CE384 Homework Packet

8/11/2019 CE384 Homework Packet

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CE 384

Introduction toEnvironmental Engineering

Problems

Dr. Crist KhachikianDepartment of Civil Engineering

2006


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1. Units, Unit Conversions and Concentrations

1.1. The air quality standard for ozone (O3) is 0.08 ppm. Express the standard in g/m3

at 1 atm pressure and T = 20oC. [160 g/m

3]

1.2. A volume of 1 L (liter) of water (H2O) contains 10 g of dissolved salt (NaCl).Express the concentration of salt in the following units:

a. mg/L [104mg/L]

b.ppm (mass of salt per mass of total solution [104ppm]

c. moles/L (M or molarity) [0.17 moles/L]

1.3. A 100 mL sample of water is found to contain 1 mg of dissolved arsenic. Expressthe concentration of arsenic as:

a. mg/L [10 mg/L]

b.ppm (mass of arsenic per mass of solution). Actually do the unit conversion anddo not use the fact that 1 mg/L ~ 1 ppm in water. [10 ppm]

c. gram-moles/L [1.3 x 10-4g-mole/L]

1.4. Suppose the average concentration of SO2in an air sample is measured to be 400g/m

3at 25

oC and 1 atm pressure. Does this exceed the (24 hour) air quality

standard of 0.14 ppm? [0.153 ppm; exceeds the standard]

1.5. A nitrogen analysis of a wastewater sample gives the following results:

Ammonia 30.0 mg/L of NH3Nitrite 0.10 mg/L of NO2

Nitrate 1.50 mg/L of NO3Organic nitrogen 15.0 mg/L of nitrogen

Find the concentration in mg/L of total nitrogen in the sample. [40.08 mg/L]

1.6. The following is from a laboratory test to determine the suspended solidsconcentration of a sample of untreated wastewater. A 100 mL sample is filteredthrough a filter pad that removes all the suspended solids. The dry and cool weightof the pad and crucible before filtration is 48.610 g. After filtration, drying, andcooling, the weight of the crucible, filter pad, and dried solids is 48.903 g. What isthe concentration of suspended solids in the wastewater sample, expressed in mg/L?[2,930 mg/L]

1.7. In Contra Costa County, CA, the median indoor airborne concentration of

chloroform (CHCl3) was found to be 0.4 g/m3.

a. Convert this concentration to a mole fraction in parts per billion.

b.A typical adult inhales about 20 m3of air each day. Calculate the amount of

chloroform (in g) swallowed by an adult each day.


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2. Chemical Mass Balances

2.1. A total mass of 500 lbs of ethanol (C2H5OH) is accidentally spilled into a river,where it is degraded by microbes. The degradation reaction involves the ethanolreacting with oxygen (O2) to form carbon dioxide (CO2) and water (H2O).

a. How many kilograms of oxygen are consumed? [474 kg O2consumed]

b.How many kilograms of CO2are produced? [434 kg CO2produced]

2.2. The use of petroleum as a fossil fuel accounts for about 1.4 x 1020Joules/year ofworld-wide energy generation. Petroleum has an approximate chemical formula ofC2H3and an energy content of about 43 x 10

6Joules/kg. The combustion processconsists of petroleum combining with oxygen (O2) to form carbon dioxide (CO2)and water vapor (H2O). Estimate the total mass of carbon dioxide emitted to theatmosphere each year by the burning of petroleum. [1.1 x 1013kg CO2/yr]

2.3. Pond water contains 15 mg/L of algae which can be represented by the chemicalformula C6H15O6N. The decomposition of algal biomass uses oxygen according tothe following reaction:

C6H15O6N+8O26CO2+NO

3+ H+ + 7H2O

Calculate the biological oxygen demand (BOD) expressed as mg of O2consumedby each liter of pond water assuming that all of the algae are decomposed. [19.5mg/L O2consumed; this is the total BOD]


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3. Mass Balances (no reactions)

3.1. Each year, a total of 600,000 acre-feet (one acre-foot is the volume equivalent toone foot of water covering one acre of land) of water from the Colorado River is

diverted for use by Southern California. The concentration of dissolved salts in theColorado River is 800 ppm. How many tons (English ton = 2000 lbs; metric ton =1000 kg) of salt are imported each year as a result of this water diversion? [592,000metric tons salt]

3.2. A city situated on a large river disposes of its treated wastes to the river on acontinuous basis. The minimum flow in the river is 210 m3/s, and the discharge ratefrom the treatment plant is 12.5 m

3/s. If the maximum acceptable limit for a certain

pollutant is 1.0 mg/L in the downstream river, and the background concentrationof this pollutant upstream is 0.4 mg/L, what is the concentration of the pollutant, inmg/L, that can be safely released from the water pollution control plant? [11.1

mg/L]

3.3. A domestic wastewater flow contains 350 mg/L of suspended solids. Primarysedimentation in a wastewater treatment plant removes 65% of these solids,forming sludge that contains 5% solids and 95% water (by weight). If the totalwastewater flow is 450 MGD (million gallons per day), what is the total volume ofsludge produced each day (expressed in m

3)? (Assume that the solids have a density

of 1500 kg/m3) [5,200 m3/day]

3.4. The L.A. Hyperion wastewater treatment plant has a total inflow of Q = 20 m3/s.Ferric chloride (FeCl3) is added to the influent to create additional suspended solidsby reacting with water (H2O) to form solid ferric hydroxide (Fe(OH)3) and

hydrochloric acid (HCl). The desirable concentration of the solid Fe(OH)3after thereaction and complete mixing with the flow is 20 mg/L. If FeCl3costs $0.27/kg,what is the total annual cost of the FeCl3addition? [$5 x 10

6/yr]

3.5. Dust removal from an airstream of a municipal incinerator is accomplished by fourdust collectors operating in parallel, each holding one fourth of the total airflow of200 m3/min. The airstream contains 10 g/m3of suspended solids. Each dustcollector removes 98% of the suspended solids passing through it.

a. What is the total mass of dust per day collected by all four collectors? [2822.4kg/day]

b.One of the dust collectors has to be taken out of service for one month. Duringthat time, one fourth of the air will still pass through the collector that is out ofservice, but no dust will be removed by that collector. The maximum permissiblesuspended solids concentration in the combined stack discharge is 1.0 g/m

3. Will

the plant be able to meet the standard during the shutdown period? [2.65 g/m3;does not meet the standard]


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3.6. Two manufacturing facilities discharge effluent containing a toxic organic pollutantthrough a common conduit into a pollution free (Ca= 0) river with a steady flow Qa= 10 m3/s and a cross-sectional area A = 100 m2. Facility A discharges a flow QA=0.1 m

3/s with a pollutant concentration CA= 10 mg/L, and facility B discharges a

flow QB= 0.2 m3/s with a pollutant concentration CB= 2mg/L.

a. What is the total mass flow of pollutant em discharged into the river? [1.4 x 10-3

kg/s]

b.What is the concentration Ceof the combined effluent flow into the river? [4.67mg/L]

c. Assuming that the pollutant discharge mixes completely with the river flow,what is the pollutant concentration Cmin the river immediately downstream from

the region of mixing? [0.14 mg/L]

3.7. A sewage treatment plant discharges effluent at a rate of Qe= 450 MGD (million

gallons per day). The mass flow of mercury dissolved in the effluent is em = 20

mg/s. The effluent discharges into a large water body with an ambient mercuryconcentration Ca= 20 ng/L. Determine the initial dilution necessary to meet thefollowing water quality constraints on the concentration of mercury after mixing:

a. Toxicity: Cm< 25 ng/L [196; difficult]

b.Chronic exposure (long-term exposure): Cm< 146 ng/L [7.8; easy]

c. Acute exposure (short-term but intense exposure): Cm < 2100 ng/L [No dilution

necessary since Cm> Cealready]

3.8. An effluent discharge Qe= 102m3/s carries a total mass flow of a dissolved metal

equal to em = 104

kg/s. The effluent discharges into a water body with an initial

dilution Sm= 50. The ambient dissolved metal concentration is zero (Ca= 0).Determine whether the following environmental regulations are met by thisdischarge:

A B

QACA

QBCB

em

CeQa

Ca Cm


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a. An effluent concentration limit: Ce10 mg/L. [10mg/L; just meets standard]

b.An in stream water quality limit (after initial mixing): Cm 0.1 mg/L [0.2mg/L; Does not meet standard]

3.9. A river carries a flow QR= 10 x 109m3/yr with a concentration if dissolved salts CR

= 0. An irrigation flow QI= 8 x 109m3/yr is diverted to crop land with a total land

area AI= 6 x 109m

2. The annual rainfall is P = 0.25 m/yr and the total loss by

evaporation from the irrigated area is E = 0.75 m/yr. The irrigation flow leaches

minerals from the soil and leaves the irrigated area with a concentration Cs= 2000ppm. The drainage from the irrigated area discharges back into and mixescompletely with the river upstream from the point of withdrawal.

Assuming steady state conditions, determine:

a. The salt concentration Cdin the river downstream. [667 ppm]

b.The rate sm at which the salt is leached from the soil. [10 x 109kg/yr]

3.10. The automobile emission standard for carbon monoxide (CO) is 3.4 g/mile. Each

day, about 10 million cars make a single trip across a region in West Los Angelesthat is about L = 10 km on a side (see figure below). Each car may be assumed to beemitting CO at the maximum permissible rate (given above). Because of theinversion layer, the atmosphere above this region may be considered to be a well-mixed volume with a height H = 1000 m. The wind from the ocean enters from thewest (across one side of the volume) and leaves the region to the east (across theopposite side) with a velocity U = 2 m/s. The concentration of CO in the cleanocean air entering the volume is Ca= 200 ppb. Assuming steady-state conditions

Effluent FlowQe

Ce, em

Mixing zone (Sm = 50)

Ca

Water body

QR,CR

Cd

QIAI

Cs

E P


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and neglecting possible reactions involving CO (i.e., assume CO is a conservativesubstance), compute the well-mixed concentration of CO in the atmosphere aboveWest L.A. Does it meet the air quality standard of 10 mg/m

3(assume the air

temperature is 25oC)? [0.37 mg/m

3; meets state standard]

Side View

Top View

L

L


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4. Mass Balances (with reactions)

4.1. A steady wastewater flow passes through a well-mixed tank with a volume V = 20m

3. While it is in the tank, the mass of the waste decreases by reaction with a first-

order rate kr= 0.15/day. Determine the magnitude of the wastewater flow that canbe handled if the desired level of treatment is 98% removal of the waste

constituents by reaction. [0.061 m3/day]

4.2. A railroad tank car spills a mass Mo= 104 kg of chemical pesticide into a river. Theriver has a rectangular cross-section with width W = 100 m and a depth H = 3 m.

