207 C HAPTER 9 Particulate Emission Control Fresh air is good if you do not take too much of it; most of the achievements and pleasures of life are in bad air. Oliver Wendell Holmes 9.1 PARTICULATE EMISSION CONTROL BASICS Particle or particulate matter is defined as tiny particles or liquid droplets suspended in the air; they can contain a variety of chemical components. Larger particles are visible as smoke or dust and settle out relatively rapidly. The tiniest particles can be suspended in the air for long periods of time and are the most harmful to human health because they can penetrate deep into the lungs. Some particles are directly emitted into the air from pollution sources. Constituting a major class of air pollutants, particulates have a variety of shapes and sizes; as either liquid droplet or dry dust, they have a wide range of physical and chemical characteristics. Dry particulates are emitted from a variety of different sources in industry, mining, construction activities, and incinerators, as well as from internal combustion engines — from cars, trucks, buses, factories, construction sites, tilled fields, unpaved roads, stone crushing, and wood burning. Dry particulates also come from natural sources such as volcanoes, forest fires, pollen, and windstorms. Other particles are formed in the atmosphere by chemical reactions. When a flowing fluid (engineering and science applications consider liquid and gaseous states as fluid) approaches a stationary object (a metal plate, fabric thread, or large water droplet, for example), the fluid flow will diverge around that object. Particles in the fluid (because of inertia) will not follow stream flow exactly, but tend to continue in their original directions. If the particles have enough inertia and are located close enough to the stationary object, they collide with the object and can be collected by it. This important phenomenon is depicted in Figure 9.1. 9.1.1 Interaction of Particles with Gas To understand the interaction of particles with the surrounding gas, knowledge of certain aspects of the kinetic theory of gases is necessary. This kinetic theory explains temperature, pressure, mean free path, viscosity, and diffusion in the motion of gas molecules (Hinds, 1986). The theory assumes gases — along with molecules as rigid spheres that travel in straight lines — contain a large number of molecules that are small enough so that the relevant distances between them are discontinuous. Air molecules travel at an average of 1519 ft/sec (463 m/sec) at standard conditions. Speed decreases with increased molecule weight. As the square root of absolute temperature increases, molecular velocity increases. Thus, temperature is an indication of the kinetic energy of gas L1681_book.fm Page 207 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 208 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK molecules. When molecular impact on a surface occurs, pressure develops and is directly related to concentration. Gas viscosity represents the transfer of momentum by randomly moving molecules from a faster moving layer of gas to an adjacent slower moving layer of gas. Viscosity of a gas is independent of pressure but will increase as temperature increases. Finally, diffusion is the transfer of molecular mass without any fluid flow (Hinds, 1986). Diffusion transfer of gas molecules is from a higher to a lower concentration. Movement of gas molecules by diffusion is directly proportional to the concentration gradient, inversely proportional to concentration, and proportional to the square root of absolute temperature. The mean free path, kinetic theory’s most critical quantity, is the average distance a molecule travels in a gas between collisions with other molecules. The mean free path increases with increasing temperature and decreases with increasing pressure (Hinds, 1986). The Reynolds number characterizes gas flow, a dimensionless index that describes the flow regime. The Reynolds number for gas is determined by the following equation: (9.1) where Re = Reynolds number p = gas density, pounds per cubic foot (kilograms per cubic meter) U g = gas velocity, feet per second (meters per second) D = characteristic length, feet (meters) η = gas viscosity, lbm/ft·sec (kg/m·sec) The Reynolds number helps to determine the flow regime, the application of certain equations, and geometric similarity (Baron and Willeke, 1993). Flow is laminar at low Reynolds numbers and viscous forces predominate. Inertial forces dominate the flow at high Reynolds numbers, when mixing causes the streamlines to disappear. 