FE Review for Environmental EngineeringProblems, problems, problemsPresented by L.R. Chevalier, Ph.D., P.E.Department of Civil and Environmental EngineeringSouthern Illinois University Carbondale

AIRFE Review for Environmental Engineering

Estimate the amount of soda ash required per m3 of exhaust gas to neutralize 20,000 g/m3 of SO2 at 20° C.

Problem Strategy Solution

• Review governing reaction• Determine the mass of soda ash needed from mole ratio

Problem Strategy Solution

232322 COSONaCONaSO

The neutralization reaction is:

MW: SO2 = 64 Na2CO3 = 106

Problem Strategy Solution

The mass of soda ash is then:

mg

SOg

CONagSOmgm CONa

125.33

64

1060.20

2

32232

Therefore, for each m3 of exhaust gas, we require33.1 mg Na2CO3

Problem Strategy Solution

Consider a box model for an air shed over a city 1 x 105 m wide with a mixing depth of 1200 m. Winds with no SO2 blow at 4 m/s against one side of the box. SO2 is emitted in the box at a rate of 20 kg/s. If SO2 is considered to be conservative, estimate the steady state concentration in the air shed.

Report your answer in mg/m3.

Problem Strategy Solution

• Draw a schematic of your system• Consider mass balance

Problem Strategy Solution

SolutionL

W = 1 x 105 m H = 1200 m

windu = 4 m/sCo = 0 mg/m3

windu = 4 m/sCe =?

Emission20 kg/s

windu = 4 m/sCo = 0 mg/m3

windu = 4 m/sCe =?

Emission20 kg/s

Ce = Co +(qL)/(uH)

L

W = 1 x 105 m H = 1200 m

Problem Strategy Solution

windu = 4 m/sCo = 0 mg/m3

windu = 4 m/sCe =?

Emission20 kg/s

Ce = Co +(qL)/(uH)

L

W = 1 x 105 m H = 1200 m

367.4110912004

20

mg

kgg

m

LLW

es

m

skg

C

Problem Strategy Solution

Consider the emission of SO2 from a coal fired power plant, at a rate of 1,500 g/s. The wind speed is 4.0 m/s on a sunny afternoon. What is the centerline concentration of SO2 3 km downwind (Note: centerline implies y=0). Stack parameters:

Height = 130 mDiameter = 1.5 mExit velocity = 12 m/sTemperature = 320°C (593° K)

Atmospheric conditions: P=100 kPa T=25° C (298° K)

Problem Strategy Solution

• Review data• Estimate effective stack height

• Determine stability class• Calculate sy and sz• Review terms and apply governing equation

Problem Strategy Solution

22

2

1exp

2

1exp,0,,

zyzy s

H

s

y

uss

QHyxC

dTTT

Pudv

Hs

ass 21068.25.1

mm

smmsm

H

44.1543.35.4

5.1593298593

1001068.25.10.4

50.112 2

H = effective stack height = h + DH = 130 m + 15.4 m = 145.4 m

Problem Strategy Solution

Atmospheric stability class: Class B

sy = ax0.894 = 156(3)0.894 = 416.6 m

sz = cxd + f = 108.2(3)1.098 + 2 = 363.5 m

Problem Strategy Solution

32

34

4

4

21

6.728

1028.7

923.01088.7

08.0exp1088.7

5.36344.145

21

exp0exp0.45.3636.416

1500,,,

mg

SOofmg

HzyxC

Problem Strategy Solution

Simplify the Gaussian dispersion model to describe a ground level source with no thermal or momentum flux, which is the typical release that occurs at a hazardous waste sites. In this situation, the effective plume rise, H, is essentially 0.

Example Solution

22

2

1exp

2

1exp,0,,

zyzy s

H

s

y

uss

QHyxC

0exp2

1exp,0,,

2

yzy s

y

uss

QHyxC

2

2

1exp,0,,

yzy s

y

uss

QHyxC

Example Solution

Consider soil under a single story house that emits 1.0 pCi/m2·s of radon gas. The house has 250 m2 of floor space, and average ceiling height of 2.6 m, and an air change rate of 0.9 ach. Estimate the steady state concentration of radon in the house, assuming that the ambient concentration is negligible.

For radon, k = 7.6 x 10-3 hr-1

Problem Strategy Solution

kV

QV

EC

V

Q

Ci

e

Volume = (250 m2)(2.6 m) = 650 m3

Q/V = 0.9Ventilation rate = Q = (650 m3)(0.9) = 585 m3/hrCi = 0E = (1.0 pCi/m2·s)(250 m2)(3600 s/hr) = 900000 pCi/hr

Problem Strategy Solution

• Review data• Review SS equation

3

11

3

1525

0076.09.0650

90000

mpCi

hrhrmhr

pCi

Ce

Problem Strategy Solution