The steady river flow is Qr= 30 m3/s. The cloud or plume of spilled pesticide

moves downstream with the river flow. As it moves, the pesticide degrades

according to a first order reaction rate kr= 1/day. What fraction of the original mass

of pesticide will be undegraded by the time the plume reaches a reservoir a distance

L = 20 km downstream? [0.1 or 10%]

4.3. A town draws its water from a river with an average flow Qa= 10 m3/s and a cross-

sectional area A = 100 m2. The town is located 10 km downstream from a discharge

of pollutant at a rate of em = 103

kg/s which may be assumed to mix completely

with the river flow. As it flows downstream, the pollutant concentration decreases

by reaction with a first-order reaction rate kr= 1/day. If a drought occurs and the

river flow decreases to Qa= 1 m3/s, will the pollutant concentration in the water

withdrawn by the town be greater or less than the pollutant concentration during

average flow conditions? Assume steady conditions and Qe


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drinking water standard specifies that water have a dioxolane concentration less

than 0.001 mg/L, how far downstream will the water by safe to drink (without

additional treatment to remove dioxolane)? [597 km]

4.6. A drainage channel discharges storm water runoff into Santa Monica Bay at a rateof Qem

3/s (which may be assumed to be constant during a very rainy week). The

bacterial level in the runoff is Ce= 104counts/100mL (one count is one E. coli

bacterium, the indicator species; you can treat these units just like concentration

units). The coastal current flowing from the south has an average velocity of aboutU = 5 cm/s and a bacterial concentration Ca= 50 counts/100mL (because of other

storm water discharges located to the south). The cross-sectional area of Santa

Monica Bay at the location of the inflow is about A = 2 x 105m

2(about 50 meters

deep and 4000 meters wide). The current leaves Santa Monica Bay by flowing to

the north past Malibu. The portion of the Bay between the discharge and where the

current leaves the Bay has a volume V = 109m

3, and may be considered to be well-

mixed. Calculate the concentration of bacteria (Cm) in the flow leaving the Bay

taking into the account that the bacteria die off at a rate given by a first order

coefficient kr= 1/day. Assume steady state conditions. [23.6 counts/100 mL]

4.7. The sewage treatment plant in Boston, Massachusetts discharges a pesticide (non-volatile organic compound) into Boston Harbor. Boston Harbor is nearly an

enclosed embayment that may be assumed to be well-mixed. The harbor has an area

A = 100 km2and a depth H = 5 m. The harbor is flushed by a pollution free (C a= 0)

tidal flow equivalent to an ambient flow rate Qa= 108m

3/day. Assume Qe


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The pesticide in the effluent has a first-order reaction kr= 0.01/day. Does the

reaction have a significant effect on the concentration of the pesticide (Cm) in the

mixed flow leaving the harbor? [Qm>> krV; so the reaction has little effect]

4.8. A sewage treatment plant discharges tertiary effluent into the Los Angeles River.

The effluent flow is Qe= 4 m3/s and the effluent nitrogen mass flow Nm = 8 x 10

4

mg/sec (as N not a compound). The ambient river flow upstream from the plant is

Qa= 1 m3/s, and the ambient N concentration is Ca= 0. The cross-sectional area of

the river is A = 5 m2and the discharge is located at a distance L = 70 km from the

ocean.

a. What is the nitrogen concentration Cmin the river just downstream from thetreatment plant? [16 mg/L]

b.Nitrogen (in the form of NH+4is converted to phytoplankton (C106H263O110N16P)according to the following chemical reaction:

106CO2+ 16NH+

4+ H2PO

4+ 106H2O C106H263O110N16P +106O2 +15H+

Assuming that all of the N is converted to phytoplankton, either in the river or in the

ocean, what is the total rate of phytoplankton mass production pm (in kg/s)? [1.3 kg/s]

c. The rate at which the N is converted to phytoplankton is kr= 1/day. What percentof the total phytoplankton mass production occurs in the river? [56%]


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4.9. A cooling tower (used to cool water for air conditioning purposes) has a steadyevaporative loss of water equal to QE= 1 m

3/s. To make up for the loss, water is

withdrawn from a nearby river which has a steady ambient flow Qa= 10 m3/s. The

steady flow withdrawn from the river is Qinand the steady discharge back into theriver is Qout. The ambient concentration of total dissolved solids in the river is Ca=

10 mg/L. The concentration of dissolved solids in the evaporative flow QEis CE= 0mg/L.

a. Determine the values of the flows Qinand Qoutrequired to limit the concentrationof dissolved solids in the cooling tower to Cmax= 20 mg/L. Assume that thecooling tower is like a well-mixed volume and that there are no reactionsoccurring in the tower. [2 m

3/sec]

b.Assuming that the concentration of dissolved solids in the discharge from thetower is Cout= Cmax= 20 mg/L, what is the mixed concentration of dissolvedsolids Cmin the river just downstream from the discharge point? [11.1 mg/L]

c. As the river flows downstream, the concentration of dissolved solids decreases asa result of a first-order reaction with constant reaction coefficient kr.

Measurements of the dissolved solids concentration CLat a distance Ldownstream have been made for a range of values of the ambient river flow Qa.A qualitative plot of these measurements looks like this:

Explain briefly why the plot looks as it does, i.e., why does the dissolved concentrationCLincrease with river flow Qaand then decrease. Assume that all other parametervalues given in the problem remain constant. [For low values of Qa, velocity is smalland the travel time is large; thus, the reaction makes CLsmall. For high velocities, Cmis small and so is CL]


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4.10. Rainfall flows steadily from a storm drain into Santa Monica Bay at the shoreline ata rate of Qr= 0.01 m

3/s and with a bacterial concentration Cb= 10

5counts/100mL.

The beach slopes downward in the offshore direction at a rate of 1:50 (vertical dropper horizontal distance). A steady current runs parallel to the shore with a uniformvelocity U = 1 cm/s. Assuming that the rainfall flow mixes completely with thealongshore flow over an offshore distance Lm= 10 m, and that the bacteria die at arate given by a first-order rate kd= 1/day, use plug flow analysis to determine if theconcentration of bacteria at a point x = 200 m along the shoreline downcurrent fromthe point of discharge meets the swimming standard of 1000 counts/100mL. [C = 4x 104counts/100mL; does not meet the standard]

4.11. A river has a steady ambient flow Qa= 10 m3

/s and a constant cross-sectional areaA = 100 m

2. A factory withdraws a flow Qe= 5 m

3/s from the river through a pipe

and discharges it at a point a distance L = 10 km upstreamfrom the point of

withdrawal (see figure). The factory discharges a mass flow fm of a toxic chemical

into the flow Qe. The volume flow of the factory in put is negligible (QF


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a. Calculate the concentration of the toxic chemical Cein the flow Qejust before itis discharged back into the river. [30 mg/L]

b.Calculate the concentration of the toxic chemical Cdin the river downstreamfrom the point where the flow Qeis withdrawn from the river. [4.7 mg/L]

c. Calculate the mass flow of toxic chemical fm discharged from the factory. [0.08kg/s]

4.12. Consider a lake with 108m2 of surface area for which the only source of phosphorusis the effluent from the wastewater treatment plant. The effluent flow rate is 0.4m

3/s and its phosphorus concentration is 10 mg/L. The lake is fed by a stream

having a flow of 20 m3/s with no phosphorus.

a. If the effective settling rate of phosphorus is estimated to be vs= 10 m/yr,estimate the average phosphorus concentration in the lake. [0.077 mg/L]

b.What percent of phosphorus removal at the treatment plant would be required to

keep the average lake concentration below 0.01 mg/L? [87%]

4.13. A river with a steady flow Qa= 1 m3/sec flows into a small harbor with a volume V

= 107

m3and a bottom area A = 10

6m

2. The flow then passes out of the harbor to

the ocean. The harbor may be considered to be well-mixed.

Factory

L

River

Qa, Ca

Qe, Ce QePipe

Cm Cd

fm

kr

River

Ca

Qa

HarborV = VolumeA = Area

Flow to Ocean


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a. Seepage from old septic tanks causes the bacterial concentration in the river (justbefore it enters the harbor) to be Ca= 10

4/100mL (i.e. 104bacteria per 100 mLsample). The bacteria die off according to a first-order reaction rate kr= 0.5/day.Does the water in the harbor meet the swimming standard which is that the well-mixed concentration of bacteria in the harbor be less than 200/100 mL?

[170/100mL meets the standard]b.A dredging operation in the river removes a total mass flow of solids dredgem =

106kg/day from the river bottom. About 1% of the mass of dredged material is

lost by leakage into the river and enters the harbor as suspended solids. If thesettling velocity of the solid material is ws= 0.1 m/day, what is the mass ofdredged solids that settles to the bottom of the harbor each day? [5400 kg/day]

4.14. Santa Monica Bay has a surface area A = 5x107m2and an average depth H = 50 m.The bay may be considered as well-mixed and as being flushed by an ambientocean current with a total flow into the bay equal to Qa= 10

4 m3/sec. The City ofLos Angeles discharges treated sewage in to Santa Monica Bay at a steady rate Qe=

10 m3/sec. It is estimated that 35% of the solids in the effluent settle to the bottomof Santa Monica Bay. The following quantities have been measured in the effluent:

Csse= total suspended solids concentration = 50 mg/L

CDDTe = total concentration of DDT = 1 g/L

CLe= total concentration of lindane = 1 g/L

a. Estimate the settling velocity of the waste particles in the bay. Assume that theambient suspended solids concentration is negligible. [9.3 m/day]

b.DDT has a sediment-water partition coefficient Ks= 106L/kg and does not react.