9.1.2 Particulate Collection Particles are collected by gravity, centrifugal force, and electrostatic force, as well as by impaction, interception, and diffusion. Impaction occurs when the center of mass of a particle diverging from the fluid strikes a stationary object. Interception occurs when the particle’s center of mass closely misses the object but, because of its size, the particle strikes the object. Diffusion occurs when small particulates happen to “diffuse” toward the object while passing near it. Particles that strike Figure 9.1 Particle collection of a stationary object. (Adapted from USEPA-84/03, p. 1-5.) Re = pU D G η L1681_book.fm Page 208 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC PARTICULATE EMISSION CONTROL 209 the object by any of these means are collected if short-range forces (chemical, electrostatic, and so forth) are strong enough to hold them to the surface (Copper and Alley, 1990). Different classes of particulate control equipment include gravity settlers, cyclones, electrostatic precipitators, wet (Venturi) scrubbers, and baghouses (fabric filters). In the following sections we discuss many of the calculations used in particulate emission control operations. Many of the calculations presented are excerpted from USEPA-81/10. 9.2 PARTICULATE SIZE CHARACTERISTICS AND GENERAL CHARACTERISTICS As we have said, particulate air pollution consists of solid and/or liquid matter in air or gas. Airborne particles come in a range of sizes. From near molecular size, the size of particulate matter ranges upward and is expressed in micrometers ( µ m — one millionth of a meter). For control purposes, the lower practical limit is about 0.01 µ m. Because of the increased difficulty in controlling their emission, particles of 3 µ m or smaller are defined as fine particles. Unless otherwise specified, concentrations of particulate matter are by mass. Liquid particulate matter and particulates formed from liquids (very small particles) are likely to be spherical in shape. To express the size of a nonspherical (irregular) particle as a diameter, several relationships are important. These include: • Aerodynamic diameter • Equivalent diameter • Sedimentation diameter • Cut diameter • Dynamic shape factor 9.2.1 Aerodynamic Diameter Aerodynamic diameter, d a , is the diameter of a unit density sphere (density = 1.00 g/cm 3 ) that would have the same settling velocity as the particle or aerosol in question. Note that because USEPA is interested in how deeply a particle penetrates into the lung, the agency is more interested in nominal aerodynamic diameter than in the other methods of assessing size of nonspherical particles. Nevertheless, a particle’s nominal aerodynamic diameter is generally similar to its con- ventional, nominal physical diameter. 9.2.2 Equivalent Diameter Equivalent diameter, d e , is the diameter of a sphere that has the same value of a physical property as that of the nonspherical particle and is given by (9.2) where V is volume of the particle. 