Intermediate flow rates

In laminar flow of Bingham-plastic types of materials the kinetic energy of the stream would be expected to vary from V2/2gc at very low flow rates (when the fluid over the entire cross section of the pipe moves as a solid plug) to V2/gc at high flow rates when the plug-flow zone is of negligible breadth and the velocity profile parabolic as for the flow of Newtonian fluids. McMillen (M5) has solved the problem for intermediate flow rates, and for practical purposes one may conclude... 

Fig. 1. HEN structures for Example 1 (a) Feasible for nominal flow rate wht = 1.0 kW/K. (b) Feasible for extreme flow rate tvhi = 1 -85 kW/K. (c) Target temperature violation of 21 K with intermediate flow rate whl = 1.359 kW/K (with A7"m = 0 K). (d) Target temperature violation of 52 K with intermediate flow rate tvh) = 1.359 kW/K (with Tm = 10 K). (e) Resilient for 1.0 whl 1.85 kW/K. (f) Resilient for modified example (T 2 = 393 K).

The rate of plasma polymerization depends on the nature of the monomer gas. In addition, such parameters as flow rate, pressure, power, frequency, electrode gap and reactor configuration also strongly influence the polymerization rate for a given monomer. Generally at low flow rates there is an abundance of reactive species so the polymerization rate is limited only by the availability of monomer supply. At high flow rates, however, there is an overabundance of monomer concentration and the polymerization rate now depends on the residence time. At intermediate flow rates these two competing processes result in a maximum. This behavior is illustrated in Figure 1 for ethane, ethylene, and acetylene (11). These data also demonstrate the effect of increased unsaturation in... 

Starting Point tor—Three to Five Thlmbie-Volumes-Swept, Intermediate Flow Rates... 

At intermediate flow rates, there is a region where the experimental results are not easily reproduced. 

Figure 2 A semiquantitative representation of the change in retention of a membrane filter with flow rate due to concentration polarization (high flow-rate domain) and aggregation in the filtration cell (low flow-rate domain). Only an intermediate flow-rate window is usable for size fractionation with a minimal artifact. (Reprinted with permission from Buffle J, Perret D, and Newman M (1992) The use of filtration and ultrafiltration for size fractionation of aquatic particles, colloids and macromolecules. In Buffle J and van Leeuwen HP (eds.) Environmental Particles. lUPAC Environmental Chemistry Series, vol. 1, pp. 171-230. Chelsea, Ml Lewis Publishers Lewis Publishers, an imprint of CRC Press, Boca Raton, FL.)...

Figure 21-7 Optimum resolution (minimum plate height) occurs at an intermediate flow rate. Curves show measured plate height in gas chromatography of n-C H36 at 175 C, using N2, He, or H2 mobile phase. [From R. R. Freeman, ed.. High Resolution Gas Chromatography (Palo Alto, CA Hewlett Packard Co., 1981).)...

Electrospray ionization mass spectrometry can be carried out over a wide range of flow rates. Technically, the term electrospray can be applied to any flow rate (it refers to the method of ionization), but additional terms have been coined to describe low-flow electrospray. Microspray describes electrospray conducted at intermediate flow rates ( 0.1-10pL/ min), and nanospray refers to very low flow electrospray (typically < lOOnL/min). 

Develop a plot that provides the work required to liquefy a unit mass of nitrogen in the Linde dual-pressure system of Fig. 4.8 as a function of the intermediate pressure for intermediate flow rate ratios, m,/m, of 0.5, 0.6, 0.7, and 0.8. The lower and upper operating pressures of the liquefier are 0.101 and 30.3 MPa, respectively. Assume isothermal and reversible compression at 300 K for the compressors and 100% effectiveness for the heat exchanger. 

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