Turbulent flow rough surfaces

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. 

This formula is another variation on the Affinity Laws. Monsieur s Darcy and VVeisbach were hydraulic civil engineers in France in the mid 1850s (some 50 years before Mr. H VV). They based their formulas on friction losses of water moving in open canals. They applied other friction coefficients from some private experimentation, and developed their formulas for friction losses in closed aqueduct tubes. Through the years, their coefficients have evolved to incorporate the concepts of laminar and turbulent flow, variations in viscosity, temperature, and even piping with non uniform (rough) internal. surface finishes. With. so many variables and coefficients, the D/W formula only became practical and popular after the invention of the electronic calculator. The D/W forntula is extensive and eomplicated, compared to the empirieal estimations of Mr. H W. 

Dissolution is uniform (etching) otherwise, for rough surfaces such as pitting, turbulent flow regimes may occur even at low solution velocities. 

For turbulent flow, Rmjpit is almost independent of velocity although it is a function of the surface roughness of the channel. Thus the resistance force is proportional to the square of the velocity. Rm/pu2 is found experimentally to be proportional to the one-third power of the relative roughness of the channel surface and may be conveniently written as ... 

The transition to turbulent flow occurred at Re of about 1,500. The authors noted that for smaller micro-channels, the flow transition would occur at lower Re. The early transition phenomenon might be affected by surface roughness and other factors. 

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. 

A stringent requirement for PF, nearly in accordance with fluid mechanics, is that it be fully developed turbulent flow. For this, there is a minimum value of Re that depends on D and on e, surface roughness ... 

Keulegan (K13) applied the semiempirical boundary-layer concepts of Prandtl and von K arm an to the case of turbulent flow in open channels, taking into account the effects of channel cross-sectional shape, roughness of the wetted walls, and the free surface. Most of the results are applicable mainly to deep rough channels and bear little relation to the flow of thin films. 

Keulegan (Kl3), 1938 Extension of Prandtl-von KdrmSn turbulent flow theories to turbulent flow in open channels. Effects of wall roughness, channel shape, and free surface on velocity distribution are considered. 

El. Eckert, E. R. G., Diaguila, A. J., and Donoughe, P. L., Experiments on turbulent flow through channels having porous rough surfaces with or without air injection. NACA Tech. Note 3339 (1955). 

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],... 

At low velocities between the metal and the solution, the solution flow is laminar, while at high velocities it is turbulent. The transition velocity depends on the geometry, flow rate, liquid viscosity, and surface roughness. The Reynolds number accounts for these effects and predicts the transition from laminar to fluid turbulent flow. The Reynolds number is the ratio of convective to viscous forces in the fluid. For pipes experiencing flow parallel to the centerline of the pipe (4,8) ... 

The transition from laminar to turbulent flow depends on the surface geometry, surface roughness, upstream velocity, surface temperature, and the type of fluid, among other things, and is best characterized by the Reynolds number. The Reynolds number at a distance x from the leading edge of a flat plate... 

For turbulent flow, surface roughness may cause the friction coefficient to increase sevetalfold. 

C What is the effect of surface roughness on the friction drag coefficient in laminar and turbulent flows ... 

It certainly is desirable to have precise values of Reynolds numbers for laminar, tran.sitional, and turbulent flows, but this is not the case in practice. This is because the transition from laminar to turbulent flow also depends on the degree of dislurbatice of the flow by surface roughness, pipe vibrations, and the fluctuations in the flow. Under most practical conditions, the flow in a tube is laminar for Re < 2300, fully turbulent for Re > 10,000, and transitional in between. But it should be kept in mind that in many cases the flow becomes fully turbulent for Re > 4000, as discussed in the Topic of Special Interest later in this chapter. Wlien designing piping networks and determining pumping power, a conservative approach is taken and flows with Re > 4000 are assumed to be turbulent. 

In practice, it is found convenient to express the pressure loss for all types of fully developed internal flosvs (laminar or turbulent flows, circular or noncLrcu-lar pipes, smooth or rough surfaces, horizontal or inclined pipes) as (Fig. 8-19)... 

FIGURE 8-19 The relation for pressure loss (and head loss) is one of the most general relations in fluid mechanics, and it is valid for laminar or turbulent flows, circular or noncircular tubes, and pipes with smooth or rough surfaces. 

Any iiregiilarily or roughness on the surface disturbs- the laminar sublayer, and affects the flow. Therefore, unlike laminar flow, the friction factor and the convection coefficient in turbulent flow are strong functions of surface roughness. 

Tubes with rough surfaces have much higher heat transfer coefficients than tubes with smooth surfaces. Therefore, tube surfaces are often intentionally roughened, corrugated, or filmed in order to enhance the convection heat iraiisier coefficient and thus the convection heat transfer rate (Fig. 8-28). Heat transfer in turbulent flow in a lube has been increased by as much as 400 percent by roughening the surface. Roughening the surface, of course, also increases the friction factor and thus the power requirement for the pump or the fan. 

A model to account for roughness in a BSR may be derived from Eq. (7). The part of Eq. (7) within parentheses represents the universal velocity profile for turbulent flow along hydraulically smooth surfaces. For nonsmooth surfaces, the same expression for the velocity profile has been proved experimentally to be adequate, but then the second constant is smaller than 5.5 the first constant, 2.5, appears not to depend on the surface roughness. From this it can be made plausible that the roughness in rod bundles could be described with an empirical roughness function, R(h ), implemented in Eq. (7) ... 

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