text: A key tool used to determine the stability of a flow is the Reynolds number (Re), first put forward by George Gabriel Stokes at the start of the 1850s. Associated with Osborne Reynolds who further developed the idea in the early 1880s, this dimensionless number gives the ratio of inertial terms and viscous terms. In a physical sense, this number is a ratio of the forces which are due to the momentum of the fluid (inertial terms), and the forces which arise from the relative motion of the different layers of a flowing fluid (viscous terms). The equation for this is
  where
  The Reynolds number is useful because it can provide cut off points for when flow is stable or unstable, namely the Critical Reynolds number . As it increases, the amplitude of a disturbance which could then lead to instability gets smaller. At high Reynolds numbers it is agreed that fluid flows will be unstable. High Reynolds number can be achieved in several ways, e.g. if  is a small value or if  and  are high values. This means that instabilities will arise almost immediately and the flow will become unstable or turbulent.