9.2.3 Sedimentation Diameter Sedimentation diameter, or Stokes diameter, d s , is the diameter of a sphere that has the same terminal settling velocity and density as the particle. In density particles, it is called the reduced sedimentation diameter, making it the same as aerodynamic diameter. The dynamic shape factor accounts for a nonspherical particle settling more slowly than a sphere of the same volume. d V e = 6 13 π / L1681_book.fm Page 209 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 210 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK 9.2.4 Cut Diameter Cut diameter, d c , is the diameter of particles collected with 50% efficiency, i.e., individual efficiency ε I = 0.5, and half penetrate through the collector — penetration Pt = 0.5. (9.3) 9.2.5 Dynamic Shape Factor Dynamic shape factor, χ , is a dimensionless proportionality constant relating the equivalent and sedimentation diameters: (9.4 ) The d e equals d s for spherical particles, so χ for spheres is 1.0. 9.3 FLOW REGIME OF PARTICLE MOTION Air pollution control devices collect solid or liquid particles via the movement of a particle in the gas (fluid) stream. For a particle to be captured, the particle must be subjected to external forces large enough to separate it from the gas stream. According to USEPA-81/10, p. 3-1, forces acting on a particle include three major forces as well as other forces: • Gravitational force • Buoyant force • Drag force • Other forces (magnetic, inertial, electrostatic, and thermal force, for example) The consequence of acting forces on a particle results in the settling velocity — the speed at which a particle settles. The settling velocity (also known as the terminal velocity) is a constant value of velocity reached when all forces (gravity, drag, buoyancy, etc.) acting on a body are balanced — that is, when the sum of all the forces is equal to zero (no acceleration). To solve for an unknown particle settling velocity, we must determine the flow regime of particle motion. Once the flow regime has been determined, we can calculate the settling velocity of a particle. The flow regime can be calculated using the following equation (USEPA-81/10, p. 3-10): (9.5) where K = a dimensionless constant that determines the range of the fluid-particle dynamic laws d p = particle diameter, centimeters or feet g = gravity force, cm/sec 2 or ft/sec 2 p p = particle density, grams per cubic centimeter or pounds per cubic foot p a = fluid (gas) density, grams per cubic centimeter or pounds per cubic foot µ = fluid (gas) viscosity, grams per centimeter-second or pounds per foot-second Pt 1 – II = ε χ = d d e s 2 Kd(gpp/µ) ppa 20.33 = L1681_book.fm Page 210 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC PARTICULATE EMISSION CONTROL 211 USEPA-81/10, p. 3-10, lists the K values corresponding to different flow regimes as: • Laminar regime (also known as Stokes’ law range): K < 3.3 •Transition regime (also known as intermediate law range): 3.3 < K , 43.6 •Turbulent regime (also known as Newton’s law range): K > 43.6 According to USEPA-81/10, p. 3-10, the K value determines the appropriate range of the fluid- particle dynamic laws that apply. •For a laminar regime (Stokes’ law range), the terminal velocity is (9.6) •For a transition regime (intermediate law range), the terminal velocity is: (9.7) •For a turbulent regime (Newton’s law range), the terminal velocity is: (9.8) When particles approach sizes comparable with the mean free path of fluid molecules (also known as the Knudsen number, Kn ), the medium can no longer be regarded as continuous because particles can fall between the molecules at a faster rate than that predicted by aerodynamic theory. Cunningham’s correction factor, which includes thermal and momentum accommodation factors based on the Millikan oil-drop studies and which is empirically adjusted to fit a wide range of Kn values, is introduced into Stoke’s law to allow for this slip rate (Hesketh, 1991; USEPA-84/09, p. 58): (9.9) where C f = Cunningham correction factor = 1 + (2A λ / d p ) A = 1.257 + 0.40 e –1.10 d p /2 λ λ = free path of the fluid molecules (6.53 × 10 –6 cm for ambient air) Example 9.1 Problem : Calculate the settling velocity of a particle moving in a gas stream. Assume the following information (USEPA-81/10, p. 3-11): Given: d p = particle diameter = 45 µ m (45 microns) g = gravity forces = 980 cm/sec 2 p p = particle density = 0.899 g/cm 3 p a = fluid (gas) density = 0.012 