# Critical Velocity

The streamline flow occurs in case of liquid, as long as its velocity does not exceed a limiting value. Osborne Reynolds saw that there are two limiting values instead of one. These two limiting values are known as critical velocity. At the $$1^{st}$$ limiting value (or, critical velocity), the liquid flow becomes unsteady, i.e., the velocity of the so-called fluid particles at any point is time dependent. At the $$2^{nd}$$ critical velocity, the liquid flow becomes turbulent. But, generally, critical velocity $$(V_c)$$ refers to the $$1^{st}$$ one. According to Reynolds, the critical velocity is given by the relation, $$V_c = \frac{K\eta}{\rho r}$$, where $$\hspace{0.2cm}$$ $$\eta =$$coefficient of viscosity of the liquid. $$\hspace{3.2cm}$$ $$\rho =$$density of the liquid. $$\hspace{3.2cm}$$ $$r =$$radius of the tube. $$\hspace{3.2cm}$$ $$K =$$proportionality constant called Reynold's number. Reynold’s number $$(K)$$ is a pure number. It has no unit or dimensions. So, it is a constant quantity in any system of units provided