Critical Velocity and Reynolds Number

The flow of a fluid, whether streamline or turbulent, is distinguished on the basis of the velocity of the flow. The velocity beyond which a streamline flow becomes turbulent is called the critical velocity. According to Osborne Reynolds (1842-1912), the critical velocity is given by:

where $v_c$ is the critical velocity of the fluid, $R_n$ is the Reynolds number, η is the fluid's coefficient of viscosity, ρ is the fluid's density, and d is the diameter of the tube through which it is flowing. Equation (2.32) can be rearranged to give the Reynolds number itself:

$R_n = \dfrac{\rho\,v_c\,d}{\eta} \qquad \text{--- (2.33)}$ …