Nikuradse friction factor

For turbulent flow in smooth tubes, the semiempirical Prandtl-von Karman/Nikuradse or Blasius models represent the friction factor quite well. Whether a tube is hydraulically smooth or rough depends upon... 

The reader will note that both the Karman-Nikuradse and the Colebrook equations are implicit in the friction factor and require a trial and error solution. For hand calculations, it is often simpler to use the friction factor chart. 

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. 

Despite the fact that equation (3.37) is applicable to all kinds of time-independent fluids, numerous workers have presented expressions for turbulent flow friction factors for specific fluid models. For instance, Tomita [1959] applied the concept of the Prandtl mixing length and put forward modified definitions of the friction factor and Reynolds number for the turbulent flow of Bingham Plastic fluids in smooth pipes so that the Nikuradse equation, i.e. equation (3.37) with n = 1, could be used. Though he tested the applicability of his method using his own data in the range 2000 < Reg(l — 4>f 3 — )< 10, the validity of this approach has not been established using independent experimental data. 

For turbulent fully developed flow (Re 10,000) m a sfnooth microtube, the Fanning friction factor can be calculated from the Karman-Nikuradse relation ... 

Nikuradse s conclusion on the roughness effect in the laminar region was disputed by Kandlikar [3]. It was shown that the experimental uncertainty in Nikuradse s data was of the same order as the pressure drop measurements between the two adjacent pressure taps. Experiments conducted [4] clearly show a roughness effect on friction factor and transition Reynolds number. A comprehensive summary of the research in this field is given by Kandlikar et al. [4, 5]. 

The necessary value of this friction factor is very much higher (i.e. two orders of magnitude) than would be expected from a consideration of the work of Nikuradse, indicating that much of the interfacial coupling between strand and gas above is probably due to transfer of momentum by particle migration into and out of the strand, and not by simply the flow of air over the rough surface of the strand. 

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