Estimate the total concentration of DDT in the water leaving the bay CDDTm,

assuming that the ambient concentration of DDT is CDDTa= 0. [0.00066 g/L]

SantaMonicaBay

Qm

CDDTmCLmCssm

QaCDDTaCLaCssa

QeCDDTeCLe

Csse


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c. Lindane has a sediment-water partition coefficient Ks= 103L/kg and a reaction

coefficient kr= 1/day. Estimate the total concentration of lindane in the waterleaving the bay CLm, assuming that the ambient concentration of lindene is 0.

[0.00026 g/L]

4.15. A steady flow QN= 30 x 10

6

m

3

/day of water from Northern California reaches theSacramento Delta Region where a steady irrigation flow QI= 20x 106m

3/day is

withdrawn. The flow QIis used to irrigate crops in a region with a (hypothetically)steady rainfall P = 0.5 m/yr and evapotranspiration ET = 1 m/year. A steady returnflow QR= l0 x 10

6m

3/day from the irrigation region returns to the main channel at a

point upstreamfrom where QIis withdrawn, resulting in a steady flow QLA= 20 x106m3/day that provides Los Angeles with drinking water. A mass flow of organic

carbon ocm enters the irrigation flow as it passes through the agricultural region.

The resulting concentration of dissolved organic carbon is Cm= 100 mg/L in theflow downstream from the point where the return flow mixes with the main channel(including in the irrigation flow QI). The dissolved organic concentration in the

flow from the north (QN) is CN= 0 mg/L.

a. What is the total area AIof the agricultural region experiencing the rainfall P andevaportanspiration ET?

b.Use a mass balance at the point where the flows QNand QRmix to determine thevalue of the organic carbon concentration in the return flow CR.

c. What is the value of the mass flow of organic carbon? [hint: use a mass balancefor the overall system]

d.The channel bringing water from the Delta to Los Angeles has a cross-sectionalarea Ac= 200 m

2and a length L = 500 km. Assuming that the disso1ved organic


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carbon degrades (into harmless products) at a rate kr= 1/day, does the flowreaching LA exceed a proposed standard for dissolved organic carbon indrinking water Cmax= 2 mg/L?

4.16. A well-mixed reservoir has a constant volume V = 10 m3 and a horizontal cross-sectional area A = 10

6m

2. The steady flows of water into and out of the reservoir

are the river inflow Qin, the outflow Qout, the rainfall P, and the evaporation E.

Suspended solids in the reservoir are generated at a rate pm = 106kg/year by the

growth of phytoplankton (C106H263O110N16P) according to the following chemicalequation:

106CO2+ 16NH4+ + H2PO4

-+ 106H2OC106H263O110N16P + 106O2+ 15H+

The concentration of suspended solids (phytoplankton) in the reservoir is Css= 50 mg/L.The fraction of the solids generated that settle to the bottom is Fs= 0.5. The remainder ofthe solids leave the reservoir in the outflow. There are no suspended solids in the inflow to

the reservoir or in the precipitation or evaporation.

a. Assuming that the rainfall is P = 1.5 m/year and the evaporation is E = 0.5m/year, use the information on the suspended solids balance to determine thevalues of the inflow Qinand the outflow Qout.[0.9 x 10

7m

3/yr; 1.0 x 10

7m

3/yr]

b.What is the settling velocity wsof the settling solids? [10 m/yr]

c. What mass flow of nitrogen Nm into the reservoir is required to maintain the

generation of phytoplankton at the rate Pm ? [6.3 x 104kg/yr]

d.If the phytoplankton decompose, the reaction given above is reversed andoxygen is consumed rather than generated. What is the BOD of a sample ofwater from the reservoir with the phytoplankton mass concentration Cssgivenabove? [47.8 mg/L]

e. A pesticide with a sediment-water partition coefficient Ks= 2 x 104L/kg entersthe reservoir in dissolved form and comes to sorption equilibrium with thesuspended solids (phytoplankton) in the reservoir. What percentage of the massflow of the pesticide settles to the bottom with the phytoplankton solids? [25%]

4.17. A steady flow Q = 107m3/year passes through a well-mixed lake that has a volumeV = 10

6m

3. The concentration of suspended solids in the flow entering the lake is

Css,in = 100 mg/L and the concentration of suspended solids in the flow leaving the


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lake is Css,out= 10 mg/L, which is lower than Css,inbecause of particle settling in thelake.

a. The flow entering the lake carries a mass flow of dissolved ammonia nitrogen

Nm = 2 x l04kg/year. In the reservoir the ammonia nitrogen is degraded to other

compounds by a reaction with a reaction rate kr= 10/year. What is theconcentration of ammonia nitrogen CNoutin the outflow from the lake?

b.The flow entering the lake carries a total mass flow of DDT DDTm = 100 kg/year

which is partially in dissolved form and partially sorbed to the suspended solidsin the inflow. The solid water partition coefficient for DDT is Ks= 5 L/mg. Whatis the total (dissolved plus sorbed) DDT concentration CDDTouttin the outflowfrom the lake?


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5. Water Supply

5.1. A country with a population of 500,000 people has a total land area of 104km2. Theannual freshwater runoff available for use is 10

9m

3, which is 20% of the total

annual rainfall:

a. Is the annual rainfall in this country more or less than the global average? [50%of global average]

b.Is this country short of water? [no, not water stressed]

5.2. A country has a total area A = 105km2and a total annual rainfall I = 0.8 m/yr ofwhich 75% evaporates and the rest is available as water runoff.

a. What is the maximum population this country can support without become waterstressed? [107people]

b.The largest city in the country discharges its treated sewage effluent into a

nearby river. The rate of BOD input into the river is em = 104kg/day. What is the

minimum river flow (Qa) necessary to keep the BOD level in the river less thanthe BODm= 5 mg/L at a point just downstream from the effluent mixing zone?Assume that the effluent mixes completely with the river flow and that theupstream BOD is zero. [2 x 10

6m

3/day]

5.3. Rain falls steadily on a watershed with an area Aw= 104km

2. The total annual

precipitation P = 75 cm. All the water that is not evaporated or transpired flows intoa reservoir as surface water runoff at a constant rate Q = 10

7m

3/day. The reservoir

may be considered as well-mixed. The outflow from the reservoir is also steady andequal to Q = 107m3/day.

a. Is the annual rainfall per unit area on this watershed greater or less than the

global average annual precipitation per unit area onto land? [less than 1m/yr]b.What is the annual evapotranspiration rate ET (in cm/yr)? [38.5 cm]

c. Assuming that the flow into the reservoir Q is the only source of fresh water,what population can this watershed support without experiencing water stress?[1,825,000 people]


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d.Human activities and other sources in the watershed create a mass flow of

phosphorus into the surface runoff equal to pm = 1000 kg/day. What is the

concentration of phosphorus Cpin the runoff entering the reservoir? [0.1 mg/L]

e. Once in the reservoir, all of the phosphorus is converted from H2PO

4to algalbiomass (C106H263O110N16P) according to the following reaction:

106CO2+ 16NH+

4+ H2PO

4+ 106H2O C106H263O110N16P +106O2+15H+

What is the rate of algal biomass production am in kg/day in the reservoir? [114,500

kg/day algae]

5.4. Water usage during peak days in small towns follows the following pattern:

Time interval Gal per capita usedMidnight - 3 AM 53AM-6AM 56AM-9AM 159AM-Noon 25

Noon-3PM 853PM-6PM 406PM-9PM 159 PM-Midnight 10

Assuming that the total daily demand is met by a pumping plant pumping continuously andsteadily at the same rate, determine the storage required to provide the peak hourly demandand the required fire flow for a town with a population of 40,000 people. [6.6 x 106gallons]

5.5. A storage reservoir is to be built to store a river flow QRand to supply a steady flowQD= 10

8m

3/year to a town with a population of 100,000 people and an irrigation

project with a total land area A = 108m2.

The town has a per capita water demand of 200 m3/person/year. The annual precipitation

and evaporation from the irrigation area are estimated to be P = 0.5 m and E = 1.0m,

respectively. In addition, the irrigation project leaches a mass flow of dissolved salts sm =

107kg/year from the soil. Assuming that the salt concentration in the water leaving thereservoir is negligible, will the flow from the reservoir QD= 10

8 m3/year be sufficient toprovide the town the needed water, to water the crops, and to insure that the concentrationof dissolved salts in the downstream river Cswill be less than the maximum drinking waterstandard which is 500 mg/L? [yes total required is 2 x 107m3/yr for town; 5 x 107m3/yrfor irrigation and 2 x 107m3/yr for dilution = 9 x 107m3/yr]

town

irrigationV

reservoirQR

P EA

Cs

QD

sm


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6. Waste Water Treatment

6.1. The concentration of suspended solids in the outflow from a well-mixedsedimentation tank Coutwas measured during steady-state operation for different

values of the tank overflow rate U (defined as flow through the tank per unithorizontal surface area) and for a constant suspended solids inflow concentrationCin:

a. Estimate the concentration of suspended solids in the inflow Cinand the settlingvelocity of the particles ws(hint: try plotting Coutvs. U). [ws= 100 m/day]

b.What overflow rate must be maintained to achieve 80% removal of solids in thetank? [25 m/day]

6.2. A water treatment plant is to be designed to treat a flow Q = 0.1 m3/s.

a. Particles entering the sedimentation unit have a diameter D = 500 m, a porosity= 0.9, and a solids density s= 1100 kg/m

3. Determine the required area of the

sedimentation unit such that 80% of these particles will be removed. [286 m2]

b.The raw water entering the treatment plant has a total concentration (dissolvedplus sorbed) of the pesticide endrin equal to Ctot= 0.001 mg/L and a totalsuspended solids concentration Css= 100 mg/L. If the sediment-water partitioncoefficient for endrin is Ks = 100 L/kg, determine if 80% solid removal issufficient for the treatment plant outflow to meet the primary drinking waterstandard for the total concentration of endrin, Ctot= 0.0002 mg/L. [Ctot~ 0.001mg/L; No]

