Reynolds number wall roughness

For smooth pipe, the friction factor is a function only of the Reynolds number. In rough pipe, the relative roughness /D also affects the friction factor. Figure 6-9 plots/as a function of Re and /D. Values of for various materials are given in Table 6-1. The Fanning friction factor should not be confused with the Darcy friction fac tor used by Moody Trans. ASME, 66, 671 [1944]), which is four times greater. Using the momentum equation, the stress at the wall of the pipe may be expressed in terms of the friction factor ... 

The friction factor depends on the Reynolds number and duct wall relative roughness e/D, where e is the average height ol the roughness in rhe duct wall. The friction factor is shown in Fig. 9.46. For a Urge Reynolds number, the friction factor / is considered constant for rough pipe surfaces. The friction pressure loss is Ap c. ... 

Friction factor Describes the relationship between the wall roughness, Reynolds number, and pressure drop per unit length of duct or pipe run. 

Flow of the liquid past the electrode is found in electrochemical cells where a liquid electrolyte is agitated with a stirrer or by pumping. The character of liquid flow near a solid wall depends on the flow velocity v, on the characteristic length L of the solid, and on the kinematic viscosity (which is the ratio of the usual rheological viscosity q and the liquid s density p). A convenient criterion is the dimensionless parameter Re = vLN, called the Reynolds number. The flow is laminar when this number is smaller than some critical value (which is about 10 for rough surfaces and about 10 for smooth surfaces) in this case the liquid moves in the form of layers parallel to the surface. At high Reynolds numbers (high flow velocities) the motion becomes turbulent and eddies develop at random in the flow. We shall only be concerned with laminar flow of the liquid. 

All models for turbulent flows are semiempirical in nature, so it is necessary to rely upon empirical observations (e.g., data) for a quantitative description of friction loss in such flows. For Newtonian fluids in long tubes, we have shown from dimensional analysis that the friction factor should be a unique function of the Reynolds number and the relative roughness of the tube wall. This result has been used to correlate a wide range of measurements for a range of tube sizes, with a variety of fluids, and for a wide range of flow rates in terms of a generalized plot of/ versus /VRe- with e/D as a parameter. This correlation, shown in Fig. 6-4, is called a Moody diagram. 

At high Reynolds numbers (high turbulence levels), the flow is dominated by inertial forces and wall roughness, as in pipe flow. The porous medium can be considered an extremely rough conduit, with s/d 1. Thus, the flow at a sufficiently high Reynolds number should be fully turbulent and the friction factor should be constant. This has been confirmed by observations, with the value of the constant equal to approximately 1.75 ... 

Turbulent flow of Newtonian fluids is described in terms of the Fanning friction factor, which is correlated against the Reynolds number with the relative roughness of the pipe wall as a parameter. The same approach is adopted for non-Newtonian flow but the generalized Reynolds number is used. 

In this correlation, the material properties are evaluated at the melting temperature. The left hand side of the correlation is the dimensionless minimum melt superheat. The right hand side of the correlation is also dimensionless, and represents a combination of the Prandtl number, Euler number, Reynolds number and Nusselt number, as well as temperature and length ratios TJTG and l0/d0. The correlation is accurate within 10%. In addition, considering the effects of the surface roughness of nozzle wall, the pre-basal coefficient in the regression expression has been increased by 25% in order to predict a safe estimate of the minimum melt superheat. 

The simplified flow analysis of Weibefs model A indicates undeveloped flow with a flat profile in the trachea for Reynolds numbers up to approximately 2,000. However, this does not consider disturbances produced by the rough walls, the eccentricity of the cross section, and the larynx. 

As might be expected, the dispersion coefficient for flow in a circular pipe is determined mainly by the Reynolds number Re. Figure 2.20 shows the dispersion coefficient plotted in the dimensionless form (Dl/ucI) versus the Reynolds number Re — pud/p(2Ai). In the turbulent region, the dispersion coefficient is affected also by the wall roughness while, in the laminar region, where molecular diffusion plays a part, particularly in the radial direction, the dispersion coefficient is dependent on the Schmidt number Sc(fi/pD), where D is the molecular diffusion coefficient. For the laminar flow region where the Taylor-Aris theory18,9,, 0) (Section 2.3.1) applies ... 

S based on experiments with water in turbulent flow, in channels icient roughness that there is no Reynolds number effect. The hydraulic radius approach may be used to estimate a friction factor with which to compute friction losses. Under conditions of uniform flow where liquid depth and cross-sectional area do not vary significantly with position in the flow direction, there is a balance between gravitational forces and wall stress, or equivalently between frictional fosses and potential energy change. The mechanical energy balance reduces to tv = g(zx — z2). In terms of the friction factor and hydraulic diameter or hydraulic radius,... 

Charts and equations describing the variation of the friction factor, /, with the Reynolds number, Rep, and wall roughness ratio, elD, where e is a measure of the roughness of the walls, are available [18],[19], [20]. A Moody chart that gives the friction factor variation is shown in Fig. 7.4. 

Water flows in a 3.0-cm-diameter tube having a relative roughness of 0.002 with a constant wall temperature of 80°C. If the water enters at 20°C, estimate the convection coefficient for a Reynolds number of 10s. 

Determine the type of flow that exists. Flow is laminar (also termed viscous) if the Reynolds number Re for the liquid in the pipe is less than about 2000. Turbulent flow exists if the Reynolds number is greater than about 4000. Between these values is a zone in which either condition may exist, depending on the roughness of the pipe wall, entrance conditions, and other factors. Avoid sizing a pipe for flow in this critical zone because excessive pressure drops result without a corresponding increase in the pipe discharge. 

Figure 4 shows the experimentally determined friction factor as a function of the Reynolds number for a laboratory PPR module with six 4-mm-thick catalyst slabs of 68-mm width and 500-mm height, spaced apart with a pitch of 11 mm, and made up from 2.2-mm-diameter glass spheres enclosed in 0.5-mm gauze mesh [6]. It can be seen that the transition of laminar to turbulent flow occurs already at a low Reynolds number (approximately 1(XX)), which is attributable to the roughness of the channel walls caused by the wire gauze. 

As discussed before, the transition from laminar to turbulent flow in the PPR channels already occurs at relatively low Reynolds number as a consequence of the roughness of the channel walls. Under typical operating conditions in practice, flow through the channels is quite turbulent, in contrast to the situation generally prevailing in monoliths as used in exhaust convertors, where due to the much smaller channel diameter and smoothness of the wall, flow is generally laminar. Therefore, in a PPR mass transfer in the gas inside the channel is generally relatively fast. 

An important point is that these results have been obtained with bundles of smooth rods, as used in heat exchangers and nuclear reactors. In circular tubes, especially the completion Reynolds number depends strongly on the relative wall roughness. Consequently, for a BSR containing strings of catalyst particles, at least the completion Reynolds numbers and probably also the onset Reynolds numbers are lower than mentioned above. 

The interface boundary inside the chaimel is shown on figures 4 and 5 as a function of the liquid Reynolds number. At large liquid flow rate the considerable part of the liquid flows in the corners and the film is thinned both on the long and short sides of the channel. This enhances the heat transfer in comparison with uniform film. At small liquid Reynolds numbers the minimum film thickness becomes the same as the wall roughness and film rupture occurs leading to stable rivulet flow. Dry areas exist on the wall, which are not wetted by liquid. This reduces the heat transfer. The... 

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