Economic Pipe Diameter, Laminar Flow

Economic Pipe Diameter, Laminar Flow Pipelines for the transport of high-viscosity liquids are seldom designed purely on the basis of economics. More often, the size is dictated by 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-Newtonian fluids, see Skelland (Non-Newtonian Flow and Heat Transfer Chap. 7, Wiley, New York, 1967). 

Vacuum Flow When gas flows under high vacuum conditions or through very small openings, the continuum hypothesis is no longer appropriate if the channel dimension is not very large compared to the mean free path of the gas. When the mean free path is comparable to the channel dimension, flow is dominated by collisions of molecules with the wall, rather than by collisions between molecules. An approximate expression based on Brown, et al. (J. Appl. Phys., 17, 802—813 [1946]) for the mean free path is 

The Knudsen number Kn is the ratio of the mean free path to the channel dimension. For pipe flow, Kn = A/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. 

Vacuum flow is usually described with flow variables different from those used for normal pressures, which often leads to confusion. Pumping speed S is the actual volumetric flow rate of gas through a flow cross section. Throughput Q is the product of pumping speed and absolute pressure. In the SI system, Q has units of Pa-m3/s. 

The mass flow rate w is related to the throughput using the ideal gas law. 

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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... 

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. 

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