Fluid flow short lines

Steffe et al. (1984) determined magnitudes of the coefficient of for a fully open plug valve, a tee with flow from line to branch, and a ninety degree short elbow as a function of GRe using apple sauce as the test fluid. They found that, as for Newtonian fluids, kf increases with decreasing values of GRe. The regression equations for the three fittings were ... 

The tracer method is the most accurate technique to measure fluid velocity. The method is well developed for fluid flows (Somerscales, 1981). It involves use of light-sensitive particles mixed with the fluid, an optical source of illumination, and a detection system. But for solid/liquid and solid/gas flows, a better approach is to use radioactive tracers. Typically, the tracers are low-level, short-lived radioactive particles that can be either introduced manually or generated on line by a neutron source. Both methods will be described latter in this chapter. 

If solids are carried in the fluid, this can present a difficult problem if they are not properly flushed from the pump on shutdown. Some spare or second pumps are selected for 100 percent spare others are selected so that each of two pumps operate in parallel on 50 percent of the flow, with each being capable of handling 67 to 75 percent of total load if one pump should fall off the line. This tlten only reduces production by about 25 percent for a short period, and is acceptable in many situations. These pumps are usually somewhat smaller than the full size spares. 

Figure 1.25 shows the boundary layer that develops over a flat plate placed in, and aligned parallel to, the fluid having a uniform velocity upstream of the plate. Flow over the wall of a pipe or tube is similar but eventually the boundary layer reaches the centre-line. Although most of the change in the velocity component vx parallel to the wall takes place over a short distance from the wall, it does continue to rise and tends gradually to the value vx in the fluid distant from the wall (the free stream). Consequently, if a boundary layer thickness is to be defined it has to be done in some arbitrary but useful way. The normal definition of the boundary layer thickness is that it is the distance from the solid boundary to the location where vx has risen to 99 per cent of the free stream velocity v . The locus of such points is shown in Figure 1.25. It should be appreciated that this is a time averaged distance the thickness of the boundary layer fluctuates owing to the velocity fluctuations.

Thus in the neighborhood of hyperbolic points the distance between fluid particles, or the length of material lines, grows exponentially in time that would lead to efficient mixing. However, since the fluid elements are quickly ejected from the vicinity of these isolated points they only have a short term transient effect with little influence on the global mixing properties of the flow. 

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