Homework Set IV - CE 310
Fall 2013
Due October 21
B.A. DeVantier
General Instructions: You may print neatly or use word processing for the written portion of your
homework. Graphs may be done by hand or computer spreadsheet software (unless specified in
the problem statement), but when done by computer, a copy of the Excel spreadsheet used must
be sent as an attachment to the class instructor’s email [email protected] verifying your
independent computer-based work. Submit your homework as a hard copy. Hard copy of
spreadsheet graphs should be submitted along with printout of the representative parts of data
and example calculations where spreadsheet formulae are used.
Problem 1
Class text End of Chapter Problem 7-4. Infiltration data from an experiment yield
an initial infiltration rate of 4.7 cm/hr and a final equilibrium infiltration rate of 0.7 cm/hr after 60
min of steady precipitation. The value of (the Horton) k was estimated to be 0.1085 hr-1. Determine
the total volume of infiltration (into an area of 1 m2) for the following storm sequence: 30 mm/hr
for 30 min, 53 mm/hr for 30 min, and 23 mm/hr for 30 min.
Problem 2
Class text End of Chapter Problem 7-10. Two piezometers have been placed along
the direction of flow in a confined aquifer that is 30 m thick. The piezometers are 280 m apart. The
difference in piezometric head between the two is 1.4 m. The aquifer hydraulic conductivity is 50
m/day, and the porosity is 20%. Estimate the travel time for water to flow between the two
piezometers.
Problem 3
Class text End of Chapter Discussion Question 7-3. When a flood has a
recurrence interval (return period) of 5 years it means that the chance of another flood of the same
or less severity occurring next year is 5%. Is this sentence true or false? If it is false, rewrite the
sentence to make it true.
It is false, because a 5-year return period means the probability of the same or higher flood
conditions in any given year is 1 in 5 or P = 1/5 (20%).
Rewritten to be true: When a flood has a recurrence interval (return period) of 5 years, it means
that the chance of another flood of the same or higher severity occurring the next year (or any
other year) is 20%.
Alternately: When a flood has a recurrence interval (return period) of 20 years, it means that the
chance of another flood of the same or higher severity occurring the next year is 5%.
Problem 4
The Faner parking lot near the crosswalk to the Engineering Buildings drains a
rectangular area 350 ft by 50 ft down a 1.1% slope with a runoff coefficient of 0.95. Estimate the
collected flow near the crosswalk for both 5-year and 10-year storms using the I-D-F curve
supplied for Cairo.
Problem 5
Class text End of Chapter Problem 9-2. Bacterial cells have been represented by
the chemical formula C5H7NO2. Compute the theoretical oxygen demand (in grams O2 / mol of
cells) assuming the following reactions apply
C5H7 NO2  5O2  5CO2  2H2O  NH3
NH3  2O2  NO3  H  H2O
Note that the first chemical reaction is a carbonaceous demand and the second is nitrogenous.
Problem 6
Class text End of Chapter Problem 9-5. If the BOD5 of a waste is 220 mg/L and
the ultimate BOD is 320 mg/L, what is the rate constant? Additionally estimate the BOD at 8 days.
Problem 7
Class text End of Chapter Problem 9-12. What sample size (in percent) is required
for a BOD of 350 mg/L, if the oxygen consumed is limited to 6 mg/L?
Problem 8
Class text End of Chapter Problem 9-26. Note that the text incorrectly refers to 929 rather than 9-25 intended. Chapter Problem 9-25: The initial ultimate BOD after mixing of the
Bergelmir River is 12.0 mg/L. The DO in the Bergelmir River after the wastewater and river have
mixed is at saturation. The river temperature is 10 C. At 10 C, the deoxygenation rate constant (kd)
is 0.30 day -1, and the reaeration constant (kr) is 0.4 day-1. Determine the critical transit time (tc*) and
the critical DO..Chapter Problem 9-26: Repeat Problem 9-25, assuming the river temperature rise
to 15 C
Problem 9
Develop a spreadsheet that will solve for the DO values downstream of the
discharge in Problem 9-26 and plot the DO results over a t* range of 0 – 4tc*.
At Standard (20C)
Temp. C
10
kr(1/day)=
0.4
kd(1/day)=
0.3
kr(1/day)=
0.50706
kd(1/day)=
1.06434
At River Mixed Temp.
La(mg/L)=
Ta(C)=
12.00
Csat
(mg/L)=
C (mg/L)
10.15
9.159798
8.322408
7.620074
7.03688
6.558573
6.172398
5.86695
5.632044
5.45859
5.338488
5.264524
5.230284
5.230074
5.258843
5.312121
5.385955
0.565
1.978056
0.00
Using 4*t-crit as the t* range
D
C
12
10
Cor D (mg/L)
D (mg/L)
0
0.990202
1.827592
2.529926
3.11312
3.591427
3.977602
4.28305
4.517956
4.69141
4.811512
4.885476
4.919716
4.919926
4.891157
4.837879
4.764045
kd(1/day)=
10.15
Da(mg/L)=
0
0.1582445
0.316489
0.4747335
0.632978
0.7912225
0.949467
1.1077114
1.2659559
1.4242004
1.5824449
1.7406894
1.8989339
2.0571784
2.2154229
2.3736674
2.5319119
0.450
15
t*crit(day)=
t*(day)
kr(1/day)=
8
6
4
2
0
0
2
4
6
t* (day)
8
10
2.6901564
2.8484009
3.0066454
3.1648898
3.3231343
4.67314
4.568232
4.452019
4.326861
4.194823
5.47686
5.581768
5.697981
5.823139
5.955177