6.3. A rectangular tank of length L, width B, and depth H is to be designed to serve bothas a well-mixed reaction tank for a dissolved constituent in the inflow as well as awell-mixed settling basin for suspended solids in the inflow. The flow through thetank is 0.1 m

3/s, the particles in the inflow have a settling velocity = 10

-3m/s, and

the reaction rate is 1/hr. For good mixing, the tank dimensions should be such thatL=2B.

a. Determine the dimensions required if the concentration of the dissolvedconstituent in the outflow is to be 20% of the inflow concentration and if 90% of


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21

the suspended particles are to be removed by settling.[B = 21.2m; L = 42.4m; H= 1.6m]

b.The outflow concentration of the dissolved constituent is 1000 mg/L. Thestandard for discharge for this compound is 0.1 mg/L. A consultant offers todesign a discharge into a nearby large water body to obtain the necessary dilution

to meet the standard (ambient concentration = 0). Do you think this is a feasiblesolution? Give your reasons. [Sm= 10,000; Very, very difficult to achieve in anywater body, therefore, the solution is not feasible]

6.4. An activated sludge secondary treatment unit is to treat an inflow Q = 0.5 m3/s withan inflow BOD concentration So= 150 mg/L so that the outflow from the unit has aBOD concentration S = 30 mg/L. The MLVSS of the plant is to be maintained at X= 2000 mg/L, and the concentration of the solids in the flow leaving the secondaryclarifier is Xs= 10,000 mg/L. Determine the bacterial growth rate , the sludge age, the aeration tank volume V, the sludge return flow Qr, the sludge volume outflowQs, and the F/M ration. Assume that Y = 0.5 mg VSS/mg BOD, m= 2.5/day, and

Ks= 100 mg/L. [= 0.58/day; c= 1.72 days; V = 2234 m2

; QR= 0.12 m

3

/s; Qs =260 m3/day; F/M = 1.45 day-1]

6.5. A sewage effluent has a total suspended solids concentration TSS = 100 mg/L.Chemical analysis of the effluent indicates the following sediment-water partitioncoefficients for three organic pollutants: For each of these constituents, calculate thefraction sorbed to the suspended solids at the following locations:

a. In the effluent flow. [0.99 for DDT; 0.91 for PCB; 0.091 for Lindane]

b.In the mixed flow resulting from mixing of the effluent with a pollution-free andparticle-free ambient water body. The dilution factor is Sm= 10. [0.91 for DDT;0.5 for PCB; 0.0099 for Lindane]

c. In the mixed flow (Sm= 10) after 90% of the solids have settled to the bottom.[0.5 for DDT; 0.09 for PCB; and 0.001 for Lindane]

6.6. A water treatment plant with a flow Q = 1 m3/sec adds FeCl3to increase theconcentration of suspended solids. The reaction of FeCl3with water that producesthe solids (in the form of Fe(OH)3is:

FeCl3+3H2O Fe(OH)3+3HCl

This reaction may be assumed to happen very rapidly and to result in the formation of smallparticles. After FeCl3addition and reaction, the flow passes through a flocculationchamber, where the size of the suspended particles increases, to a sedimentation basinwhere a fraction of the particles are removed by settling, and finally to a filter whereessentially all of the remaining suspended solids are removed.


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a. In the flocculation chamber, which may be considered well-mixed, the smallparticles are converted to large particles with a first-order rate kr= 20/hr. What isthe required flocculation basin detention time = V/Q, where V is the basinvolume, in order that 90% of the small particles are converted to large particlesby this reaction? [0.45/hr]

b.If the large particles have a settling velocity vs= 500 m/day, what is the requiredoverflow rate vo= Q/A, where A is the area of the settling basin, in order that90% of the large particles are removed by the settling process? [55.6 m/day]

c. Calculate the FeCl3mass inflow3FeCl

m necessary for the treatment plant to

remove 90% of a toxic compound that is dissolved in the inflow and that has asediment-water partition coefficient Ks= 1 L/mg. Assume that the suspendedsolids concentration in the inflow to the plant is negligible compared to thesuspended solids generated by the addition of FeCl3and that the toxic compoundreaches sorption equilibrium with the suspended solids in the flocculation basin.[1,170 kg/day]

6.7. Water hardness is defined as the concentration of calcium and magnesium (Ca++and Mg

++). One way to soften water is to add a chemical that will combine with

these ions to form solid precipitate that can be settled out. For calcium hardness,soda ash (Na2CO3) may be added to produce the following reaction:

Ca+++ Na2CO3CaCO3(s) + 2Na+

where the calcium carbonate (CaCO3) is in solid form.

a. A water treatment plant must soften a total flow of Q = 1m3/s that has a calciumion concentration of 100 mg/L. What mass of soda ash must be added each dayto completely remove the calcium hardness? [22,848 kg]

b.The softened water passes into a settling basin. If the solid CaCO3particles havea settling velocity vs= 100m/day, what should the area A of the settling basin beif the objective is to remove 80% of the CaCO3solids? [3,456 m

2]

6.8. The table and diagram below give the flows of water, solids, and BOD for theHyperion Treatment Plant in Los Angeles. Use this information to answer thefollowing questions:


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23

a. Does the secondary effluent (#7) meet the water quality requirements that thetotal suspended solids concentration and the BOD concentration must both beless than 30 mg/L? [14 mg/L]

b.What percent of the solids in the primary influent (#4) are removed by primarysettling? [14 mg/L]

c. How many kg per day of solids are generated by the secondary treatment plant?[3.9 x 10

5lb/day]

d.How many kg per day of solids are degraded back to soluble material in the

anaerobic digesters? [5.7 x 10

5

lb/day]e. Is the net effect of the total treatment process, including sludge processing, to

create or diminish the mass of solids in the waste? [-1.7 x 105lb/day; solids lost!]

6.9. In a wastewater treatment plant, sludge from the primary clarifier and waste-activated sludge from the secondary system are mixed and thickened in a gravitythickener. The primary sludge contains 1250 kg of dry solids per day with a 4%solids content by volume (relative to the total volume including liquid) and the


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24

waste-activated sludge contains 525 kg dry solids per day with a solids content byvolume of 1.2%. After thickening, the mixture has a solids content by volume of3%. Assume that all dry solids have a density of 1000 kg/m

3.

a. Calculate the volume of thickened sludge produced each day. [59 m3/day]

b.Calculate the percent volume reduction in the thickener. [79% = volume after

thickening/volume before thickening]

6.10. An activated sludge secondary treatment unit has the following configuration:

Q = inflow to the secondary unit = 1000 m3/dayQr= sludge return flow = 200 m

3/dayX = bacterial biomass concentration = 2000 mg/LXs= sludge return biomass concentration = 10,000 mg/LV = aeration tank volume = 500 m3

a. In the aeration tank, the organic matter in the inflow (C5H12) reacts with oxygento form bacterial biomass (C5H7NO2) according to the following reaction:

C5H12+ 3O2+ NH3C5H7NO2+ 4H2O

If the molecular weights are C = 12g, H = 1g, O = 16g, and N = 14g, determine

the theoretical maximum yield of the reaction Y = bacterial biomass producedper mass of BOD (organic matter) consumed. [1.2]

b.Assuming the entire system is at steady-state, what is the growth rate of thebacteria in the aeration tank? [0.4/day]

c. Assuming the system is at steady-state, find the sludge outflow rate Qs. Neglectthe bacterial biomass flow in the outflow from the settling tank, i.e., assume allof the solids entering the settling tank end up in the sludge outflow or sludgereturn flows. [40 m

3/day]


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25

6.11. A water treatment plant consists of a flocculation tank, a settling basin, and afiltration unit. The plant is to be designed to treat a total flow of Q =1 m

3/s.

Css= 0 Css= 25 mg/L Css= 5 mg/L Css= 0

Q Q

a. To increase the suspended solids concentration, a mass flow of dissolved FeCl3,

3FeClm , is added to the flocculation tank. In this tank, the dissolved FeCl3is

converted to solid Fe(OH)3in a reaction with a first order rate coefficient kr=12/hr. Determine the necessary volume of the flocculation tank, V, such that

90% of the FeCl3is converted to Fe(OH)3. You may assume that QFeCl3


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26

a. The regulatory limit on the BOD concentration in the effluent is CBOD< 30mg/L. Does the effluent meet this regulatory limit? [13.9 mg/L; meets standard]

b.What are the advantages to an environmental regulator of placing a limit on theeffluent concentration rather than the concentration in the receiving water bodyafter mixing has occurred?

c. What is the yield Y (bacterial biomass produced per mass of BOD consumed) inthe secondary treatment process of this plant? [0.42]

d.In the sludge digester, which has a volume V = 10 L and may be consideredwell-mixed, a fraction of the suspended solids are converted back to a dissolvedform by a first order reaction. What is the reaction coefficient krfor the digestionprocess in the sludge digester? [0.0096/day]

e. Is the treatment plant a net sink or source of suspended solids, i.e. is the totalmass flow of suspended solids coming out of the plant greater or less than thetotal flow of suspended solids entering the plant? [Total inflow of solids isgreater than total outflow; solids get consumed in digestion; Plant is a net sinkofsolids]

6.13. A sewage treatment plant that uses activated sludge as the secondary treatmentprocess treats a flow Q = 1 m3/sec. The suspended solids and BOD concentrationsin the inflow to the plant are Css,in = 250 mg/L and So= 250 mg/L, respectively, andthe suspended solids and BOD concentrations in the outflow are Css,out = 50 mg/Land S = 50 mg/L, respectively. The yield of the secondary process is Y = 0.5 kgbacterial mass/kg BOD consumed. The effluent from the plant (Qe ~ Q) isdischarged into a river with a steady discharge Qa= 10 m

3/sec, a constant cross-

sectional area A = 100 m2, and a suspended solids concentration Css,a= 1 mg/L.


