Pipe flow economical diameter

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

The catalyst beds are mounted in a single reactor vessel because it is more economical than using multiple vessels. The spacing between beds is set at 1 m. The length-to-diameter aspect ratio of the vessel is 10. Because a multibed reactor must have internal piping, flow distributors, and bed supports, a multi-bed reactor vessel is more expensive than a simple vessel. We assume that each additional bed increases reactor capital cost by about 25%, as shown in Table 5.2. 

Figure 6.21 shows such a plot. It can be used to rapidly select the economic pipe diameter for laminar flow, subject to the restriction that the economic data on the line to be installed must be the same as those shown on the plot. Figure 6.21 has nomenclature similar to that of Fig. 6.13, and the comments on the latter are applicable here. Figure 6.21 also shows the economic diameter for turbulent flowJ... 

In the same way, direct costs, or variable costs, comprising mostly the costs of power for pressure drop plus costs of minor items such as repairs and maintenance, can be related to pipe size. For a given flow, the power cost decreases as the pipe size increases. Thus, direct costs decrease with pipe size. And total costs, which include fixed charges, reach aminimum at some optimum pipe size. The ultimate solution leading to the optimum economic diameter is found from the graph shown in Figure 5.5. 

Economic Pipe Diameter, Laminar Flow Pipehnes for the transport of high-viscosity liquids are seldom designed purely on the basis of economics. More often, the size is dictated oy operability considerations such as available pressure drop, shear rate, or residence time distribution. Peters and Timmerhaus (ibid.. Chap. 10) provide an economic pipe diameter chart for laminar flow. For non-Newtouiau fluids, see SkeUand Non-Newtonian Flow and Heat Transfer, Chap. 7, Wiley, New York, 1967). 

The following analysis can be used to determine economic pipe diameters for the turbulent flow of Newtonian fluids. The working expression that can be used is ... 

Piping systems should be designed for an economic flow velocity. For relatively clean fluids, a recommended velocity range where minimum corrosion can be expected is 2 to 10 fps. If piping bores exist, maximum fluid velocities may have a mean velocity of 3 fps for a 3/8-in. bore to 10 fps for an 8-in.-diameter bore. Higher flow velocities are not uncommon in situations that require uniform, constant oxygen supply to form protective films on active/passive metals. 

The bend radii of pipes should be designed to be as large as possible. A minimum of three times the pipe diameter is recommended to maintain safe, economic flow velocities. 

There were several studies of hydraulic transport in the 1950s, sparked off particularly by an interest in the economic possibilities of transportation of coal and other minerals over long distances. Newitt et al.p2) working with solids of a range of particle sizes (up to 5 fim) and densities (1180-4600 kg/m3) in a 25 mm diameter pipe, suggested separate correlations for flow with a bed deposit and tor conditions where the particles were predominantly in heterogeneous suspension. 

In the case of a venturi flow, the most economical technique for increasing cavitation intensity would be to reduce the length of venturi, but for higher volumetric flow rates there could be a limitation due to the possibility of flow instability and super-cavitation. A similar argument can be given for the enhancement in the cavitation intensity by reducing the venturi throat to pipe diameter ratio. 

Other detailed studies of line optimization are made by Happel and Jordan (Chemical Process Economics, Dekker, New York, 1975) and by Skelland (1967). The latter works out a problem in simultaneous optimization of pipe diameter and pumping temperature in laminar flow. 

Fewell, M. E., Reid, R. L., Murphy, L. M., and Hard, D. S., "First and Second Law Analysis of Steam Steadily Flowing through Constant-Diameter Pipes," Proc. 3rd Annual Conference on Systems Simulation, Economic Analysis/Solar Heating and Cooling Operational Results, pp. 712-718,... 

The preceding analysis clearly neglects a number of factors that may have an influence on the optimum economic pipe diameter, such as cost of capital or return on investment, cost of pumping equipment, taxes, and the time value of money. If the preceding development of Eq. (39) for turbulent flow is refined to include the effects of taxes and the cost of capital (or return on investment) plus a more accurate expression for the frictional loss due to fittings and bends, the result is t... 

Prepare a plot of optimum economic pipe diameter versus the flow rate of fluid in the pipe under the following conditions ... 

Nomograph for estimation of optimum economic pipe diameters with turbulent or viscous flow based on Eqs. (15) and (16). 

Economic Pipe Diameter, Turbulent Flow The economic optimum pipe diameter may be computed so that the last increment of investment reduces the operating cost enough to produce the required minimum return on investment. For long cross-country... 

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