## Related questions with answers

What is the physical significance of the Reynolds number? How is it defined for (a) flow in a circular pipe of inner diameter D and (b) flow in a rectangular duct of cross section $a imes b?$

Solution

Verified$\text{\color{#c34632}Reynolds number }$is the ratio between inertial forces to viscous forces in the fluid, on which the flow regime depends mainly.

$\color{#4257b2} Re = \dfrac{\text{Inertial forces}}{\text{Viscous forces}}= \dfrac{\rho\ D_{\text{h}}\ V}{\mu}$

Where $(\rho)$ is the density of the fluid, $(D)$ the hydraulic diameter in which the fluid flows in, $(\mu)$ is the dynamic Viscosity of the fluid.

At large Reynolds numbers, the inertial forces, which are proportional to the fluid density and the fluid velocity, are large comparing with viscous forces, So, viscous forces cannot prevent the random and rapid fluctuations of the fluid. At small or moderate Reynolds numbers, however, the viscous forces are large enough to suppress these fluctuations and to keep the fluid “in line.” Thus the flow is turbulent in the first case and laminar in the second.

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