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27

a. Assuming that all the BOD reduction occurs in the secondary treatment unit,

what is the total mass flow of sludge sm produced in both the primary and

secondary units (before any sludge digestion)? [25,920 kg/day]

b.If the overflow rate of the settling tank in the secondary unit is U = 50 m/day andthe tank removes 90% of the bacterial solids, what must be the effective settling

speed wsof the bacterial solids? [450 m/day]

c. The effluent contains DDT which has a sediment-water partition coefficient Ks =5 L/mg. Could the concentration of DDT in the river be significantly affected bythe settling of solid particles in the river? [yes, because fraction sorbed = 0.96]

6.14. The Hyperion wastewater treatment plant has a total inflow Q = 20 m3/s with a totalsuspended solids concentration TSS = 300 mg/L.

a. Ferric chloride (FeCl3) is to be added to the influent to create additionalsuspended solids by reacting with water (H2O) to form solid ferric hydroxide(Fe(OH)3) and hydrochloric acid (HC1). The desirable concentration of the solid

Fe(OH)3after the reaction and complete mixing with the flow is 20 mg/L. IfFeCl3costs $0.27/kg, what is the total annual cost of the chemical addition?[$5x106/yr]

b.The inflow with the original TSS and the added ferric hydroxide solids enters aprimary settling basin The total solids concentration of the inflow to the basin isCin = 320 mg/L. The concentration of suspended solids (influent solids andFe(OH)3) in the outflow from the settling basin is Cout= 80 mg/L. What is the

mass flow of sludge sm that must be removed from the settling basin (expressed

in kg/day)? [4.1 x 105kg/day]

c. If the settling basin has a total bottom area A = 105m2, estimate the settlingvelocity of the solids ws. Assume the settling basin is well-mixed. [51 m/day]

6.15. A sewage treatment plant uses primary treatment and activated sludge secondary

treatment to treat a flow Q = 105m3/day. The concentration of suspended solids isTSSin, = 350 mg/L in the inflow and TSSe= 50 mg/L in the effluent. The BOD ofthe flow entering the secondary treatment is So= 350 mg/L and the BOD of theeffluent is BODe= 50 mg/L. The dissolved oxygen concentration of the effluent isDOe= 0. The effluent flow Qe~ Q discharges into a river with a constant velocityU = 10

4rn/day, a cross-sectional area A = 100 m

2, an ambient BODa=0, and an

ambient DOa= DOsat = 12 mg/L.


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a. If the total sludge mass flow generated by the plant is 5 x 104kg/day, what is theyield Y = bacterial biomass produced per mass of BOD consumed of theactivated sludge secondary treatment process? [0.67]

b.Calculate the minimum dissolved oxygen concentration DOmin. Assume that thereaeration coefficient is kr= 0.5/day and the deoxygenation coefficient is kd=0.2/day. [10.7 mg/L]

6.16. A population of 5xl06people live in a region with an area AL= 104km2. Thefreshwater runoff available to this population is 40% of the rainfall falling on thisarea. The sewage flow generated by the population is Q = 10 m

3/sec, which is 50 %

of the available freshwater runoff. The sewage flow is treated in a treatment plantwith an activated sludge secondary treatment system. The effluent from the plantdischarges into a large waterbody.

`The characteristics of the treatment plant are:

Inflow to the plant:BODin= ultimate BOD in the inflow = 300 mg/LTSSin= total suspended solids concentration in the inflow = 300 mg/L

Primary settling tank:Percent of TSS entering tank that is removed = 60%Percent of BOD entering tank that is removed = 30% oQ/A = Overflow ratio 50 m/day

Secondary unit:Percent of TSS entering unit that is removed = 90%Percent of BOD entering unit that is removed = 90%


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Yield of activated sludge process = 1.0

F/M = food to mass ratio = SoQ/XV = 0.5/day

So= BOD concentration entering the unitX = bacterial mass concentration in the aeration tankV = aeration tank volume

Sludge flow:Percent solids by volume = 5%

s= solids density = 1500 kg/m3

Effluent discharge:BODm,max= maximum permissible value of BOD after dilution =3 mg/LBODa= ambient BOD = 0 mg/L.

a. Is this region water stressed? [126 m3/person/yr; very water stressed]

b.Is the annual rainfall (expressed as depth = volume/area) greater or less than the

global average? [0.16 m/yr; much less than the global average]

c. What is the settling velocity wsof the particles in the primarly settling tank? [75m/day]

d.What is the growth rate of the bacteria in the secondary unit? [0.45/day]

e. What is the total volume flow Qsof sludge generated (including water) from boththe primary and secondary units including the suspended solids and bacterialsolids removed? [5495 m3/day]

f. What fraction of a toxic chemical present in the inflow to the plant is removedfrom the effluent (to the sludge) by the treatment plant if the solid-water partitioncoefficient of the chemical is Ks= 1000 L/kg? [22%]

g.What value of dilution Smis required to meet the regulatory limit on BODm? Isthis value of dilution easy or difficult to achieve? [7; easy]


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7. BOD in surface waters

7.1. Wastewater saturated with dissolved oxygen (DOsat= 12 mg/L) is discharged into ariver that has zero BOD and is saturated with oxygen (also DOsat= 12 mg/L)

upstream of the discharge point. The minimum DO in the river downstream fromthe discharge is DOmin=2 mg/L. Calculate the five-day biological oxygen demand(BOD5) of the wastewater being discharged, assuming that kd= 0.2/day, kr=0.42/day, and the ratio of the river flow to the wastewater flow is Qa/Qe= 10. [286mg/L]

7.2. After receiving the discharge from a waste treatment plant, a river has a dissolvedoxygen concentration of 8 mg/L and an ultimate BOD of 20 mg/L. The saturationdissolved oxygen concentration is DOsat= 10 mg/L, kd= 0.2 day

1, and kr= 0.6

day1. The river travels at a velocity of 10 km/day. Calculate the location of thecritical point (time and distance) and the oxygen deficit and concentration at the

critical point.

7.3. The ultimate BOD of a river just below a sewage outfall is 50.0 mg/L and the DO isat the saturation value of 10.0 mg/L. The deoxygenation rate coefficient is 0.3/d(kd) and the reaeration rate coefficient is 0.90/day (kr). The river is flowing at aspeed of 48.0 miles/day. The only source of BOD on this river is this single outfall.

a. Find the critical distance downstream at which the DO in the river is a minimum.[87.9 miles]

b.Find the minimum DO value. [0.38 mg/L]

c. If a wastewater treatment plant is to be built, what fraction of the BOD wouldhave to be removed from the sewage to assure a minimum of 5.0 mg/L of DOeverywhere downstream. [48% removed]


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7.4. A municipality discharges sewage with an ultimate BODe= 300 mg/L and a DOe=0 mg/L. The discharge is into a large coastal water body with an ambient BODa= 0

and a saturated dissolved oxygen level Doa= DOsat = 10 mg/L.

a. If the BOD and the DO concentrations immediately after initial mixing ismeasured to be BODm= 6 mg/L and DOm= 9.8 mg/L, what is the initial dilutionSm? [50]

b.The mixed flow is carried along the coastline with a velocity U = 1km/day. Ifthe deoxygenation and reaeration rates are kd= 0.25/day and kr= 0.5/day,respectively, what will the dissolved oxygen concentration DOx be in the mixedflow at a distance x = 1 km down the coast? Use the values of BODmand DOm

given in part (a). [8.85 mg/L]c. For the same conditions as part (b), what will be the ultimate BODxmeasured in

a water sample from the mixed flow taken a distance x = 1 km down the coast.[4.7 mg/L]

7.5. A well-mixed oxidation pond with a total volume V = 100 m3treats a steady waterflow Q = 100 m

3/day. Measurements indicate that the dissolved oxygen

concentration is reduced from DOin= 10 mg/L in the inflow to DOout= 5 mg/L inthe outflow as a result of the BOD in the inflow consuming oxygen within the pond.The pond is covered, so there is no reaeration occurring within the pond

coastline

BODeDOe

BODa

DOa

BODm

DOm

BODxDOx

Mixingzone

U

COVER

Pond

kd V

Q

DOinCinBODin

Q

DOoutCout


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a. The oxygen-consuming organic material in the flow is C5H12and the reaction is:

C5H12+ 3O2+ NH3C5H7NO2+ 4H2O

where C5H7NO2is bacterial biomass and the molecular weights are H = 1, C = 12, N =14, and O = 16. If Cinand Cout are the concentrations of C5H12in the inflow and outflow

respectively, calculate the concentration change C = Cin Cout. [3.75 mg/L]

b.Assuming that BOD in the pond reacts with a first-order coefficient kd=0.25/day, calculate the ultimate biological demand of the inflow BODin. [25mg/L]

c. If the cover is removed and reaeration occurs, will C increase or decrease orstay the same? Why? [stays the same]

d.If the cover is removed and reaeration occurs, will DOoutincrease or decrease orstay the same? Why? [increase]

7.6. A sewage treatment plant discharges a steady flow of effluent into a river upstream

from the point where the river discharges into the ocean. The river has a constantcross-sectional area AR= 100 m

2, and upstream from the sewage treatment plant the

average river velocity is steady and equal to UR= 104m/day, the dissolved oxygen

concentration is DOR=10 mg/L, and the biological oxidation demand is BODR=0mg/L. The effluent flow from the treatment plant is QP= 10

5m

3/day, the effluent

dissolved oxygen concentration is DOP= 0 mgIL, and the ultimate BOD of theeffluent is BODP= 100 mg/L. The discharge from the plant mixes completely withthe river flow and passes into a section of the river that extends a distance LR=11,000 m to the ocean and that is covered so that no oxygen exchange with theatmosphere can take place. The coefficient of deoxygenation in the river is kd=1.2/day.

a. The ambient dissolved oxygen concentration in the ocean is DOo= 8 mg/L. Withthe present river channel configuration, the dilution of the river flow by oceanwater is Sm=2. For these conditions, what is the dissolved oxygen concentrationDOmin the ocean after initial dilution? [5.4 mg/L]


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b.The EPA requires that the dilution be increased. Your consultant offers toredesign the discharge of the river into the ocean to obtain additional dilutionsuch that the dissolved oxygen concentration in the ocean after mixing becomesDOm= 7.99 mg/L for DOo= 8 mg/L and for the worst case condition when thedissolved oxygen level of the river discharge into the ocean is zero. Do you

think this is a feasible proposal? Why? [800; no; Smtoo large; not practical]

7.7. A combined sewer (sewage mixed with stormwater) carries a steady flow Qs= 0.5m

3/sec in a culvert with a cross-sectional area As= 50 m

2and a length ls= 1500 m.

