text: In 1883, scientist Osborne Reynolds conducted a fluid dynamics experiment involving water and dye, where he adjusted the velocities of the fluids and observed the transition from laminar to turbulent flow, characterized by the formation of eddies and vortices. Turbulent flow is defined as the flow in which the system's inertial forces are dominant over the viscous forces. This phenomenon is described by Reynolds number, a unit-less number used to determine when turbulent flow will occur. Conceptually, the Reynolds number is the ratio between inertial forces and viscous forces.
  The general form for the Reynolds number flowing through a tube of radius  (or diameter ):
  where  is the velocity of the fluid,  is its density,  is the radius of the tube, and  is the dynamic viscosity of the fluid. A turbulent flow in a fluid is defined by the critical Reynolds number, for a closed pipe this works out to approximately
  In terms of the critical Reynolds number, the critical velocity is represented as