Reynolds number and shear stress

The ratio w/t/ represents the velocity gradient in the fluid, and thus the group ifxu/d) is proportional to the shear stress in the fluid, so that (pu )j((xufd) = dup/fi) = Re is proportional to the ratio of the inertia forces to the viscous forces. This is an important physical interpretation of the Reynolds number. 

In turbulent flow with high values of Re, the inertia forces become predominant and the viscous shear stress becomes correspondingly less important. 

In steady streamline flow the direction and velocity of flow at any point remain constant and the shear stress Ry at a point where the velocity gradient at right angles to the direction 

In sti eamline flow, E is very small and approaches zero, so that ti/p determines the shear stress. In turbulent flow, E is negligible at the wall and increases very rapidly with distance from the wall. Laufer using very small hot-wire anemometere, measured the velocity fluctuations and gave a valuable account of the stracture of turbulent flow. In the operations of mass, heat, and momentum transfer, the transfer has to be effected through the laminar layer near the wall, and it is here that the greatest resistance to transfer lies. 

If the surface over which the fluid is flowing contains a series of relatively large projections, turbulence may arise at a very low Reynolds number. Under these conditions, the frictional force will be increased but so will the coefficients for heat transfer and mass iransier, and therefore turbulence is often purposely induced by this method. 

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