At the upstream end of the culvert the BOD in the sewer is LSO= 20 mg/L and thedissolved oxygen is at the saturated value DOSO= 10 mg/L. The culvert enters ariver with a steady flow QR= 5 m

3/sec and a cross-sectional area AR= 250 m

2at a

distance lp. = 4 km downstream from a dam. The river flow leaving the dam haszero BOD and a dissolved oxygen concentration DORO= 5 mg/L. The rate ofdeoxygenation of BOD in the culvert is k = 0.25/day, and the rate of reaeration inthe river is kr= 0.5/day.

a. Assuming that no reaeration occurs in the culvert, what is the BOD (LS) anddissolved oxygen concentration DOsin the culvert flow at the point where itmeets the river (before mixing with the river water)? [Ls= 12.9 mg/L and DOs=2.9 mg/L]

b.What is the dissolved oxygen concentration DORin the river right before itmixes with the culvert flow? (Assume that DOsat = 10 mg/L everywhere.) [8.4mg/L]

c. What is the BOD and the dissolved oxygen concentration in the river aftermixing with the culvert flow (LMand DOM)? [L = 1.2 mg/L and DO = 7.9 mg/L]

7.8. A sewage treatment plant discharges treated effluent into a large water body. Thetotal flow through the plant is Q = 10

4m

3/day. The BOD of the effluent entering the

secondary treatment unit is So= 350 mg/L and the BOD of the effluent is S = 50mg/L. The BOD and dissolved oxygen in the water body at the end of the mixing


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8. Groundwater

8.1. In a laboratory test, a one cubic meter sample of an aquifer saturated with water wasfound to weight 1400 kg. After being allowed to drain thoroughly, the sample

weighed 1100 kg. After being crushed and thoroughly dried, the sample weighed900 kg. Calculate the specific yield, the porosity, the specific retention, and the

specific gravity of the solids (ratio of solid density to that of water). [= 0.5; Sy=0.3; Sr= 0.2; Specific gravity = 1.8]

8.2. Radioactive material is spilled accidentally into an aquifer. The groundwaterelevation of the aquifer at the site of the spill is 10 m above the water surface of ariver 1.5 km away. Neglecting any effects of retardation, estimate the length oftime required for the material to reach the river if the aquifer material is:

a. Gravel [12.5 days]

b.Clay [2.3 x 108days]

c. Sandstone [7500 days]

d.Granite [5 x 106days]

8.3. An accidental spill of pollutant creates a ``blob'' of contaminated groundwatermoving horizontally in an unconfined aquifer. Two wells are drilled a distance L =100 m apart directly in the path of the blob. At each well, a continuous

measurement is made of the water level in the well and the concentration of thepollutant in the aquifer at the site of the well.

a. If the water levels in the wells are observed to be steady at h1= 100 m and h2 =90 m, and the pollutant concentrations are as shown in the plots, estimate thehydraulic conductivity of the aquifer, K. Assume that the pollutant is not

retarded by sorption and that the porosity of the soil is = 0.5. [2 m/day]

b.Assuming that the pollutant undergoes a first-order reaction that decreases theconcentration as it moves, use the information on pollutant concentration toestimate the first order reaction coefficient, kr. Assume that dispersion isnegligible. [2.5 x 10

-3/day]

h1 h2L

BLOBc1 c2

1.3 mg/L

250 days

500 days

0.7 mg/L

c1

c2


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c. Discuss briefly and qualitatively how retardationand dispersion will affect thetime history of and concentrations measured at the wells. [retardation willincrease all the travel times; dispersion will spread out the concentration overmore groundwater, reducing the peak concentrations]

8.4. A confined aquifer with a thickness B = 10 m and width W = 100 m iscontaminated with a toxic pollutant over a region with a length L = 500 m. The soil

in the aquifer has a hydraulic conductivity K = 1 cm/s and a porosity = 0.2. Theretardation factor for the pollutant R = 10. To clean up the contamination a uniformflow of water is created in the aquifer by pumping out contaminated water on oneside and pumping in clean water on the other. The total rate of pumping is Q = 0.02m3/sec.

a. What is the difference in the piezometric head h between the injection andremoval wells? [1 m]

b.How long will the pumping have to last to remove the pollutant completely?[578 days]

c. If the initial total concentration of pollutant (sorbed and dissolved) is C tot= 100mg/L, what is the initial concentration of dissolved pollutant in the waterpumped out of the aquifer? [50 mg/L]

8.5. An accidental spill results in 100 gallons of a toxic liquid chemical entering anunconfined aquifer. The aquifer has a porosity of 0.25 and a hydraulic conductivityof 10

-3m/s. The density of the liquid is 1200 kg/m

3and the sorption to solids is

negligible. Groundwater samples show that the chemical quickly dissolved inwater, forming a blob with a total volume of 105m3.

a. What is the minimum volume of porewater that must be pumped out to removethe contaminant? [2.5 x 10

4m

3]

Contaminated Soil

h

Q Q

Flow

L

B

W


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b.What is the concentration of the chemical in the porewater within the blobimmediately after dissolution in the groundwater? [18 mg/L]

c. The aquifer water table has a constant slope given by h/L = 0.001. The blob ismoving with the groundwater. As it moves, the chemical is degraded by reactionat a rate of 1/yr. How far will the blob move before the concentration is reduced

to 1% of its initial value? [580 meters]

8.6. An unlined landfill is located on a hill above a populated area. The landfill area is100 m2and the bottom of the landfill is 100 m above the water table. Thegroundwater flows at a Darcy velocity of 1 m/d toward a drinking water well (1 kmaway). The hydraulic conductivity of the soil is 10 m/d and the porosity is 0.4.Estimate how long it will take a contaminant plume with a retardation factor of 5 toreach the well by leaching from the landfill and traveling horizontally with thegroundwater flow.

8.7. A landfill is lined with a 10cm thick layer of clay (porosity = 0.45, K=5 x 10-8cm/s)

overlying sandy soil (porosity = 0.35, K=10

-2

cm/s). Estimate how long it will takefor the leachate to penetrate the clay liner. Also, If the liner was not there, howlong would it take a toxic compound with a retardation factor of 5 to reach thewater table 10 m below the landfill?

8.8. Municipal solid wastes are placed and compacted in a landfill (layers of 2m deep).Before placement, the material has a density of 300 kg/m3of which 25% (byweight) is water. After compaction the waste has a density of 600 kg/m

3and a

maximum moisture content of 0.3. The annual rainfall is 900 mm, of which 67% islost to evaporation and 17% to runoff. Estimate the time for one layer of waste tobecome saturated (achieve maximum water content) with rain.

8.9. An agricultural area (of 104 m2) is fertilized with sludge containing high levels ofarsenic that pose a health threat. The area gets an annual rainfall P = 1 m and anannual evaporation E = 0.5 m. Water enters the area as irrigation flow QIand

leaves as seepage downward to the soil. The aquifer has a h/L = 0.1, K = 0.01

m/d, and = 0.4.

a.Estimatethe magnitude of the irrigation flow QI(in m3/day) necessary to keep

the agricultural area saturated (for growing rice).[290 m3/day]

b.Once the arsenic reaches the aquifer, how much time will it take to read adrinking water well located 50 m from the area in the direction of flow? Assumethat arsenic has an R = 2.

8.10. The annual precipitation and evaporation for a watershed of area Aw= 109m2 are P

= 1 m/year and E = 0.5 m/year. Infiltration is negligible because of a relativelyimpermeable clay layer close to the ground surface. To allow rainfall to be astoredas groundwater, rainfall is routed to a spreading basin constructed with a bottomsurface in contact with soil with a coefficient of permeability K = 1m/day and aporosity n = 0.4 at all depths. Water flowing from the watershed and then throughthe bottom of the spreading basin eventually reaches the water table of a regional


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unconfined aquifer located a distance La= 10 m below the spreading basin. The

water table of the regional aquifer has a slope h/L = 0.001. The runoff from thewatershed contains bacteria that sorb to the solids in the soil with a retardationcoefficient R = 2.

a. What should the area Asof the spreading basin be to allow all of the excessrainfall (precipitation less evaporation) to reach the groundwater? Assume thatall processes are stead and that the water depth in the spreading basin is verysmall relative to La.

b.A nearby town has a water supply well located a distance Lw= 1.0 km from thespreading basin. What is the total time it takes for a bacterial cell to travel fromthe spreading basin to the well?

8.11. A total volume Vo= 104

m3

of oil stored in an unlined reservoir leaks into the soilbelow. After some time all of the oil reaches the water table, where it floats on top

of the water without mixing with the water. The density of the oil is o= 900 kg/m3

and the viscosity of the oil is o= 10-1kg/m-sec.

watershed (Aw)

Impermeable

layer

Spreadingbasin

Aquifer(K, n)

well

watertable

Lw

LaAs

P E

h/L


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Oil reservoir

Floating oil

Leak

L QQ

Reaction Tank

a. If the hydraulic conductivity of the soil is K = 10 m/day and the porosity of the

soil is 0.4, how long will it be before the oil first reaches the water table, which isa distance L = 10 m below the surface of the oil reservoir (assume that the oillevel in the reservoir remains nearly constant during this interval)? Assume that

the effects of sorption are negligible (R = 1). [note: the viscosity of water is o=10-3kg/m-sec] [44.4 days]

b.If the porosity of the soil is 0.4, and the oil completely saturates the soil, what isthe total volume of solid material (soil) that is contaminated after all of the oilreaches the water table? (do not include the soil between the reservoir and thewater table.) [1.5 x 10

4m

3solids only]

c. A pump and treat system is to be used to clean up the floating oil. Oil is pumpedfrom the ground at a rate Q = 1 m

3/day into a well-mixed reaction tank where the

oil is degraded by bacteria at a first-order rate kr=0.1/day. The undegraded oiland water generated by the reaction is pumped back into the ground. Whatshould the volume V of the tank be so that 50% of the oil entering the tank isdegraded? [10 m3]

d.The oil degradation is accomplished by a culture of bacteria (C5H7NO2) thatconsume the oil (C2H3) according to the following reaction:

20C2H3+ 15O2+ 8NH38C5H7NO2+ 14H20

After all of the oil is degraded, what will be the total mass of bacteria generated by thepump and treat system?

