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July 2021 / 17 candidates to consider line step- ping. Contrary to what common sense may suggest, determining whether stepping is a possibility depends on the absolute pressure ratio between the system's pickup and terminal pressures rather than the system's length. One drawback to consider is that stepping the conveying lines on a system that has several diverter valves near its terminal end (where the material discharges to the atmosphere) will require enlarging the valves, which may be prohibitively expensive. Example problem A conveying system that uses a Schedule 40, 4-inch pipe where the conveying line inside diameter is 4.026 inches and the line length is 200 feet would require 1,024 scfm of air at 25 psig to convey 705 lb/ min of material with a true density of 100 lb/ft 3 , a maximum particle size of 45 mesh (354 microns), and a The larger diameter line should start at a point in the system where the system pressure has reduced enough to ensure that the velocity at the point where the larger diam- eter line starts will be at or above the desired velocity. Typically, the original pickup velocity is a good target to use as the minimum resulting velocity immediately after a line step. Since this approach is limited by the number of pipe sizes avail- able, especially in the US pipe system, the difference in pressure between the system's pickup point and its terminal end (called the absolute pressure ratio) must be large enough to maintain the desired velocity using these pipe sizes. Therefore, stepping a conveying line is only feasible when operating above 8 psig on a pressure system and above 10 inches mercury on a vacuum system. Dense-phase conveying systems that operate at pressures greater than 30 psig are TABLE 1 Example problem required air volumes for Schedule 40 pipe Nominal diameter (inches) Inside diameter (inches) Inside cross- sectional area (square feet) Required air volume (acfm) 4 4.026 0.0884 378 5 5.047 0.1390 596 6 6.065 0.2006 860 8 7.981 0.3474 1,489 TABLE 2 Example problem maximum system pressures for Schedule 40 pipe Nominal diameter (inches) Required air volume (acfm) Maximum system pressure (psia) (psig) 4 378 39.7 25.0 5 596 25.2 10.5 6 860 17.5 2.8 median particle size of 200 mesh (74 microns). This results in a super- ficial air velocity at the pickup of 4,287 fpm. Let's consider stepping this conveying line to the Schedule 40 pipe sizes shown in Table 1. (More sizes are available if we use tub- ing or other pipe schedules.) We calculate the actual air volume in actual cubic feet per minute (acfm) through a given pipe diameter by multiplying the velocity — in this case, 4,287 fpm — by the pipe's cross-sectional area in square feet. Calculating the conveying line lengths. Of the four diameters listed, we can only step the con- veying line to three. We can't step to the 8-inch-diameter line since it would require 1,489 acfm and we're only using 1,024 scfm. To allow stepping, the system pressure must be reduced so that the air expands to the necessary air volume (acfm) to maintain the desired velocity. For the 6-inch line, we calculate: volume 1 = 1,024 cfm volume 2 = 860 cfm pressure 1 = 14.7 psia 1,024 x 14.7 = pressure 1 = 17.5 psia or 2.8 psig 860 We can calculate the maximum system pressures for the various pipe sizes to maintain the desired velocity as shown in Table 2. To calculate the stepping point, we start from a known point in the conveying system, either the pickup point or the terminal end. Since this is a pressure conveying system, we know that the pres- sure at the system's terminal end is 0 psig (14.7 psia). (If this were a vacuum conveying system, the pressure at the system's pickup point would be 0 psig.) Since we're stepping the convey- ing line to larger-diameter pipe,