Annulus, fluid flow turbulent

The situation is often encountered in which a fluid flows through a conduit having a noncircular cross section, such as an annulus. The heat-transfer coefficients for turbulent flow can be determined by using the same equations that apply to pipes and tubes if the pipe diameter D appearing in these equations is replaced by an equivalent diameter De. Best results are obtained if... 

In order to predict Lhe transition point from stable streamline to stable turbulent flow, it is necessary to define a modified Reynolds number, though it is not clear that the same sharp transition in flow regime always occurs. Particular attention will be paid to flow in pipes of circular cross-section, but the methods are applicable to other geometries (annuli, between flat plates, and so on) as in the case of Newtonian fluids, and the methods described earlier for flow between plates, through an annulus or down a surface can be adapted to take account of non-Newtonian characteristics of the fluid. 

Annulus. From the drill pipe, the drilling fluid is jetted out of the bit nozzles and into the annulus. The jets are designed to remove drilled cuttings away from the drill bit. The pressure drop across the nozzles accounts for about 60% of the total frictional pressures losses during the circulation of the drilling fluid. About 90% of the pressure drop across the nozzles is due to the turbulence at the outlet, with only about 10% due to the flow through the nozzles. 

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