Parallel piped

Water is pumped at 1.4 m3/s from a tank at a treatment plant to a tank at a local works through two parallel pipes, 0.3 m and 0.6 m diameter respectively. What is the velocity in each pipe and, if a single pipe is used, what diameter will be needed if this flow of water is to be transported, the pressure drop being the same Assume turbulent flow, with the friction factor inversely proportional to the one quarter power of the Reynolds number. 

A condenser consists of 30 rows of parallel pipes of outer diameter 230 mm and thickness 1.3 mm, with 40 pipes, each 2 m long, per row. Water, inlet temperature 283 K, flows through the pipes at 1 m/s, and steam at 372 K condenses on the outside of the pipes. There is a layer of scale 0.25 mm thick, of thermal conductivity 2.1 W/m K. on the inside of the pipes. 

Two-phase flow in parallel pipes, fed from a common manifold, displays interesting phenomena, as two phases may split unevenly when entering the parallel piping. Ozawa et al. (1979, 1989) performed experimental smdies on two-phase flow systems in parallel pipes of 3.1 mm diameter. They simulated the flow in boiling channels by injection of air and water into the pipes. 

Tshuva M, Bamea D, Taitel Y (1999) Two-phase flow in inclined parallel pipes. Int J Multiphase Flow 25 1491-1503... 

Simpler optimization problems exist in which the process models represent flow through a single pipe, flow in parallel pipes, compressors, heat exchangers, and so on. Other flow optimization problems occur in chemical reactors, for which various types of process models have been proposed for the flow behavior, including well-mixed tanks, tanks with dead space and bypassing, plug flow vessels, dispersion models, and so on. This subject is treated in Chapter 14. 

The optimal diameter sizes, thicknesses, and lengths of any required parallel pipe loops on each arc of the network... 

The relatively new technique of laser scanning confocal microscopy enabled the determination of the number of gap junctions within one disk to be in the order of 50 or even more [Gourdie et al., 1990] with a diameter of up to 1.3 pm/gap junction. Within the gap junction the channels themselves are arranged as parallel pipe-like structures. From freeze-fractured junctions it has been estimated that about 12.9 103 channels are located in 1 pm2 gap junction (rat right ventricular myocardium) [Chen et al., 1989]. 

After filling a mold in the form of a thin rectangular parallel pipe, a reactive mass can be represented by a layer of width H and length L (H < < L). This layer is positioned between the mold wall at temperature Tm, and the surface of the item is at temperature Ti (Fig. 4.14). 

In the case of a-K2Cr04, the estimation was carried out on a crude assumption that the interatomic charge could be assigned equally to the Cr and the four O atoms. Staudenmann et al. (69) have proposed a different method to define the effective region of an atom, where an atomic region is represented by an assembly of many small parallel piped volume elements for computational convenience. This method may enable us to define the effective atomic region more precisely for covalent molecules. From a practical point of view, however, it seems to be difficult to define an exact atomic region in this way. 

Two parallel pipes 5 cm and I0 cm in diameter are totally surrounded by loosely packed asbestos. The distance between centers for the pipes is 20 cm. One pipe carries steam at l I0°C while the other carries chilled water at 3°C. Calculate the heat lost by the hot pipe per unit length. 

A row of 10 parallel pipes that are 5 m long and have tin outer diameter of 6 cm are used to transport steam at 145°C through the concrete floor (k = 0.75 W/ui °C) of a 10-m X 5-m room that is maintained at 20°C. The combined convection and radiation heal transfer coefficient at the floor is 12 W/m °C. If the surface temperature of the concrete floor is not to exceed 35°C, determine how deep the steaip pipes should be buried below the surface of the concrete floor. 

The pressure in the preheat train is maintained high, perhaps 500 psi, to prevent vaporization, because the flow must distribute accurately among parallel piping as it passes through the preheat furnace. 

Foams are fluids that depend on shear history. The texture of a foam will reach an equilibrium state at a particular shear rate. Finer textured, more dynamically stable foams are produced at high shear rates, higher pressure, and with higher quantities of surfactant (36). Reidenbach et al. (11) observed that at higher shear rates, finer more uniform bubbles were created. This information indicates that at downhole conditions during fracture stimulation when conditions of high pressure and shear are present, foams are finely textured with parallel-piped uniform bubbles. 

In the absence of a catalyst the reaction is often immeasurably slow, = Oj then, v = The rate is usually proportional to the concentration of the catalyst. The analogy to an electrical network of parallel resistances (Fig. 32.11a) or to parallel pipes carrying a fluid (Fig. 32.11b) is apparent. In each case the flow through the network is the sum of that passing through each branch. 

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