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July 2021 / 19 Conclusions The stepped conveying line in the example discussed here changes a system that's operating at 25 psig when conveying material at 705 lb/ min with velocities between 4,287 fpm and 11,583 fpm to a system that's operating at 13.7 psig when conveying the same number of pounds per minute with velocities between 5,995 fpm and 8,388 fpm. The same system's capacity could be increased to operate at 25 psig when conveying 1,400 lb/min with velocities between 4,287 fpm and 6,753 fpm. Stepping a conveying line has a greater effect when the system operating pressure or vacuum is high (above 8 psig or 10 inches mercury) and when the convey- ing velocities are high (above 3,000 fpm). Column notes The analysis used here is based on equations 11.1, 11.2, and 11.10 in chapter 11 of Fluidization and Fluid- Particle Systems by Frederick A. instead of 5 inches, as shown in Table 6. As the table shows, the con- veying system produces the same system pressure with 33 feet of 4-inch-diameter line or 105 feet of 5-inch-diameter line, since both produce 10.5 psig. We continue by calculating the length of 4-inch- diameter line required to produce a system pressure of 25.0 psig, as shown in Table 7. By stepping the conveying line from 61 feet of 4-inch-diameter line to 79 feet of 5-inch-diameter line to 60 feet of 6-inch-diameter line, the system has a total length of 200 feet but can now convey 1,400 lb/min, instead of the 705 lb/min it could convey when the entire conveying line was 4 inches in diameter. The stepped conveying line also oper- ates with the same air volume of 1,024 scfm at 25 psig. The stepped conveying line's other major advantage is that it greatly reduces the velocity, as shown in Table 8, reducing material degradation and system wear. TABLE 8 Effect of stepped conveying line on velocity Capacity (lb/min) Conveying line configuration, length, and diameter System pressure (psig) Velocity (fpm) Start* End* Start* End* 705 One size: 4-inch line 25.0 0 4,287 11,583 705 Stepped: 61 feet of 4-inch line 13.7 5.6 5,995 8,388 79 feet of 5-inch line 5.6 1.4 5,321 6,710 60 feet of 6-inch line 1.4 0 4,659 5,104 1,400 Stepped: 61 feet of 4-inch line 25.0 10.5 4,287 6,753 79 feet of 5-inch line 10.5 2.8 4,287 6,188 60 feet of 6-inch line 2.8 0 4,287 5,104 *The terms "start" and "end" are used rather than "pickup" and "terminal end" to indicate the start and end of stepped sections as well as the system start and end. Zenz and Donald E. Othmer (New York, Reinhold, 1960). Equation 11.1 is used for horizontal convey- ing when the conveying velocity is above the saltation velocity; this type of conveying is commonly called stream flow. Equation 11.2 is used for vertical conveying, and Equation 11.10 is used for horizon- tal conveying when the conveying velocity is below the saltation veloc- ity but isn't a pulsed-piston flow. While this type of conveying is typ- ically called dense phase, the more correct term is two-phase flow. The computerized version of the above information is PneuCalc, a software originally developed by Pneumatic Conveying Consul- tants but now available from Hatch (www.pneucalc.com). PBE For further reading Find more information on this topic in articles listed under "Pneumatic conveying" in the article archive on PBE's website, www.powderbulk. com. Jack Hilbert (jack.hilbert@hatch. com, 610-657-5286) is principal consultant at Pneumatic Conveying Consultants, LLC, Schnecksville, PA, and a pneumatic conveying subject matter expert (SME) for Hatch. He holds a BS and an MS in mechanical engineering from Penn State Univer- sity, State College, PA, and has more than 48 years of experience in the application, design, detailed engi- neering, installation, and operation of pneumatic conveying systems. FOLL OW US ON