Critical Velocity:
Streamline flow occurs for small values of the velocity of the fluid. In fact, it is observed that there are actually two critical velocities, a lower one at which streamline flow is unstable and turbulence is possible and a higher one above which turbulence is inevitable. Here, we shall confine our discussion to the lower critical velocity, vc.
The critical velocity vc of the liquid flowing through a narrow tube is a function of a density ρ, the viscosity η of the liquid and the diameter d of the tube. In view of this, we could find an expression for vc, using the method of dimensions, through writing:
vc = k η/ρ d
where, k is a number ~ 1150 (for water). The usual way in which this expression is written is to combine v, ρ and η to give a dimensionless product :
k = vc ρ d/η
where k is called the Reynold's number.