8.12. A superfund site contains a large number of buried barrels of hazardous wastecontaining PCBs. The barrels begin leaking slowly, which results in a

concentration of 5 g/L in the groundwater directly beneath the barrels. A privatedrinking well is located one kilometer from the site in the direction of groundwaterflow.


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a. The Darcy velocity in the aquifer is V = 0.2 m/day, the porosity of the aquifer is0.4, and the retardation factor for PCB is R = 5. How long will it take for thePCBs to reach the drinking water well? [10,000 days]

b.If the first-order rate constant for degradation of PCB in the aquifer is 4 x 10-4

/day, what will be the concentration of PCB in the groundwater when the PCBs

reach the drinking water well? [0.092 g/L]

8.13. Use the Kozeny-Karman equation to determine:

a. The hydraulic conductivity of sand with a uniform grain size of 0.1 mm and aporosity of 0.35. [5.5 x 10

-3cm/s]

b.The conductivity of the same sand with respect to a flow of oil with a specific

gravity of 0.9 and a viscosity oil= 0.1 kg/m-sec. [~5 x 10-5

cm/s; oil moves 100times slower]

8.14. A 750-meter long section of river runs parallel to a channel 1000 m away. Aconfined aquifer connecting the two has a hydraulic conductivity equal to 7.0 m/day

and a thickness of 10 m. The surface of the river is 5.0 m higher than the surface ofthe channel. Estimate the rate of seepage from the river to the channel. Whatmaterial is the aquifer made of? [262.5 m3/d; based on the K, sandstone]

8.15. A confined aquifer with a porosity = 0.5, height B = 10 m, and constant width W= 100 m connects directly to a lake with a surface area AL= 10

5m

2. The

groundwater flow in the aquifer is toward the lake with a steady Darcy velocity V =0.1 m/day. There is no outflow from the lake and the flow from the aquifer isbalanced by evaporation from the lake surface.


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a. What is the rate of evaporation from the lake surface E, expressed as meters peryear? [0.365 m/yr]

b.The piezometric head at a distance L = 100 m from the lake is h1= 16 m, and the

piezometric head at the lake is h2= 15 m (all relative to the datum at the bottomof the aquifer). What is the hydraulic conductivity of the aquifer K? [10 m/day]

An old underground tank is leaking PCB steadily into the aquifer at a distance L 100 mfrom the lake. The flow of PCB from the tank mixes uniformly with the groundwaterflow in the aquifer as it passes by the tank, creating a uniform dissolved PCBconcentration C1 = 2 x 10

-2mg/L in the aquifer at that point. The dissolved PCBconcentration in the aquifer just before it flows into the lake is C2= 1 x 10

-2mg/L.

c. What is the mass flow of PCB leaking from the tank? Assume that there are noother sources of PCB and that the volume flow of the leak is negligible comparedto the flow in the aquifer. [2 g/day]

d.The PCB degrades with a first-order reaction coefficient kr= 10-4/day in the

aquifer. What is the retardation coefficient R of the PCB in the aquifer? [13.9]

The dissolved PCB concentration in the lake water is CL= 9 x 10-5mg/L. The lake has a

steady suspended solids concentration Css= 1 mg/L and a steady particle settlingvelocity of ws= 1m/day. The sediment partition coefficient between the PCB and theseparticles is Ks= 10

5L/kg. The PCB is concentration in the lake fish with abioconcentration factor BCF = 105L/kg. The fish are caught and completely consumedby the residents of a nearby town with a population of 1,000 at a rate of 1 fish weighing10 g per day per person.

e. Assuming that the PCB also degrades in the lake with a first-order coefficient kr

= 10-4

/day, determine the rate (mass/time) at which the PCB in the lake:i) degrades in the lake [9 mg/day]ii) sorbs to suspended solids in the lake and settles to the bottom [900

mg/day]iii) is removed with the fish [90 mg/day]

f. The carcinogenic potency of the PCB for oral ingestion is 7.7 [mg/kg/day]-1.How many of the occupants of the town will die of cancer from eating the fish


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from the lake? Assume that all the people are adults weighing 70 kg and thatthey eat fish all their adult life. [9.9 or 10 people will die]


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9. Solid and Hazardous Waste

9.1. An incinerator burning chlorobenzene has an inflow rate of chlorobenzene of 153kg/hr and an outflow rate of 0.01 kg/hr. The outflow rate of HCl (measured after

pollution control) is 1.2 kg/hr and the outflow rate of particulates is 3.615 kg/hr(measured at 7% O2). The stack gas flow is 375.24 dscm (dry standard cubicmeters) per minute.

a. Does the incinerator meet a target DRE of 99.99% for chlorobenzene?

b.Assuming that all of the chlorine in the chlorobenzene is converted to HCl, doesthe incinerator meet the standards on HCl specifying that the outflow will be lessthan the larger of 1.8 kg/hr or 1% of the HCl in the stack gas before pollutioncontrol? (compute both limits, assume 1 mole of chlorobenzene gives 1 mole ofHCl)

c. Does the incinerator meet the target of 180 mg/dscm of particulates (measured at

7% O2)?

9.2. Solid waste is generated by a small municipality with a population of 100,000. Thetotal waste generated is 2.5 kg/person-day. Characteristics of the waste are shownbelow. The compaction ratio is the ratio of the compacted to uncompacted density:

Type % of total (by

weight)

Density (kg/m3) Compaction ratio

Paper 45 80 5.0Food 15 300 2.5

Rubbish 15 160 4.0

Ash/Metal 25 480 3.0

Estimate the area of land required for a landfill with an average depth of 7.5 metersthat will serve the municipality for 20 years assuming that the volume of waste is85% of the total landfill volume (the rest being fill). [5 x 105m2]

9.3. Municipal solid wastes are placed and compacted in a landfill (layers of 2m deep).Before placement, the material has a density of 300 kg/m3of which 25% (byweight) is water. After compaction the waste has a density of 600 kg/m

3and a

moisture content of 0.3. The annual rainfall is 900 mm, of which 67% is lost toevaporation and 17% to runoff. Estimate the time for one layer of waste to becomesaturated (achieve maximum water content) with rain. [2.14 years]

9.4. Domestic municipal solid waste is a small fraction of the total solid waste. Whyshould we care about recycling our papers and plastics if we contribute a smallfraction of the total waste? Shouldnt the focus be on industries rather thanindividuals?

9.5. An incinerator burns toxic waste, producing a plume that extends downwind.Before pollution control equipment is installed, the rate of sulfur dioxide (SO2) gas


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emission is measured to be 100 kg/day. For the most common wind andatmospheric stability conditions the maximum concentration of SO2is measured at a

point one kilometer downwind to be 100 g/m3.

9.6. Vinyl chloride is used by a manufacturing facility which discharges to a nearby

river a steady effluent flow QeF= 0.01 m

3

/sec with a vinyl chloride concentrationCeF= 1 mg/L. The river has a steady flow Qa= 1 m3/sec, a constant cross-sectional

area A = 100 m2, and an ambient vinyl chloride concentration Ca= 0. The facilityalso pumps a quantity of the vinyl chloride to a treatment plant which alsodischarges to the river, at a distance Lp= 1000 m downstream from the facilitydischarge, a steady effluent flow QeP= 0.5 m

3/sec with a vinyl chloride

concentration CeP= 0.01 mg/L. A sludge flow inm , from the treatment plant is

burned in an incinerator with a destructive removal efficieny DSR = 99.99% and a

mass flow outm =10-4kg/day of vinyl chloride in the stack gas (leaving the

incinerator).

a. Assuming that the vinyl chloride has a first-order decay rate kr= 1/day in theriver, calculate the concentration of vinyl chloride CmPimmediately downstreamfrom the discharge from the treatment plant. (neglect any decay in the channelsleading to the river.)

b.Calculate the mass flow of vinyl chloride in kg/day used by the facility. (do notconsider any decay of the vinyl chloride in the facility, treatment plant, or sludgeflow.)


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10. Air Quality

10.1. A single story home with infiltration rate of 0.5 ach has 200 m2 of floor space and atotal volume of 500 m

3. If 0.6 pCi/m

2-s of radon is emitted from the soil and enters

the house, estimate the steady-state indoor radon concentration.

10.2. A manufacturing company has gathered the following information on annual massflows of methylene chloride (CH2Cl2) in and out of the manufacturing plant:

Purchases of CH2Cl2: 228 barrels

Concentration of CH2Cl2in theflow to the treatment plant:

4.04 mg/L

Discharge to the treatment plant: 0.076 m3/s

CH2Cl2shipped out as hazardous:228 barrels (25% CH2Cl2by volume)

Unused barrels of pure CH2Cl2: 8

Estimate the annual mass emissions of CH2Cl2from the plant to the atmosphere. (Note: 1barrel = 0.12 m3and the density of CH2Cl2is 1326 kg/m3)

10.3. A manufacturing plant receives shipments of pure chlorine (Cl2) at a rate of ( inm )

750 kg/day. The plant manufactures trichloroethylene (TCE) (C2HCl3) which it

ships out ( outm ) at a rate of 700 kg/day. Liquid and solid waste from the plant

passes through a settling basin at a rate of Q = 1000 m3/day. TCE in the sludge

from the settling basin is removed at a rate of sm = 100 kg/day. The concentration

of TCE vapor in the air inside the plant is Cp= 10 mg/m3. The air flow through the

plant volume achieves a ventilation rate I = 1/hr, and the inside volume of the plantis V = 10

5m

3. The ambient concentration of TCE in the outside air is zero.

a. Assuming that the above quantities are the only mass flows in and out of theplant, and that there is no storage of Cl2or TCE inside the plant, what is theconcentration Coutof TCE in the flow out of the settling basin?

