Turbulent Flow in Straight, Smooth Ducts, Pipes, and Tubes of Circular Cross Section

Turbulent Flow in Straight, Smooth Ducts, Pipes, and Tubes of Circular Cross Section 

In double-pipe and shell-and-tube heat exchangers, fluids flow through straight, smooth pipes and tubes of circular cross section. Many correlations have been published for the prediction of the inside-wall, convective heat transfer coefficient, /i when no phase change occurs. For turbulent flow, with Reynolds numbers, = D,G/ ji, greater than 10,000, three empirical correlations have been widely quoted and applied. The first is the Dittus-Boelter equation (Dittus and Boelter, 1930) for liquids and gases in fully developed flow (Z ,/L 60), and with Prandtl numbers, = Cp[iJk, between 0.7 and 100  

The Colburn equation (Colburn, 1931) also applies to liquids and gases and is almost idra-tical to the Dittus-Boelter equation, but is usually displayed in a j-factor form in terms of a Stanton number, = hJGCp. It is considered valid to a Prandtl number of 160  

In Section 2.5.1 of Hewitt (1992), prepared by Gnielinski, a more accurate and more widely applicable correlation is given, which accounts for tube diameter-to-tube length ratio for 0 DJL 1, and IS apphcable to Avide ranges of Reynolds and Prandtl numbers of 2,300 to 1,000,000 and 0.6 to 2,000, respectively. The correlation has a semitheoretical basis in the Prandtl analogy to skin friction in terms of the Darcy friction factor,/ ,  

The Darcy friction factor is related to the Fanning friction factor by = 4/. The application of Eq. (13.14) is made easy because all properties are evaluated at the bulk fluid conditions. However, for viscous liquids, the right-hand side is multiplied by a correction factor K, where 

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