measurements do not vary over the averaging interval.
If Q = 0.004 m³/s through diameter 20 mm, mean speed is Q/A = 12.7 m/s. Water Re = ρUD/μ ≈ 254,000, so a laminar Poiseuille model is not defensible for the bulk nozzle flow, though viscous wall effects still exist.
Model failure is informative
A mismatch between predicted pressure drop and measured flow may indicate roughness, separation, air entrainment, pump curve interaction, or wrong geometry. Do not repair a failed model by adding an unexplained correction factor before locating the missing physics.
Work it: Write a one-page model for a fountain nozzle: system boundary, known measurements, unknowns, balances, constitutive assumptions, dimensionless groups, and one falsifiable prediction.