At pipe wall

Rr Shear stress at pipe wall in fluid within bed N/m2 ML- T ... 

Flow dynamics predict that flow through a pipe is nonuniform with regard to velocity across the diameter of a pipe, for instance. The flow at pipe walls is assumed to be zero. In our idealized biochemical reactor, this concept is represented by a boundary layer in contact with the biofilm. It does not have, of course, a discrete dimension. Rather, it is represented as an area in the structure that has reduced flow and therefore different kinetics than what we would assume exist in a bulk liquid. The boundary layer is affected by turbulence and temperature and this is unavoidable to a degree. Diffusion within the boundary layers is controlled by the chemical potential difference based on concennation. Thus the rate of transfer of pollutant to the organisms is controlled by at least two physical chemical principles, and these principles differentiate an attached growth bioreactor from a suspended growth bioreactor. 

T Shear stress, N/m or Ib /ft at pipe wall Tq, threshold stress in... 

Fig. 8.4 Thickness dependence of clean layer of liquid at pipe wall on volume concentration of particles.

As velocity continues to rise, the thicknesses of the laminar sublayer and buffer layers decrease, almost in inverse proportion to the velocity. The shear stress becomes almost proportional to the momentum flux (pk ) and is only a modest function of fluid viscosity. Heat and mass transfer (qv) to the wall, which formerly were limited by diffusion throughout the pipe, now are limited mostly by the thin layers at the wall. Both the heat- and mass-transfer rates are increased by the onset of turbulence and continue to rise almost in proportion to the velocity. 

Piping supports, guides, and anchors increase local stresses on the pipe wall at the point of attachment. These stresses derive from continuously acting loads owing to the weight of the piping system carried at these points (pipe, contents, insulation), the pressure in the pipe, and any other loads such... 

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 ... 

For steady-state laminar flow of any time-independent viscous fluid, at average velocity V in a pipe of diameter D, the Rabinowitsch-Mooney relations give a general relationship for the shear rate at the pipe wall. 

In annular flow, liquid flows as a thin film along the pipe wall and gas flows in the core. Some liquid is entrained as droplets in the gas core. At veiy high gas velocities, nearly all the liquid is entrained as small droplets. Inis pattern is called spray, dispersed, or mist flow. 

FIG. 10-18 Square -edged or sharp-edged orifices. The plate at the orifice opening must not be thicker than one-thirtieth of the pipe diameter, one-eighth of the orifice diameter, or one-fourth of the distance from the pipe wall to the edge of the opening, (a ) Pipe-line orifice, (h ) Types of plates. 

Because of low thermal conductivity, temperature gradients through the pipe wall may he siihstantial. Tabulated limits apply where more than half the wall thickness is at or above the stated temperature. 

Internal surfaces were moderately tuberculated (Fig. 3.14). Extremely thick, hard magnetite shells capped large internal cavities (Fig. 3.9). Pipe cross-sectional area was reduced by at least 30% in some places. Tubercles were aligned with flow, indicating that growth occurred during service. No failure occurred, and deepest metal loss was only 0.093 in. (0.033 cm) from the nominal pipe wall thickness of 0.225 in. (0.572 cm). 

For efficient current distribution, steel-reinforced concrete walls should be provided at the wall entrance of pipes and at least 1 m around them and up to the soil surface with at least 2 mm thick electrically insulating layers of plastic or bitumen. This is also recommended if the pipelines are laid in soil parallel to steel-reinforced concrete foundations and the closest spacing is smaller than twice the pipe diameter or smaller than 0.5 m [2]. 

Fig. 12-5 Voltage cone AU and pipe/soil potentials at a wall entrance in a steel-reinforced concrete foundation.

Within 2 years the pipe/soil potential immediately at the wall entrance of the pipeline changed from f/cu-cuS04 = -0.45 V to -0.7 V. Favorable potential values at these points are to be expected if the foundations have insulating coatings. 

Structures or pits for water lines are mostly of steel-reinforced concrete. At the wall entrance, contact can easily arise between the pipeline and the reinforcement. In the immediate vicinity of the pit, insufficient lowering of the potential occurs despite the cathodic protection of the pipeline. Figure 12-7 shows that voltage cones caused by equalizing currents are present up to a few meters from the shaft. With protection current densities of 5 mA mr for the concrete surfaces, even for a small pit of 150 m surface area, 0.75 A is necessary. A larger distribution pit of 500 m requires 2.5 A. Such large protection currents can only be obtained with additional impressed current anodes which are installed in the immediate vicinity of the pipe entry into the concrete. The local cathodic protection is a necessary completion of the conventional protection of the pipeline, which would otherwise be lacking in the pit. 

Flow distribution in a packed bed received attention after Schwartz and Smith (1953) published their paper on the subject. Their main conclusion was that the velocity profile for gases flowing through a packed bed is not flat, but has a maximum value approximately one pellet diameter from the pipe wall. This maximum velocity can be 100 % higher than the velocity at the center. To even out the velocity profile to less than 20 % deviation, more than 30 particles must fit across the pipe diameter. 

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