Turbulent pipe flow

Vieltisch and co-workers [29] and Schmickler and co-workers [30] have recently used a ring electrode under pipe turbulent flow in order to achieve higher stationary mass transport conditions and therefore study very fast electrode kinetics (k° > 1cm s 1). 

Takami, T., K. Sudo and Y. Tomita, Flow of non-Newtonian Ruids in Curved Pipes (Turbulent Flow), JSME Int. J., 33, 476-485 (1990). 

CO2 corrosion often occurs at points where there is turbulent flow, such as In production tubing, piping and separators. The problem can be reduced it there is little or no water present. The initial rates of corrosion are generally independent of the type of carbon steel, and chrome alloy steels or duplex stainless steels (chrome and nickel alloy) are required to reduce the rate of corrosion. 

The predetonation distance (the distance the decomposition flame travels before it becomes a detonation) depends primarily on the pressure and pipe diameter when acetylene in a long pipe is ignited by a thermal, nonshock source. Figure 2 shows reported experimental data for quiescent, room temperature acetylene in closed, horizontal pipes substantially longer than the predetonation distance (44,46,52,56,58,64,66,67). The predetonation distance may be much less if the gas is in turbulent flow or if the ignition source is a high explosive charge. 

One of the most efficient implementations of the slurry process was developed by Phillips Petroleum Company in 1961 (Eig. 5). Nearly one-third of all HDPE produced in the 1990s is by this process. The reactor consists of a folded loop with four long (- 50 m) vertical mns of a pipe (0.5—1.0 m dia) coimected by short horizontal lengths (around 5 m) (58—60). The entire length of the loop is jacketed for cooling. A slurry of HDPE and catalyst particles in a light solvent (isobutane or isopentane) circulates by a pump at a velocity of 5—12 m/s. This rapid circulation ensures a turbulent flow, removes the heat of polymeriza tion, and prevents polymer deposition on the reactor walls. 

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 ). 

Here, h is the enthalpy per unit mass, h = u + p/. The shaft work per unit of mass flowing through the control volume is 6W5 = W, /m. Similarly, is the heat input rate per unit of mass. The fac tor Ot is the ratio of the cross-sectional area average of the cube of the velocity to the cube of the average velocity. For a uniform velocity profile, Ot = 1. In turbulent flow, Ot is usually assumed to equal unity in turbulent pipe flow, it is typically about 1.07. For laminar flow in a circiilar pipe with a parabohc velocity profile, Ot = 2. 

The Colebrook foriTuila (Colebrook, y. Inst. Civ. Eng. [London], II, 133-156 [1938-39]) gives a good approximation for the/-Re-( /D) data for rough pipes over the entire turbulent flow range ... 

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) ... 

Noncircular Channels Calciilation of fric tional pressure drop in noncircular channels depends on whether the flow is laminar or tumu-lent, and on whether the channel is full or open. For turbulent flow in ducts running full, the hydraulic diameter shoiild be substituted for D in the friction factor and Reynolds number definitions, Eqs. (6-32) and (6-33). The hydraiilic diameter is defined as four times the channel cross-sectional area divided by the wetted perimeter. For example, the hydraiilic diameter for a circiilar pipe is = D, for an annulus of inner diameter d and outer diameter D, = D — d, for a rectangiilar duct of sides 7, h, Dij = ah/[2(a + h)].T ie hydraulic radius Rii is defined as one-fourth of the hydraiilic diameter. 

The Knudsen number Kn is the ratio of the mean free path to the channel dimension. For pipe flow, Kn = X/D. Molecular flow is characterized by Kn > 1.0 continuum viscous (laminar or turbulent) flow is characterized by Kn < 0.01. Transition or slip flow applies over the range 0.01 < Kn < 1.0. 

For a trumpet-shaped rounded entrance, with a radius of rounding greater than about 15 percent of the pipe diameter (Fig. 6-13Z ), the turbulent flow loss coefficient K is only about 0.1 (Vennard and Street, Elementary Fluid Meehanies, 5th ed., Wiley, New York, 1975, pp. 420-421). Rounding of the inlet prevents formation of the vena eontraeta, thereby reducing the resistance to flow. 

Trumpet-shaped enlargements for turbulent flow designed for constant decrease in velocity head per unit length were found by Gibson (ibid., p. 95) to give 20 to 60 percent less friclional loss than straight taper pipes of the same length. 

Miller Internal Flow Systems, 2d ed.. Chap. 13, BHRA, Cranfield, 1990) gives the most complete information on losses in bends and curved pipes. For turbulent flow in circular cross-seclion bends of constant area, as shown in Fig. 6-14 7, a more accurate estimate of the loss coefficient K than that given in Table 6-4 is... 

Figure 6-40 shows power number vs. impeller Reynolds number for a typical configuration. The similarity to the friction factor vs. Reynolds number behavior for pipe flow is significant. In laminar flow, the power number is inversely proportional to Reynolds number, reflecting the dominance of viscous forces over inertial forces. In turbulent flow, where inertial forces dominate, the power number is nearly constant. 

The value of the Reynolds number which approximately separates laminar from turbulent flow depends, as previously mentioned, on the particular conhg-uration of the system. Thus the critical value is around 50 for a him of liquid or gas howing down a hat plate, around 500 for how around a sphere, and around 2500 for how tlrrough a pipe. The characterishc length in the dehnition of the Reynolds number is, for example, tire diameter of the sphere or of the pipe in two of these examples. 

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. 

Uneven wear in parts is often due to turbulence. Bad piping designs or poorly sized valves can cause turbulence and uneven wear in pumps. Whenever possible, use straight pipe sections before and after the pump. Uneven flow creates turbulent flow and excessive wear occurs. 

It is not recommended to place an elbow at the suction of any pump (Figure 16-2, next page). This will cause a turbulent flow into the pump. If elbows are needed on both sides of the pump, you should u.se long radius elbows with flow straighteners. You should have 10 pipes diameters before the first elbow on the suction piping (Example If the pump has a 4 inch suction nozzle, you should respect 40 inch of straight pipe before the first suction elbow.) Short radius elbows cause vibrations and pressure imbalances that to lead to wear and maintenance on the pump. 

A handy relationship for turbulent flow in eommercial steel pipes is ... 

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