Equivalent roughness values for some commercial pipes

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Unformatted text preview: ew pipes, and the relative roughness of pipes may increase with use as a result of corrosion, scale buildup, and precipitation. As a result, the friction factor may increase by a factor of 5 to 10. Actual operating conditions must be considered in the design of piping systems. Also, the Moody chart and its equivalent Colebrook equation involve several uncertainties (the roughness size, experimental error, curve fitting of data, etc.), and thus the results obtained should not be treated as “exact.” It is usually considered to be accurate to 15 percent over the entire range in the figure. The Colebrook equation is implicit in f, and thus the determination of the friction factor requires tedious iteration unless an equation solver is used. An approximate explicit relation for f is given by S. E. Haaland in 1983 (Ref. 9) as 1 f 1.8 log 6.9 Re /D 3.7 1.11 (8-74) The results obtained from this relation are within 2 percent of those obtained from Colebrook equation, and we recommend using this relation rather than the Moody chart to avoid reading errors. In turbulent flow, wall roughness increases the heat transfer coefficient h by a factor of 2 or more [Dipprey and Sabersky (1963), Ref. 5]. The convection heat transfer coefficient for rough tubes can be calculated approximately from the Nusselt number relations such as Eq. 8–70 by using the friction factor determined from the Moody chart or the Colebrook equation. However, this approach is not very accurate since there is no further increase in h with f for f 4fsmooth [Norris (1970), Ref. 20] and correlations developed specifically for rough tubes should be used when more accuracy is desired. TABLE 8–3 Equivalent roughness values for new commercial pipes* Roughness, Material Glass, plastic Concrete Wood stave Rubber, smoothed Copper or brass tubing Cast iron Galvanized iron Wrought iron Stainless steel Commercial steel ft mm 0 (smooth) 0.003–0.03 0.9–9 0.0016 0.5 0.000033 0.01 0.000005 0.00085 0.0015 0.26 0.0005 0.00015 0.000007 0.15 0.046 0.002 0.00015 0.045 *The uncertainty in these values can be as much as 60 percent. Developing Turbulent Flow in the Entrance Region The entry lengths for turbulent flow are typically short, often just 10 tube diameters long, and thus the Nusselt number determined for fully developed turbulent flow can be used approximately for the entire tube. This simple approach gives reasonable results for pressure drop and heat transfer for long tubes and conservative results for short ones. Correlations for the friction and heat transfer coefficients for the entrance regions are available in the literature for better accuracy. r 0 Turbulent Flow in Noncircular Tubes The velocity and temperature profiles in turbulent flow are nearly straight lines in the core region, and any significant velocity and temperature gradients occur in the viscous sublayer (Fig. 8–25). Despite the small thickness of laminar sublayer (usually much less than 1 percent of the pipe diameter), the characteristics of the flow in this layer are very important since they set the stage for flow in the rest of the pipe. Therefore, pressure drop and heat transfer characteristics of turbulent flow in tubes are dominated by the very thin (r) Turbulent layer Overlap layer Laminar sublayer FIGURE 8–25 In turbulent flow, the velocity profile is nearly a straight line in the core region, and any significant velocity gradients occur in the viscous sublayer. cen58933_ch08.qxd 9/4/2002 11:29 AM Page 444 444 HEAT TRANSFER viscous sublayer next to the wall surface, and the shape of the core region is not of much significance. Consequently, the turbulent flow relations given above for circular tubes can also be used for noncircular tubes with reasonable accuracy by replacing the diameter D in the evaluation of the Reynolds number by the hydraulic diameter Dh 4Ac /p. Flow through Tube Annulus Tube Di Do Annulus Some simple heat transfer equipments consist of two concentric tubes, and are properly called double-tube heat exchangers (Fig. 8–26). In such devices, one fluid flows through the tube while the other flows through the annular space. The governing differential equations for both flows are identical. Therefore, steady laminar flow through an annulus can be studied analytically by using suitable boundary conditions. Consider a concentric annulus of inner diameter Di and outer diameter Do. The hydraulic diameter of annulus is FIGURE 8–26 A double-tube heat exchanger that consists of two concentric tubes. TABLE 8–4 Nusselt number for fully developed laminar flow in an annulus with one surface isothermal and the other adiabatic (Kays and Perkins, Ref. 14) Di /Do Nui — 17.46 11.56 7.37 5.74 4.86 3.66 4.06 4.11 4.23 4.43 4.86 4 (D2 o (Do 4Ac p Nui hi Dh k (b) Roughened surface Roughness FIGURE 8–27 Tube surfaces are often roughened, corrugated, or finned in order to enhance convection heat transfer. Do Di (8-75) and Nuo ho Dh k (8-76) For fully developed turbulent flow, the inner and outer convection coefficients are approximately equal to each other, and the tube ann...
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