Plant

V Cp

Settling basin

sm

outm inm

I

Cout

Q


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b.A total of 100 workers in the plant (each assumed to weigh 70 kg) are exposed tocancer risk by breathing the air at a rate of 20 m3/day for 50 years out of their 70year lifetimes. The potency factor for TCE by inhalation is 1.3 x 10

-2

[mg/kg/day]-1

. The benefit of reducing the risk is estimated to be $2 x 106per

life saved. If the cost of ventilation is $100,000 x I, where I is measured in hr-1,

should the ventilation rate be increased (or decreased) so that the benefits equalthe costs?

c. The sludge from the settling basin is continuously removed and burned in ahazardous waste incinerator. The mass flow of TCE in the airflow from theincinerator is 10

-3kg/day. Does the incinerator meet a performance standard of

DRE 99.99%?

10.4. Determine the PSI and the air quality description for a day in which the followingmaximums occurred: [PSI = 150]

1-hr O3concentration 230 g/m3

8-hr CO concentration 12 mg/m3

24-hr TSP concentration 200 g/m324-hr SO2concentration 325 g/m

3

1=hr NO2concentration 100 g/m3

10.5. A freeway has 10,000 vehicles per hour passing a house 200 m away. Each caremits an average of 1.5 g/mile of NOx, and the wind is blowing at 2 m/s across thefreeway toward the house. Estimate the NOxconcentration at the house on a clearsummer day at noon (neglect any reactions involving NOx). [0.038 mg/m

3]

10.6. A stack emitting 80 g/s of NO has an effective stack height of 100m. The windspeed is 4 m/s at 10m, and it is a clear summer day with the sun nearly overhead.

Estimate the ground level concentration at the following locations:a. Directly downwind at a distance of 2 km [38 g/m3]

b.At a point located 2 km downwind and 0.1 km off the downwind axis. [36

g/m3]

10.7. Sidestream smoke from a cigarette contains roughly 100 g of benzo-a-pyrene.How many cigarettes per day would yield enough sidestream smoke to increase thecancer risk for a non-smoker by 1 x 10

-6if that individual spends all of his time

indoors in a 150-m3home having 0.5 air exchanges per hour? Assume that benzo-a-pyrene has a half-life of 3 days, an inhalation potency factor of 6.11 [mg/kg/day]

-

1, and that its ambient concentration is negligible. [0.01 cigarettes/day]

10.8. An office building with a volume V = 2000 m3and an infiltration rate I = 1/hr is

exposed to the 100 g/m3SO2concentration so that the ambient concentrationaround the office building is Ca= 100 g/m

3. Assuming thatthere are no othersources of SO2in the office, and that the reaction rate for SO2is K = 0.23/hr,determine if the concentration of SO2in the office air exceeds the recommended

limit of 80 g/m3.


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a. If the SO2emission rate is reduced to 20 kg/day, what will be the maximum SO2concentration one kilometer downwind form the most common wind andatmospheric conditions?

b.To reduce the SO2emission rate from 100 to 20 kg/day, a wet scrubber isinstalled that injects lime (CaO) and water (H2O) into the air flow leaving the

incinerator. The lime and water react with the SO2, creating solid calcium sulfitedihydrate (CaSO32H2O) according to the following reaction:

CaO + SO2+ 2H2OCaSO32H2O

c. Determine the mass flow of solid calcium sulfite dihydrate generated in thescrubber, assuming that the required reduction in SO2output is achieved and thatall of the injected lime reacts.

10.9. A tank full of liquid chlorine ruptures and chlorine vapor (Cl2) is emitted at a massrate of 30 kg/min at ground level. The wind speed is 3 m/s. You are asked by the

fire marshal whether she should evacuate an apartment building that is located at adistance L = 300 m downwind from the tank car. The threshold concentration ofCl2vapor for health effects is 1.0 ppm. What is your recommendation?

10.10. A plume of particulate material from a point source has a centerline concentration

C1= 100 g/m3at a distance x1= 100 m from the source. The atmospheric stability

condition is B.

a. What is the centerline concentration of particulates C2in the plume at a distancex2= 1000m from the source?

b.Health data from adult workers exposed to the particulates at a concentration Cw

= 1000 g/m3for a total duration Td= 0.1 years indicate that the risk of dyingfrom this exposure is 10-6. What is the risk to the same adults if they were to

u

H

plume

C1 C2

em

X1

X2


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breath the air in the plume at concentration C1= 100g/m3for a lifetime T1= 70

years.

c. A building with a volume V = 100 m3is exposed to the plume so that the

ambient concentration of the particulates for the building is Ca= C1 = 100g/m3.

There are no sources of particulates in the building. The concentration of the

particulates inside the building C has been measured for different values of theair exchange rate I, as shown on the following plot:

What is the decay coefficient K (same as krand ) for the particulates inside thebuilding?

10.11. The centerline (y = 0) ground level (z = 0) concentration of benzo(a)pyrene at adistance x = 1000 m downwind from a smokestack with an effective height H = 50

m is Cg= 10 g/m3at a time when the wind velocity at the effective height is u = 10m/sec and the atmospheric stability class is C.

a. What is the mass flow the of benzo(a)pyrene out of the stack (kg/day)? [294]

b.If the carcinogenic potency of benzo(a)pyrene is 6.1 [mg/kg/day]-1, what is the

lifetime risk to a person exposed to Cg= 10 g/m3, assuming that the person

breaths 20 m3/day of air and weighs 70 kg? [Risk = 0.017; high]

0

10

20

30

40

50

60

70

80

90

100

0 1 2 3 4 5 6 7 8 9 10

I (1/hr)

C(g/m3)

u

H

plume

em

x

Cg


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c. What is the lifetime risk from exposure to benzo(a)pyrene of a person (with thesame weight and rate of breathing as in part (b)) who spends all the time in a

building exposed to the concentration cg = 10 g/m3(i.e. Cg= Cafor thebuilding), assuming that the building has a volume V = 1000 m

3and an air

exchange rate I = 0.5/hr, that the benzo(a)pyrene has a half-life T1/2= 3 hours,

and that there is no source of benzo(a)pyrene in the building? [Risk = 0.012]

10.12. A factory located on property with dimensions 200 m by 200 m emits a total massflow m = 100 kg/day of a conservative (no decay) toxic compound from a ventlocated a height H = 10 m off the ground (assume this is the effective height ofrelease). The wind speed magnitude, measured at 10 m above the ground, isconstant at u = 5 m/s. but the direction of the wind can vary. The ambientconcentration of the compound is zero. Compute the time averagedconcentration ofthe toxic compound experienced by an individual living at ground level (z = 0) onthe boundary of the factory property which is a distance L = 100 m from the source.Do this computation in two ways:

a. Use the worst-case atmospheric stability condition and assume that the individualexperiences the laterally centered plume concentration (y = 0) at ground level (z= 0) a total of 10% of the time. The other 90% of the time the individualexperiences no effect from the source. Use Table 7.8 and Figure 7.48 in the text.[3.2 x 10

-8kg/m

3]

b.Assume that the air volume over the property is well-mixed to an inversionheight of 50 m and that the individual experiences the mixed concentration 100%of the time. Assume the airflow into and out of the volume is through one of the200 m long sides at the velocity given above. [2.3 x 10

-8kg/m

3]

10.13. A tank truck carrying liquid chlorine overturns and the chlorine vapor (Cl2) is

emitted at a rate em = 0.5 kg/sec, generating a potentially toxic plume. The wind is

estimated to have a speed of u = 3 m/sec directly toward an office building filledwith people that is located a distance L = 300 m downwind.


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a. The fire marshal asks you to help estimate if the people in the building couldpossibly, in the worst case conditions, be exposed to a plume concentrationgreater than 10 ppm of Cl2. What advice do you give her? [238 ppm; evacuate]

b.Experiments with chlorine vapor indicate that in a room with a volume V = 100m3and an infiltration rate I = 1/hr, the concentration inside the room (C) isrelated to the ambient concentration (Ca) by the following plot:

Use this information to estimate the reaction coefficient kr(also K) of the chlorine in the

room. Assume that there is no other source of the chlorine other than the ambient air.[4/hr]

10.14. An unlined hazardous waste landfill is located on a hill above a populated area. Thelandfill area is AL= 100 m

2and the bottom of the landfill is a height LL= 100 m

above the water table. The groundwater flows with a Darcy velocity V = 1 m/daytoward a well located a distance Lw= 1 km from the edge of the landfill. The

hydraulic conductivity of the soil is K = 10 m/day everywhere and the porosity is = 0.4 everywhere. A wind with velocity u = 10 m/s carries a plume of hazardouswaste vapor toward the well site at a height H = 50 m above the ground. Theatmospheric stability category is C.


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a. Estimate how long will it take a contaminant plume with a retardation factor R =5 to reach the well by leaching from the landfill and traveling horizontally with

the groundwater flow. [5.5 years]b.After the contaminant reaches the well, the concentration in the well water is Cw

= 10 mg/L. If the porewater concentration of the contaminant in the landfill is CL= 100 mg/L, what is the area of the aquifer AAthough which the groundwaterflows? Assume that the contaminant leaching is a continuous process that hasreached steady state and that the leaching flow mixes uniformly over the aquiferarea. [10

4m

2]

c. The measured concentration of contaminant vapor in the air is CA= 10 mg/m3at

ground level at the well site. Use the dispersion diagrams in your text to estimatethe rate of contaminant vapor emission Qv(mass/time) from the landfill. [3.5kg/sec]

d.If a person living near the well breathes 20 m3of air a day and drinks 2 L a dayof water from the well, what is the ratio of the risk of cancer from breathing tocancer from drinking? Use the values for CAand Cwgiven above. [Risk of cancerfrom breathing is 10 times the risk of cancer from drinking]

10.15. A recent article in theNew York Timessaid that airline passengers are complainingof headaches they claim are caused by reduced rates of ventilation of the passengercabi

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