g/cm 3 µ = fluid (gas) viscosity = 1.82 × 10 –4 g/cm-sec C f = 1.0 (if applicable) vgp(d)/(µ pp = 2 18 ) v.g(d)(p)/[µ(p ) . p . p a . = 0 153 071 114 071 043 0229 ] v 1.74(gd p /p ) pp a 0.5 = vgp(d)C/(µ pp f = 2 18 ) L1681_book.fm Page 211 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 212 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK Solution : Step 1. Use Equation 9.5 to calculate the K parameter to determine the proper flow regime: The result demonstrates that the flow regime is laminar. Step 2. Use Equation 9.9 to determine the settling velocity: Example 9.2 Problem : Three differently sized fly ash particles settle through the air. Calculate the particle terminal velocity (assume the particles are spherical) and determine how far each will fall in 30 sec. Given: Fly ash particle diameters = 0.4, 40, 400 µ m Air temperature and pressure = 238°F, 1 atm Specific gravity of fly ash = 2.31 Because the Cunningham correction factor is usually applied to particles equal to or smaller than 1 µ m, check how it affects the terminal settling velocity for the 0.4- µ m particle. Solution : Step 1. Determine the value for K for each fly ash particle size settling in air. Calculate the particle density using the specific gravity given: Calculate the density of air: Kd(gpp/µ) ppa . = 233 0 =× ×45 10 [980(0.899)(0.012)/1.82 10 –4 –4 ) 2 ]] .033 = 3.07 vgp(d)C/(µ pp f = 2 18 ) =× ×980(0.899)(45 10 ) (1)/[18(1.82 10 –4 2 –4 ))] = 5.38 cm/sec P p particle density (specific gravity o== ffflyash)(density of water) = 2.31(62.4) = 144.14 lb/ft 3 L1681_book.fm Page 212 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC PARTICULATE EMISSION CONTROL 213 (USEPA-84/09, p. 167) Determine the flow regime ( K ): For d p = 0.4 µ m: where 1 ft = 25,400(12) µ m (USEPA-84/09, p. 183) For d p = 40 µ m: For d p = 400 µ m: Step 2. Select the appropriate law, determined by the numerical value of K : K < 3.3; Stokes’ law range 3.3 < K < 43.6; intermediate law range 43.6 < K < 2360; Newton’s law range For d p = 0.4 µ m, the flow regime is laminar (USEPA-81/10, p. 3-10) For d p = 40 µ m, the flow regime is also laminar For d p = 400 µ m, the flow regime is the transition regime For d p = 0.4 µ m: For d p = 40 µ m: p ==air density PM/RT =+=(1)(29)/(0.7302)(238 460) 0.0569 lb/ftt 3 µ ===×airviscosity 0.021 cp 1.41 10 –5 llb/ft-sec Kd(gpp/µ) ppa . = 2033 K = [(0.4)/(25,400)(12)][32.2(144.14)(0.05699)/(1.41 10 ) ] 0.0144 –5 2 0.33 ×= K = [(40)/(25,400)(12)][32.3(144.14)(0.0569))/(1.41 10 ) ] 1.44 –5 2 0.33 ×= K = [(400)/(25,400)(12)][32.2(144.14)(0.05699)/(1.41 10 ) ] 14.4 –5 2 0.33 ×= vgp(d) µ pp = 2 18/( ) (32.2)[(0.4)/25,400)(12)] (144.14)/(18)( 2 = 11.41 10 ) –5 × =×3.15 10 ft/sec –5 vgp(d) µ pp = 2 /( )18 (32.2)[(40)/25,400)(12)] (144.14)(18)(1. 2 = 441 10 ) –5 × 0.315 ft/sec= L1681_book.fm Page 213 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 214 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK For d p = 400 µ m (use transition regime equation): Step 4. Calculate distance. For d p = 40 µ m, distance = (time)(velocity): For d p = 400 µm, distance = (time)(velocity): For d p = 0.4 µm, without Cunningham correction factor, distance = (time)(velocity): For d p = 0.4 µm with Cunningham correction factor, the velocity term must be corrected. For our purposes, assume particle diameter = 0.5 µm and temperature = 212°F to find the C f value. Thus, C f is approximately equal to 1.446. Example 9.3 Problem: Determine the minimum distance downstream from a cement dust-emitting source that will be free of cement deposit. The source is equipped with a cyclone (USEPA-84/09, p. 59). Given: Particle size range of cement dust = 2.5 to 50.0 µm Specific gravity of the cement dust = 1.96 Wind speed = 3.0 mi/h The cyclone is located 150 ft above ground level. Assume ambient conditions are at 60°F and 1 atm. Disregard meteorological aspects. µ = air viscosity at 60°F = 1.22 × 10 –5 lb/ft-sec (USEPA-84/09, p. 167) µm (1 µm = 10 –6 ) = 3.048 × 10 5 ft (USEPA-84/09, p. 183) v = 0.153g (d ) (p ) /(µ p 0.71 