Reynolds number effect, smooth

However, the two mechanisms interact and molecular diffusion can reduce the effects of convective dispersion. This can be explained by the fact that with streamline flow in a tube molecular diffusion will tend to smooth out the concentration profile arising from the velocity distribution over the cross-section. Similarly radial dispersion can give rise to lower values of longitudinal dispersion than predicted by equation 4.39. As a result the curves of Peclet versus Reynolds number tend to pass through a maximum as shown in Figure 4.6. 

Semenov (S6) considered generally the effects of a gas drag at the film interface for all the cases listed above for smooth laminar film flow (see Section III, F, 2), and later experimental work confirmed these results (K20, K10, S7) for the case when the film thickness is very small, with no waves present on the film surface, and at moderate gas flow rates. The early treatment by Nusselt (N6, N7) also gave results in agreement with the experimental data obtained under these restricted conditions. Brauer s treatment of the problem (Section III, F, 2) (Bl8) also assumed laminar flow of the film and absence of surface waves. The experimental work of Feind (F2), which refers to countercurrent gas/film flow in a vertical tube, showed that, although such a treatment was useful in predicting the qualitative effects of the gas stream on the film thickness and other properties, the Reynolds number range in which it applied strictly was very limited. 

The constants in this relation will be different for different critical Reynolds numbers. Also, the surfaces are assumed to be smooth, and the free stream to be turbulent free. For laminar flow, the friction coefficient depends on only the Reynolds number, and the surface roughness has no effect. For turbulent flow, however, surface roughness causes the friction coefficient to increase sevcralfold, to the point that in fully turbulent regime the friction coefficient is a function of surface roughness alone, and independent of the Reynolds number (Fig. 7-8). Tliis is also the case in pipe flow. 

Note that the surface roughnesses associated with smooth stone, galvanized steel, and painted surfaces are hydraulically smooth, that is they should have no substantial effects on boundary profiles and hence deposition velocity. Between 0.33 and 3mm, transition from laminar to turbulent flow may occur, depending on the Reynolds number. 

Heat Transfer. The Stanton number over a rough surface behaves similarly to the skin friction coefficient at sufficiently high roughness Reynolds numbers k+, the Stanton number becomes independent of the free-stream velocity. At a given Re or Res, roughness causes an increase in local Stanton number over the smooth-plate value. These effects are shown in Fig. 6.48 for five values of the free-stream velocity. The geometry of the rough surface used in these experiments was the densest array of spheres of radius r as shown in Fig. 

Tube Bundles. The average heat transfer coefficient in a bundle of finned tubes is influenced by both vapor shear and condensate inundation, although the effects are not as large as for smooth tubes [88,102-107]. At low vapor velocities, Webb and Murawski [107] express the local coefficient for the Mh row in terms of the local film Reynolds number ... 

Figures 14 and 15 show the normalized pressure drop factor for a densely packed bed of monosized spherical particles. For Rem < 7,fv is fairly independent of Rern, and at high Rem values, it increases fairly linearly with Rem. The data points are the experimental results taken from Fand et al. (110), where the bed diameter is D = 86.6 mm and the particle diameter is ds = 3.072 mm. One can observe that the 2-dimen-sional model of Liu et al. (32), referred to as equation 107, agrees with the experimental data fairly well in the whole range of the modified Reynolds number. From Figure 14, one observes a smooth transition from the Darcy s flow to Forchheirner flow regime. The one-dimensional model of Liu et al. (32) (i.e., equation 106) showed only slightly smaller fv value. Hence, the no-slip effect or two-dimensional effect for this bed is small. As shown in Figures 14 and 15, the Ergun equation consistently underpredicts the pressure drop. The deviation becomes larger when flow rate is increased.

The ANSI values do not consider the effect of velocity on the drag coefficient, which is a function of the Reynolds number. If the drag coefficient is considered, the ANSI values are conservative with a safety factor of about 2 to 3 depending on the smoothness of the vessel. 

Huid turbulence has had many descriptions. It is random, chaotic, dissipative, and multiple scaled. The turbulent flows describable by the Navier- tokes equations present these properties when the nonlinear terms, which represent the convective effect of fluid motion, become relatively large compared with the other terms, such as the viscous forces. The Re5molds number can be regarded as one such measure for the ratio. At small Reynolds numbers, or when the viscous effects dominate the nonlinearity in the system, the solutions of the Navier-Stokes equations are regular and smooth, a state commonly referred to... 

For turbulent flow, the thermal entrance region is shorter than for laminar flow (with the exception of liquid metals which have a very low Prandtl number), and thus the fully developed values of the Nusselt number are frequently used directly in heat transfer design without reference to the thermal entrance effects. The turbulent fully developed Nusselt number in a smooth channel can be expressed as a function of the Reynolds number and of the Prandtl number. 

The transitions observed at lower Reynolds numbers are due to the presence of roughness on the wall surface. In order to smdy the effect of roughness on transition to turbulence, a systematic experimental study was conducted by Kandlikar et al. [7]. A test fixture was developed with 10 mm-wide channels and an adjustable gap to allow for different channel sizes. The two side walls were removable, and different surface features could be machined on them. For smooth channels, the transition was noted to occur between Rej = 2,300 and Rej = 2,500. Different roughness features were introduced by machining ridges onto the walls. As the relative... 

Ward Smith reported the experimental observation of flow through smooth pipe bends of circular-arc curvature [43], The effects of bend angle, radius ratio, cross-sectional shape and Reynolds number also were examined. 

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