CEE 577

29 Oct 1997

MID-TERM EXAM

Closed book, 1 sheet of notes allowed.

Answer both questions. Please state any additional assumptions you made, and show all work.

 

  1. (60%) Crystal Creek emerges from pristine headwaters and runs through an agricultural region before it reaches the city of Metropolis. The BOD of the headwaters is essentially zero, and the dissolved oxygen is at saturation (10.1 mg/L for 15oC). Starting at mile point zero, there is a significant non-point agricultural runoff of BOD amounting to 50 kg/mile/day. At mile point 8.0, the stream leaves the agricultural area, and is met by the Metropolis WWTP outfall. Here a WW flow of 4 cfs is discharged with a BOD of 20 mg/L and a DO of 6 mg/L. Calculate the dissolved oxygen concentration 2 miles downstream of the Metropolis WWTP outfall (T=15oC). Assume the flow is constant at 40 cfs from the headwaters to the WWTP outfall. Assume no significant SOD.

 

Additional Information:

U = 0.150 ft/sec = 2.45 miles/day T = 15oC

DOsat or Cs = 10.1 mg/L (at 15oC) H = 6 ft = 1.83 m

CBOD deoxygenation rate (kd) = 0.8 day-1 (at 15oC) for kd, q =1.047

CBOD settling rate (ks) = 0.080 day-1 (at 15oC) for reareation, q =1.024

 

 

SOLUTION:

Segment #1

General Parameters

U =

0.15

ft/s =

2.45455

mi/day =

0.04572

m/s

T =

15

deg-C

Cs =

10.1

mg/L

H =

6

ft =

1.82882

m

kd =

0.8

/d @

15

deg-C

ks =

0.08

/d @

15

deg-C

SOD =

0

g/m2/d @

15

deg-C

x =

8

miles =

42240

ft

Upstream Water

Qu =

40

cfs

Lou =

0

mg/L

Cu =

10.1

mg/L

Point Source

Qw =

0

cfs

Low =

0

mg/L

Cw =

0

mg/L

Non-Point Source (Lrd or Sd)

runoff=

50

kg/mi/d

runoff=

1.254026224

mg/L/d

run+SOD=

1.254026224

mg/L/d

Parameter Calculations

Tdesign =

15

deg-C

kd =

0.8

/d @

15

deg-C

kr =

0.88

/d @

15

deg-C

ka =

0.301931678

/d @

15

deg-C

O'Connor-Dobbins Formula

sb' =

0

mg/L/d @

15

deg-C

Initial Values (from mass balance)

Lo =

0

mg/L

Co =

10.1

mg/L

Do =

0

mg/L

x/U =

3.259259259

d

Dissolved Oxygen Deficit Terms

Net

CBOD Terms

Net

Desired x

Diss

CBOD

(miles)

Init-D

PS

NPS-1

NPS-2

Oxygen

PS

NPS-1

8

0.00

0.00

2.36

-0.63

8.36

0.00

1.34

1.34

 

Segment #2

General Parameters

U =

0.15

ft/s =

2.45455

mi/day

T =

15

deg-C

Cs =

10.1

mg/L

H =

6

ft =

1.82882

m

kd =

0.8

/d @

15

deg-C

ks =

0.08

/d @

15

deg-C

Sb =

0

g/m2/d @

15

deg-C

x =

2

miles =

10560

ft

Upstream Water

Qu =

40

cfs

Lou =

1.344

mg/L

Cu =

8.3607

mg/L

Point Source

Qw =

4

cfs

Low =

20

mg/L

Cw =

6

mg/L

Non-Point Source (Lrd or Sd)

runoff=

0

kg/mi/d

runoff=

0

mg/L/d

run+SOD=

0

mg/L/d

Parameter Calculations

Tdesign =

15

deg-C

kd =

0.8

/d @

15

deg-C

kr =

0.88

/d @

15

deg-C

ka =

0.301931678

/d @

15

deg-C

O'Connor-Dobbins Formula

sb' =

0

mg/L/d @

15

deg-C

Lo =

3.040074887

mg/L

Co =

8.146078374

mg/L

Do =

1.953921626

mg/L

x/U =

0.814814815

d

Dissolved Oxygen Deficit Terms

Net

CBOD Terms

Net

Desired x

Diss

CBOD

(miles)

Init-D

PS

NPS-1

NPS-2

Oxygen

PS

NPS-1

2

1.53

1.24

0.00

0.00

7.34

1.48

0.00

1.48

 

II. (40%) Lake Noir is an urban surface water that has received inputs of cadmium for many years. Efforts to clean up the lake have resulted in the termination of all cadmium loads. Lake levels have dropped due to decay (0.00005 d-1) and hydraulic flushing. Unfortunately, Senator Porkbarrel has succeeded in getting his brother's newly established business exempted from the cadmium ban. This metal plating plant will be discharging 400 kg/d of cadmium into the lake on its first day of operation. It is expected to grow at a constant rate for at least the next 5 years. Estimates of its growth translate to an increase in cadmium loading of 60,000 kg for each year of operation. On the first day of operation of Porkbarrel and sons Metal Plating Inc, the lake concentration of cadmium was 0.5 mg/L. Calculate the expected cadmium concentration 5 years later. The lake has a volume of 1.75 billion cubic meters, a surface area of 0.11 billion square meters, and an outflow of 1.0 million cubic meters per day. Ignore any temperature effects.

 

 

Solution: