Fluid friction roughness effect

The empirical correlations presented above, with the exception of Eq. (6-7), apply to smooth tubes. Correlations are, in general, rather sparse where rough tubes are concerned, and it is sometimes appropriate that the Reynolds analogy between fluid friction and heat transfer be used to effect a solution under these circumstances. Expressed in terms of the Stanton number,... 

Tverherg, J.C., Effect of Surface Roughness on Fluid Friction, Flow Control, 8,11,1995. 

Extensive studies (6) have been conducted to understand the effect of pipe roughness on friction loss in turbulent flow of Newtonian fluids in rough pipes. The phenomenon of turbulent flow with non-Newtonian fluids in rough pipes, however, has received very little attention (7). 

Handbook). Nevertheless, a number of phenomena unique to micro-conduits still prevail, causing pressure drops, flow rates, and/or friction factors to differ from results obtained for macrochannels [2]. Examples include dominant entrance effects because the conduits are very short, significant surface roughness effects due to the closeness of the channel walls, earlier onset of turbulence because of induced instabilities, measurable viscous dissipation effects resulting from steep velocity gradients, possible fluid-slip on channel walls depending upon the physical-chemical characteristics of the (coated) surfaces, and significant effects of low-level forces usually not relevant in macro-devices, such as surface tension and electrostatics. 

The following analysis enables one to calculate the diameter of a pipeline transporting any compressible fluid. The required inputs are volumetric flow rate, the specific gravity of the gas relative to air, flow conditions, compressibility factor Z where Z is defined by nZRT = PV, the pressure at the point of origin and the destination, the pipe length, and pipe constants such as effective roughness. The working equations have been obtained from the literature. Since the friction factor... 

Judy J, Maynes D, Webb BW (2002) Characterization of frictional pressure drop for liquid flows through micro-channels. Int J Heat Mass Transfer 45 3477-3489 Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 Koo J, Kleinstreuer C (2004) Viscous dissipation effects in microtubes and microchannels. Int J Heat Mass Transfer 47 3159-3169... 

More complex equations have been developed for the flow of power-law fluids under turbulent flow in pipes [85,86,90], The foregoing applies to smooth pipes. Surface roughness has little effect on the friction factor for laminar flow, but can have a significant effect when there is turbulent flow [85],... 

Neglecting end effects, i.e. I cl. the pressure drop per unit length of pipe due to friction px—p jl = Apt/1, will be a function of the pipe diameter d, the surface roughness e, average flow velocity it across the cross-section, and fluid density p and viscosity p (Figure 2). 

Die thermal conductivity k for use in the Nu relations above should be evaluated at the bulk mean fluid temperature, which is the arithmetic average of the mean fluid temperatures at the inlet and the exit of the tube. For laminar flow, the effect of suiface roughness on the friction factor and the heat transfer coefficient is negligible. 

A large body of literature is available on estimating friction loss for laminar and turbulent flow of Newtonian and non-Newtonian fluids in smooth pipes. For laminar flow past solid boundaries, surface roughness has no effect (at least for certain degrees of roughness) on the friction pressure drop of either Newtonian or non-Newtonian fluids. In turbulent flow, however, die nature... 

There are insnfficient data in the literatnre to provide a reliable estimate of the effect of roughness on friction loss for non-Newtonian flnids in tnrbnlent flow. However, the influence of roughness is normally neglected, since the laminar bonndary layer thickness for such fluids is typically much larger than for Newtonian fluids (i.e., the flow conditions most often fall in the hydraulically smooth range for common pipe materials). An expression by Darby et al. (1992) for / for the power law flnid, which applies to both laminar and turbulent flow, is... 

In microreactors, the friction factor is not independent of wall surface roughness. Moreover, molecular interaction with the walls increases relative to intermolecular interactions when compared to macro-scale flows. In macro-scale systems, two boundary conditions will be applied, that is, a no-slip-flow in which the fluid next to the wall exhibits the velocity of the fluid normally being zero in the most common conditions, and a slip flow in which the velocity of the fluid next to the wall is not zero, and is affected by the wall friction effects and shear stress at the wall. In the case of the slip-flow conditions, a significant reduction in the friction pressure drop and thus reducing the power consumption required to feed the fluid into the microchannel reactor. For most cases in microreactors, the = 0.1 continuum flow with slip boundary conditions is applied. In addition, the pressure drop inside the microreactor is minimal in comparison to that of macro-scale systems (Hessel et ai, 2005b). 

Loss of energy in water due to frictional resistance at the static-bed surface arises within the (laminar or the turbulent) boundary layer. For nonbreaking waves, this is essentially the only mechanism that operates at the bed surface, and its magnitude depends on how rough the surface is. All other mechanisms are effective within the bed, and therefore require descriptions of dissipation that depend on the state (continuum or two-phased particle-water mixture, solid, or fluid) of the bottom. Several basic rheological models are available to predict ki (Table 27.1). 

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