Reynolds number

Meaning: Re compares inertial forces, which keep fluid moving and stir it into eddies, with viscous forces, which damp disturbances. When viscosity dominates (small Re), layers slide past each other smoothly, which is laminar flow. When inertia dominates (large Re), eddies form, which is turbulent flow. In a long straight pipe, flow is typically laminar below roughly 2000 and turbulent above roughly 4000, with an unstable transition in between. Passages usually supply the cutoffs.

Equation: Re = ρvD/η, where ρ is fluid density (kg/m³), v is average flow speed (m/s), D is pipe diameter (m), and η is viscosity (Pa·s). Re is dimensionless, so it has no unit.

On the MCAT: A passage describes a pipe, an airway or a blood vessel and asks what happens to the flow when speed, diameter or fluid changes. Re is directly proportional to ρ, v and D, and inversely proportional to η. For example, if blood speeds up through a narrowed vessel, Re rises and turbulence becomes more likely. You may also be asked to plug in values and compare the result with a given cutoff. Turbulent flow dissipates more energy, and Poiseuille's law applies to laminar flow only.

Common confusion: Students often put viscosity in the numerator and decide that a thicker fluid is more turbulent. Viscosity is in the denominator, so a thicker fluid has a lower Re and stays laminar more easily.