Reynolds number roughness

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

Effects of surface roughness are also evident in the boundary layer mean velocity profiles shown in Fig. 6.46. The profiles still exhibit a near-wall logarithmic behavior, but with a dependence on the roughness Reynolds number k = ksu lv. The law of the wall for a rough surface may be written as... 

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. 

Boundary layer flows often are characterized by the shear velocity, u, or the roughness Reynolds number Re = u D/v, where D represents the grain size of the bed. Shear velocity is generally calculated from the law-of-the-wall equation (Schlichting 1987 Weissburg and Zimmer-Faust 1993) that relates velocity to distance above the bed. 

Slatter [4] defined Rer as the roughness Reynolds number for yield pseudoplastic slurry... 

As the Reynolds number rises above about 40, the wake begins to display periodic instabiUties, and the standing eddies themselves begin to oscillate laterally and to shed some rotating fluid every half cycle. These still laminar vortices are convected downstream as a vortex street. The frequency at which they are shed is normally expressed as a dimensionless Strouhal number which, for Reynolds numbers in excess of 300, is roughly constant ... 

For laminar flow (Re < 2000), generally found only in circuits handling heavy oils or other viscous fluids, / = 16/Re. For turbulent flow, the friction factor is dependent on the relative roughness of the pipe and on the Reynolds number. An approximation of the Fanning friction factor for turbulent flow in smooth pipes, reasonably good up to Re = 150,000, is given by / = (0.079)/(4i e ). 

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 ... 

In laminar flow,/is independent of /D. In turbulent flow, the friction factor for rough pipe follows the smooth tube curve for a range of Reynolds numbers (hydrauhcaUy smooth flow). For greater Reynolds numbers,/deviates from the smooth pipe cui ve, eventually becoming independent of Re. This region, often called complete turbulence, is frequently encountered in commercial pipe flows. The Reynolds number above which / becomes essentially independent of Re is (Davies, Turbulence Phenomena, Academic, New York, 1972, p. 37) 20[3.2-2.46ln( /D) ... 

For commercial steel pipe, with a roughness of 0.046 mm, the friction factor for fully rough flow is about 0.0047, from Eq. (6-38) or Fig. 6-9. It remains to be verified that the Reynolds number is sufficiently large to assume fully rough flow. Assuming an abrupt entrance with 0.5 velocity heads lost,... 

For commercial pipe with roughness e = 0.046 mm, the friction factor is about 0.0043. Approaching the last hole, the flow rate, velocity and Reynolds number are about one-tenth their inlet values. At Re = 16,400 the friction factor/is about 0.0070. Using an average value of/ = 0.0057 over the length of the pipe, 4/Z73D is 0.068 and may reasonably be neglected so that Eq. (6-151) may be used. With C, = 0.62,... 

The relationship between adsorption capacity and surface area under conditions of optimum pore sizes is concentration dependent. It is very important that any evaluation of adsorption capacity be performed under actual concentration conditions. The dimensions and shape of particles affect both the pressure drop through the adsorbent bed and the rate of diffusion into the particles. Pressure drop is lowest when the adsorbent particles are spherical and uniform in size. External mass transfer increases inversely with d (where, d is particle diameter), and the internal adsorption rate varies inversely with d Pressure drop varies with the Reynolds number, and is roughly proportional to the gas velocity through the bed, and inversely proportional to the particle diameter. Assuming all other parameters being constant, adsorbent beds comprised of small particles tend to provide higher adsorption efficiencies, but at the sacrifice of higher pressure drop. This means that sharper and smaller mass-transfer zones will be achieved. 

In theses equations f is the friction factor, Re the Reynolds number, and e/D is the relative roughness of the conduit. Inspection of the second equation reveals that for... 

Hence, to determine the friction factor, the input information needed is the relative roughness e/D and the Reynolds number. 

To allow for the effect of roughness one can use the results of empirical tests in ducts that have been artificially roughened with particles glued on the surface. This approach allows roughness levels to be determined as a function of the particle diameter k. The following friction factor equation has been derived for large Reynolds numbers ... 

This is an ultimate case, when the friction factor is no longer a function of the Reynolds number and is a function of roughness the pressure loss is now Ap tv", where w is the fluid velocity in the duct. The surface roughness of typical manufactured ductworks varies between the values of a theoretically fully smooth duct and an artificially roughened one. Accordingly the pressure loss varies between Ap w -w and f =/ (Re, roughness). 

Resistance factors are taken from the Moody chart, when the Reynolds number and roughness are known. 

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. ... 

Scope, 52 Basis, 52 Compressible Flow Vapors and Gases, 54 Factors of Safety for Design Basis, 56 Pipe, Fittings, and Valves, 56 Pipe, 56 Usual Industry Pipe Sizes and Classes Practice, 59 Total Line Pressure Drop, 64 Background Information, 64 Reynolds Number, R,. (Sometimes used Nr ), 67 Friction Factor, f, 68 Pipe—Relative Roughness, 68 Pressure Drop in Fittings, Valves, Connections Incompressible Fluid, 71 Common Denominator for Use of K Factors in a System of Varying Sizes of Internal Dimensions, 72 Validity of K Values,... 

Equations 2-60 and 2-61 are illustrated graphically in Figure 2-21. This chart is called a Moody diagram, and it may be used to find the friction factor, given the Reynolds number and the surface roughness. 

The Fanning friction factor (/ in the above equation) varies with Reynolds number and relative roughness of... 

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