CE 254 (Fall 2001)
Assignment #2
Due: Thursday Oct 11
Problem 1 Erosion
An acre of land is exposed to 15 inches of rain in a year. What equivalent depth of soil
(in inches) is eroded if the annual average concentration of TSS in the runoff from this
acre is 200 mg/L. Assume that the average specific gravity of soil particles is 2.2, and
that the runoff coefficient (C) for an annual rational formula calculation (Q = CiA) is 0.85
(bare ground).
Problem 2 Volatilization
Imagine an accident on a bridge involving a tank truck carrying a load of
tetrachloroethylene. If 50 lb of the tetrachloroethylene falls into the river in the space of a
minute, and the volatilization rate coefficient is 0.02/min, estimate how many miles
downstream you’d have to go to find water that met the water quality objective (standard)
of 0.005 mg/L. Assume that the river flow is 15,000 cfs, that the average cross sectional
area of the river is 1200 ft2, and that the tetrachloroethylene completely mixes with the
river under the bridge.
Problem 3 Adsorption
Let’s consider the equilibrium between dissolved and adsorbed pentachlorophenol (a
wood preservative with a molecular weight of 266.34), which has a (linear) partitioning
coefficient of 6.3x10-4 mg/g per mg/L.
(a) Suppose the Sacramento River has a TSS of 150 mg/L (mostly made up of silts and
clays) and a pentachlorophenol concentration of 10 g/L. At equilibrium, what is the
total mass (in all phases) of pentachlorophenol per liter? What fraction is in the
liquid phase and what fraction is in the solid phase?
(b) Now suppose the sediments settle out and form a layer of material in the bottom of
the river with a porosity of 0.4. Assuming the pore water has the same concentration
of pentachlorophenol as before, what is the mass of pentachlorophenol in a liter of the
sediment? What fraction is in the liquid phase and what fraction is in the solid
phase? Assume the sediment has a specific gravity of 2.2.
Problem 4 Eutrophication
Given the stoichiometric equations presented in class for algae growth and oxygen
demand as algae decay, estimate (a) the mass of algae growth that would result from 50 lb
of nitrate being added to the water, and (b) the mass of oxygen taken from the water when
these algae die.
1
Problem 5 DOSAG Exercises
Start with the DOSAG model emailed to you separately.
(a) Demonstrate, using hand calculations, that for the conditions specified, the
concentration at x = 35 km matches the value shown in the calculated table.
(b) Let’s presume that the river in the model is fairly clear and that the wastewater
has very few settleable particles. Print a copy of the original graph. Now sketch
on that graph what you think the oxygen profile would look like (i) if the river
had a lot of algae in it (daytime only), and (ii) if the wastewater BOD was mainly
in the form of large particles that settled rapidly. In addition to the graph, provide
a couple of sentences for each case describing why your sketched profile looks the
was it does.
(c) Imagine you are writing the discharge permit for this facility and that you need to
protect an endangered trout by keeping the dissolved oxygen concentration in the
river above 6 mg/L. Using the model, determine the maximum BOD5
concentration that can be allowed in the waste discharge. Print and submit the
calculation page and the graph with both the original condition and your proposed
solution.
(d) Suppose that you want to investigate the possibility of protecting the trout by
increasing the flow from an upstream dam instead of providing more treatment
(i.e., the BOD5 of the discharge stays at 30 mg/L). Use the model to determine
the flow needed. Assume that the velocity increases proportionately with the flow
(i.e., if the flow doubles, the velocity doubles). Print and submit the calculation
page and the graph with both the original condition and your proposed solution.
If needed. Adjust your x values so that the minimum concentration can be seen on
the graph.
(e) The environmental conditions shown in the model correspond to Spring and Fall.
Winter and summer conditions are shown below. Using your BOD5 result from
Part (b), model the river under summer and winter conditions. Print and submit
the calculation page and a graph showing all three seasons. Comment on whether
your proposed solution in Part (b) is adequate.
Winter
Qriver (m3/s)
u (m/s)
T (C)
Spring/Fall
(starting values)
1.0
0.05
12
4.0
0.15
6
Summer
0.5
0.03
18
Criver upstream = 85% of the saturation value in all seasons.
BOD5 in river upstream = 5 mg/L in all seasons.
Temperature adjustments for constants can be made using the values provided in
the spreadsheet.
2
Problem 6 pH effects
Shown below is a titration curve for Putah Creek, a coastal stream (sedimentary rock
formations). In making this curve, 0.02 N H2SO4 was added to 250 mL of the creek
water.
(a) What’s the alkalinity of this water? Report your answer in equivalents per L of
sample.
(b) Using the curve, estimate the drop in pH if 100 qpm of a waste (0.5 N) is discharged
to the creek. Assume the creek flow is 50 cfs.
(c) Would you expect water from the American River to have a larger or smaller
alkalinity? Explain why.
3