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CIEG 434 Air Pollution Control

CIEG 434 Air Pollution Control. Review of some things you should know:. Ideal gas law Mass/energy balance Bernoulli equation …and applications of the above.

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CIEG 434 Air Pollution Control

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  1. CIEG 434 Air Pollution Control Review of some things you should know: • Ideal gas law Mass/energy balance Bernoulli equation …and applications of the above Note: you can see the calculation spreadsheets explaining any worked example here. To do this, exit the show by right-clicking then select “Edit slides.” Then right-click on the answer and select “Worksheet Object…Open.”

  2. Ideal Gas Law • PV = nRT,  = mass/vol, so PM = RT • R = 0.08206 L-atm-mol-1-K-1 • (Table 1.5 has R in lots of combinations of units) • At STP (P=1 atm, T=25oC=298K), this gives • molar volume of any ideal gas as • V/n = RT/1 ≈ 24.466 L/mol

  3. Ideal Gas Law • MW = molecular weight (actually, mass) • units: grams/mole (g/mol) • mol is sometimes referred to as “gmol”

  4. Ideal Gas Law • To treat “air” as an ideal gas, we need its molecular weight • Air is approximately 78% N2, 21% O2, 1% Ar • Assuming N2, O2, and Ar are ideal gases, • MW of air = 0.78(28) + 0.21(32) + 0.01(40) = 28.964 ≈ 29 (g/mol, kg/kmol, lb/lbmol)

  5. Unit Conversions Using Ideal Gas Law • Common units for gases: ppm, ppb, g/m3 • Common units for particulates: g/m3, mg/m3 • Gaseous concentrations in ppm and ppb are on a volume basis, not a mass basis

  6. Unit Conversions Using Ideal Gas Law • Concentration in ppm = • (mole fraction, volume fraction, or partial pressure) x 106 • Concentration in ppb = • (mole fraction, volume fraction, or partial pressure) x 109 • Note: I prefer to use the notations “ppmv” and “ppbv” to clearly indicate that these are volume/volume measurements. However, this is invariably the case when dealing with airborne substances. • How to convert between ppm and g/m3?

  7. Unit Conversion Examples The secondary NAAQS (National Ambient Air Quality Standard) for SO2 is 0.5 ppm. Convert the concentration to g/m3. Answer: (Click to see spreadsheet calcs) • California's air quality standard for NO2 is 470 g/m3. Express the concentration in ppm. Answer: (Click on table to see spreadsheet calcs) Note: to see the calculation spreadsheet, you have to exit the show by right-clicking then select “Edit slides.” Then right-click on the answer and select “Worksheet Object…Open.”

  8. Unit Conversion Examples (cont'd) An air containing 50 ppm Cl2 passes through a 10-in. duct at 250oF and 100 psig. The gas velocity is uniform at 25 ft/s. What is the emission rate of chlorine (in lb/d)? Ans: (Click on table to see spreadsheet calcs)

  9. Mass / Energy Balance • Maccum = Min - Mout + Mformed - Mconsumed • Eaccum = Ein - Eout + Eproduced - Econsumed • (e.g., 1st law of thermo: DU = Q - W)

  10. 50 g H2O condensed in 15 min dried air humid air Q = 30 L/min 20oC 200oC 790 mmHg 730 mmHg [NO2] = 800 ppm [NO2] = ?? Mass Balance Example Example 1.11 (p. 38): What is the [NO2] in the humid air? Answer: (Click on table to see spreadsheet calcs)

  11. Bernoulli Equation • u2/2 + ∫dP/ + gz = constant (frictionless flow) • For small P and incompressible flow, energy per unit mass is constant = u2/2 + P/ + gz • u12/2 + P1/ + gz1 = u22/2 + P2/ + gz2 + losses

  12. Bernoulli Equation • If using the average cross-sectional flow for u in the Bernoulli equation, the average kinetic energy (~u2) will be poorly estimated. • include a kinetic energy correction factor, (a =2 for laminar/circular, 1.01-1.1 for turbulent flow)

  13. 2 ( P P ) / - r ) 1 2 (u2 is proportional to u = D P 2 2 - a a ( A A ) / 2 1 2 1 Bernoulli Equation • One application of Bernoulli's equation is flowrate measurement (venturi & orifice meters) • Without heat/work or Dz, and if u2A2 = u1A1 • If α1= α2=1, and A2/A1 =B2, we get equ. 1.17 • If ideal gas, r = PM/RT (equations 1.20-1.24)

  14. Bernoulli Equation & Energy Balance • Besides the 3 mechanical energies, a fluid also has internal energy (per unit mass), U • Total energy per mass = u2/2 + P/ + gz + U • = u2/2 + PV + gz + U (V = vol/mass = 1/) • = H + u2/2 + gz ( H = enthalpy = U + PV) • Q - W = (DH + aDu2/2 + gDz) . m Note! Equ. 2.7 in Cooper & Alley has α in the denominator instead of the numerator. This is incorrect but, of course, does not matter if α is assumed as unity.

  15. Q (volumetric) = CDAo√2DP/r = CDAo√2gDh (CD = 0.3-1.0, depends on Re & Ao; CD ≈ 0.61 for Re>10,000) Q (volumetric) = CDA1A2√2gDh / √A12-A22 Bernoulli Equation • For orifice meter, • For venturi meter,

  16. cool air hot air To cyclone Cooler Blower 20 lbmol/min 20 lbmol/min 1.2 atm 1 atm 125 F 450 F 250 ft/sec 150 ft/sec Heat (removed Work (electricity) by cooling water) 10 hP, 50% effic. Energy Balance Example Example 2.2 (p. 82): Calculate the heat removed by cooling water.

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