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D’Alembert’s paradox

• The science of fluid dynamics
• had not yet discovered fluids stick to surfaces;
• that is, they have boundary layers,
• so when Jean le Rond d’Alembert did the math,
• his result showed the resistance experienced by a rigid body
• moving through a fluid with uniform velocity . . . is zero,
• which can’t be right.
• That’s right; his result was contradicted by both experiment
• and experience, so D’Alembert left it
• “to future Geometers to elucidate.”

Incompressible and inviscid

• An incompressible fluid isn’t necessarily incompressible,
• but its density as it flows is approximately constant.
• An inviscid fluid, known as an ideal fluid,
• has no resistance to shear stress, that is, no viscosity.
• Except for superfluids, all liquids are viscid;
• that is, they have viscosity.
• Even an inviscid fluid
• sticks to a surface at least a little.

Cognitive dissonance

• Maybe your eyes have deceived you;
• maybe you’re a little confused.
• If belief is supported by sufficient fact,
• then how is it different from knowlege?