critical speed
Summary
Critical speed is the fluid speed above which smooth laminar flow in a tube becomes turbulent. It rises with viscosity and falls with fluid density and tube diameter. Turbulence is likely when the actual speed exceeds it.
Detail
Meaning: At low speed a real fluid in a tube moves in smooth parallel layers (laminar flow). Above the critical speed, eddies form and the flow becomes turbulent. The threshold comes from the Reynolds number, which compares inertial effects to viscous effects. Turbulence dissipates more energy, so Poiseuille's law no longer applies. A second MCAT sense is in circular motion: the critical speed at the top of a vertical loop is the minimum speed that keeps an object on its path, v = √(gr).
Equation: vc = NR η / (ρD), where vc is critical speed (m/s), NR is the Reynolds number (dimensionless), η is viscosity (Pa·s), ρ is fluid density (kg/m³), and D is tube diameter (m).
On the MCAT: Passages ask whether flow, such as blood through a narrowed artery, is laminar or turbulent. Compare the actual speed with vc, or predict how vc changes when η, ρ or D changes. Continuity (A₁v₁ = A₂v₂) is often combined with it.
Common confusion: Critical speed is a threshold, not the speed of the flow. Narrowing a tube raises vc (vc ∝ 1/D), but at constant flow rate the actual speed rises faster (v ∝ 1/D²), so turbulence becomes more likely, not less.
Sources
- Physics (Cutnell and Johnson)
- Fundamentals of Physics (Halliday, Resnick, Walker)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.