p 1.14 p 0.71 0.43 0.29 )) 0.153(32.2) [(400)/(25,400)(12)] ( 0.71 1.14 = 1144.14) /[(1.41 10 ) (0.0569) 0.71 –5 0.43 0.29 × ]] = 8.90 ft/sec Distance 30(0.315) 9.45 ft== Distance 30(8.90) 267 ft== Distance 30(3.15 10 ) 94.5 10 ft –5 –5 =×=× Thecorrected velocity 3.15 10 ( –5 == ×vC f 11.446) 4.55 10 ft/sec –5 =× Distance 30(4.55 10 ) 1.365 10 ft –5 –3 =×=× L1681_book.fm Page 214 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC PARTICULATE EMISSION CONTROL 215 Solution: Step 1. A particle diameter of 2.5 µm is used to calculate the minimum distance downstream free of dust because the smallest particle will travel the greatest horizontal distance. Step 2. Determine the value of K for the appropriate size of the dust. Calculate the particle density (p p ) using the specific gravity given: Calculate the air density (p). Use modified ideal gas equation, PV = nR u T = (m/M)R u T Determine the flow regime (K): For d p = 2.5 µm: where 1 ft = 25,400(12) µm = 304,800 µm (USEPA-84/09, p. 183) Step 3. Determine which fluid-particle dynamic law applies for the preceding value of K. Compare the K value of 0.104 with the following range: K < 3.3; Stokes’ law range 3.3 ≤ K < 43.6; intermediate law range 43.6 < K < 2360; Newton’s law range The flow is in the Stokes’ law range; thus it is laminar. Step 4. Calculate the terminal settling velocity in feet per second. For Stokes’ law range, the velocity is p p = (specific gravity of fly ash)(density oof water) = 1.96(62.4) = 122.3 lb/ft 3 P = (mass)(volume) = PM / R T u =+=(1)(29)/[0.73(60 460)] 0.0764 lb/ft 3 Kd(gpp ) pp . = a /µ 2033 K = [(2.5)/(25,400)(12)][32.2)(122.3)(0.07644)/(1.22 10 ) ] 0.104 –5 2 0.33 ×= vgp(d)/ µ pp = 2 18() (32.2)[2.5/(25,400)(12)] (122.3)/(18)(1. 2 = 222 10 ) –5 × 1.21 10 ft/sec –3 =× L1681_book.fm Page 215 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC 216 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK Step 5. Calculate the time for settling: Step 6. Calculate the horizontal distance traveled: 9.4 PARTICULATE EMISSION CONTROL EQUIPMENT CALCULATIONS Different classes of particulate control equipment include gravity settlers; cyclones; electrostatic precipitators; wet (Venturi) scrubbers (discussed in Chapter 10); and baghouses (fabric filters). In the following section, we discuss calculations used for each of the major types of particulate control equipment. 9.4.1 Gravity Settlers Gravity settlers have long been used by industry for removing solid and liquid waste materials from gaseous streams. Simply constructed (see Figure 9.2 and Figure 9.3), a gravity settler is actually nothing more than a large chamber in which the horizontal gas velocity is slowed, allowing particles to settle out by gravity. Gravity settlers have the advantage of having low initial cost and are relatively inexpensive to operate because not much can go wrong. Although simple in design, Figure 9.2 Gravitational settling chamber. (From USEPA, Control Techniques for Gases and Particulates, 1971.) t(outlet height)/(terminal velocity)= 150/1.21 10 –3 =× 1.24 10 sec 34.4 h 5 =× = Distance (time for descent)(wind speed)= =×(1.24 10 )(3.0/3600) 5 = 103.3 miles L1681_book.fm Page 216 Tuesday, October 5, 2004 10:51 AM © 2005 by CRC Press LLC [...]... CONTROL 235 Table 9. 7 Collection Efficiency for Each Particle Size Weight fraction wi Average particle size dp, µm i 0.2 0.2 0.2 0.2 0.2 3.5 8 13 19 45 0 .93 25 0 .99 79 0 .99 99 0 .99 99 0 .99 99 η = 1 – exp(–kd p ) 0.5 = 1 – exp[–K(0 .9) ] Solving for K, K = 0.77 Calculate the collection efficiency using the Deutsch–Anderson equation where dp = 3.5: η = 1 – exp[(–0.77)(3.5)] = 0 .93 25 Table 9. 7 shows the collection... Calculate the overall collection efficiency η = Σw i ηi = (0.2)(0 .93 25) + (0.2)(0 .99 79) + (0.2)(0 .99 99) + (0.2)(0 .99 99) + (0.2)(0 .99 99) 9 = 0 .98 61 = 98 .61% where η = overall collection efficiency wi = weight fraction of the ith particle size ηi = collection efficiency of the ith particle size Is the overall collection efficiency greater than 98 %? Yes Step 2 Does the outlet loading meet USEPA’s standard?... 