Roughness flows

For commercial steel pipe, with a roughness of 0.046 mm, the friction factor for fully rough flow is about 0.0047, from Eq. (6-38) or Fig. 6-9. It remains to be verified that the Reynolds number is sufficiently large to assume fully rough flow. Assuming an abrupt entrance with 0.5 velocity heads lost,... 

This equation represents the change-over section between a smooth tube and a fully developed rough flow. 

There are two kinds of convective flow. The kind dealt with here is called laminar, which means smooth or honeylike in flow. There is another kind that is much more difficult to deal with theoretically this is turbulent flow, the kind of rough flow that occurs at waterfalls. 

Surface roughness Flow ability, segregation potential, dilution potential, lubricant sensitivity... 

At the beginning of the pipe, the temperature is greater, giving greater viscosity and a Reynolds number of 3.6 x 10. Over the entire pipe length the Reynolds number is very large and the fully rough flow friction factor choice was indeed valid. 

Suggested rough flow diagram showing extraction process for fish-oil recovery. (Details are not included and changes may be necessary.)... 

It was natural to expect from the very beginning that a real turbulent penetrable roughness flow of any kind is associated with a number of vortices shed from individual obstructions within the PR. The visualization of such a flow has been shown in Fig. 1.18. A number of vortices born within the PR can brake up or coalesce during their spreading down and diffuse into external boundary layer. Figures 3.29,A and B display this expected behaviour. This should result in the especially intense mixing of any properties. However, the real behaviour of vortices turns out to be somewhat... 

Figure 8.8 Skimming, Interference Flow and Isolated Roughness Flow visualizations using Laser light sheet (Chang and Meroney, 2003 [111, 112]).

Heat Transfer in Rough Circular Ducts The Nusselt number for a complete, rough flow regime in a circular duct is given in Table 5.12. The term/in this table denotes the friction factor for fully rough flow. It is given by the Nikuradse [60] correlation shown in Table 5.9. The recommended equations for practical calculations are those correlations by Bhatti and Shah [45] shown in Table 5.12. 

This implicit formula is applicable for 5 < Re. < 70, spanning the transition, hydraulically smooth, and completely rough flow regimes. 

TABLE 5.12 Nusselt Numbers for Fully Developed Turbulent Flow in the Fully Rough Flow Regime of a Circular Duct [45]... 

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