Reynolds numbers high viscosity fields

Inertial forces of the fluid increase with density and the square of velocity (pw ), whereas viscous forces decreases with increasing diameter of tube (r u/d) and increase with viscosity and velocity. High Reynolds numbers (Re > 4000) result in turbulent flow with low Reynolds number (Re > 2000), the flow is laminar. Laminar flow results from formation of layers of fluid with different velocities after a certain flow distance, as illustrated in Figure 2.22, segment A. Flow at the walls is zero and increases on approach to the center of the tubes. The laminar flow pattern results from mobile-phase layers with different velocities traveling parallel to each other. The maximum flow at the center is twice the average flow velocity of fluid. Molecules in the field can exchange between fluid layers by molecular diffusion. Most open tubular columns operate under laminar flow conditions. 

Fully turbulent flow. At very high Reynolds numbers, the inertial forces due to fluctuating velocities overwhelm the viscous forces, so the flow field becomes independent of fluid viscosity. Mean velocity profiles scale with a characteristic velocity and length scale, and drag coefficients (e.g., the power number) become independent of Reynolds number. 

It can be shown that the Reynolds number represents the ratio of inertial forces to viscous forces in the flow field. Flows at sufficiently low Re therefore behave as if highly viscous, with httle to no fluid acceleration possible. At the opposite extreme, high Re flows behave as if lacking viscosity. One consequence of this distinction is that very high Reynolds number flow fields may at first seem to contradict the no-slip condition, in that they seem to slip along a solid boundary exerting no shear stress. This dilemma was first resolved in 1905 with Prandtl s introduction of the boundary layer, a thin region of the flow field adjacent to the boundary in which viscous effects are important and the no-slip condition is obeyed [19-21]. 

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