10:51 AM 220 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK Table 9. 1 Particle Size Distribution Data Particle size range, µm Average particle diameter, µm 0–20 20–30 30–40 40–50 50–60 60–70 70–80 80 94 94 Total 10 25 35 45 55 65 75 85 94 Inlet Grains/scf wt% 0.0062 0.01 59 0.0216 0.0242 0.0242 0.0218 0.0161 0.0218 0.0782 0.23 2.7 6 .9 9.4 10.5 10.5 9. 5 7 9. 5 34 100 Example 9. 5 Problem: A settling chamber... October 5, 2004 10:51 AM 222 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK 100 90 80 Efficiency, % 70 60 50 40 30 20 10 0 0 20 40 60 80 100 120 Particle size, microns Figure 9. 4 Size efficiency curve for settling chamber (Adapted from USEPA-84/ 09, 136.) Table 9. 2 Collection Efficiency for Each Particle Size dp, µm , % 94 90 80 60 40 20 10 100 92 73 41 18.2 4.6 1.11 Table 9. 2 provides the collection efficiency... Press LLC L1681_book.fm Page 234 Tuesday, October 5, 2004 10:51 AM 234 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK Table 9. 6 Particle Size Distribution Weight range 0–20% 20–40% 40–60% 60–80% 80–100% Average particle size dp, µm 3.5 8 13 19 45 ηt = (0.5)(η1 ) + (2)(0.25)(η2 ) = (0.5) (96 .84) + (2)(0.25) (99 .90 ) = 98 .37% Example 9. 10 Problem: A vendor has compiled fractional efficiency curves describing... equation (method) (Copper and Alley, 199 0): [d p ]cut = {9 B/[2πn t (pp − pg )]} (9. 19) where [dp]cut = cut diameter, feet (microns) µ = viscosity, pounds per foot-second (pascal-seconds) or (kilograms per meter-second) B = inlet width, feet (meters) © 2005 by CRC Press LLC L1681_book.fm Page 224 Tuesday, October 5, 2004 10:51 AM 224 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK Inner vortex Zone of inlet... L1681_book.fm Page 226 Tuesday, October 5, 2004 10:51 AM 226 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK pp − p = pp = 2 .9( 62.4) = 180 .96 lb/ft 3 Calculate the cut diameter: [d p ]c ut = [ (9) (0.02)(6.72 × 10 –4 )(2.5)/(2π)5(50)(180 .96 )]0.5 = 3.26 × 10 –5 ft = 9. 94 µm Step 2 Complete the size efficiency table (Table 9. 5) using Lapple’s method (Lapple, 195 1) As mentioned, this method provides the collection... (1.0)/[1.0 + (d p / [d p ]cut )2 ] Table 9. 5 Size Efficiency Table dp, µm 1 5 10 20 30 40 50 60 >60 wi dp/[dp]cut i,% wii% 0.03 0.2 0.15 0.2 0.16 0.1 0.06 0.03 0.07 0.1 0.5 1 2 3 4 5 6 — 0 20 50 80 90 93 95 98 100 0 4 7.5 16 14.4 9. 3 5.7 2 .94 7 Step 3 Determine overall collection efficiency: Σw i n i (%) = 0 + 4 + 7.5 + 16 + 14.4 + 9. 3 + 5.7 + 2 .94 + 7 = 66.84% Example 9. 7 Problem: An air pollution control... gravity, 9. 8 m/sec2 (32.1 ft/sec2) dp = particle diameter, microns pp = particle density, kilograms per cubic meter (pounds per cubic foot) pa = gas density, kilograms per cubic meter (pounds per cubic foot) © 2005 by CRC Press LLC (9. 11) L1681_book.fm Page 218 Tuesday, October 5, 2004 10:51 AM 218 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK µ = gas viscosity, pascal-seconds (pound-feet-second) pa... = 1 − exp[–(288)(0.4)/(33.33)] = 0 .96 84 = 96 .84% What is the collection efficiency (η2) of the duct with 25% of gas flow in each? Calculate the volumetric flow rate of gas through the duct in actual cubic feet per second: Q = (4000)/(4)(60) = 16.67 acfs Calculate the collection efficiency (η2) of the duct with 25% of gas: η2 = 1 − exp[–(288)(0.4)/(16.67)] = 0 .99 90 = 99 .90 % Calculate the new overall collection . by CRC Press LLC 218 ENVIRONMENTAL ENGINEER’S MATHEMATICS HANDBOOK µ = gas viscosity, pascal-seconds (pound-feet-second) p a = N/m 2 N = kilogram-meters per sec 2 Equation 9. 11 can be rearranged. efficiency (Table 9. 3). Figure 9. 4 Size efficiency curve for settling chamber. (Adapted from USEPA-84/ 09, 136.) Table 9. 2 Collection Efficiency for Each Particle Size d p , µm , % 94 100 90 92 80 73 60. Alley, 199 0): (9. 19) where [d p ] cut = cut diameter, feet (microns) µ= viscosity, pounds per foot-second (pascal-seconds) or (kilograms per meter-second) B = inlet width, feet (meters) Table 9. 3