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

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