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33. a. From the geometry of the building foundation, it is evident that the
water table must be lowered by 2.5 m at a distance of 15 m from the
b. For this transient case, the Theis equation must be used. First
estimate the value of ufrom Eq. (3.12):
c. If a well is installed in each corner, the drawdown in the center of
the excavation area due to each well being pumped only needs to
34. a. To determine if you can rule out the possibility of drawing in water
from beneath the gas station, estimate the hydraulic gradient that
occurs due to the superposition of the natural gradient and the
gradient due to pumping. Use Eq. (3.6) to estimate the hydraulic
gradient due to pumping:
e99CHAPTER 3 SOLUTIONS
b. The estimation of the hydraulic gradient due to pumping assumes
a constant aquifer thickness, steady state, and a constant hydraulic
35.
36. a. First estimate a retardation factor to see if this accounts for the
e100 SOLUTIONS MANUAL ONLINE
b. The pH could be dropping as an indirect result of gasoline
contamination due to redox reactions. Microbial activity could be
37. a. First estimate how many moles of heptane remain in the aquifer:
e101CHAPTER 3 SOLUTIONS
38. The pH of the precipitation, 3.9, is so low that H
þ
is almost entirely
from H
2
SO
4
, a strong acid that can be treated as fully ionized:
H2SO4!2HþþSO42
39. The initial reaction is oxidation of acetate ions using O
2
, until O
2
is
depleted. Carbon changes oxidation state from (0) to (þIV) during this
reaction:
e102 SOLUTIONS MANUAL ONLINE
a. The Deffeyes diagram of Fig. 2.20 would not be adequate to model
b. The first step in the sequence of chemical evolution of the water is
4
40. a. First estimate where the peak location will occur by using Eqs. (3.5)
and (2.3a):
e103CHAPTER 3 SOLUTIONS
max
b. The hydrophobic organic chemical will not move at the seepage
velocity, but will be retarded due to sorption. First calculate
a distribution coefficient using Eq. (3.26):
c. First estimate an overall pseudo-first-order rate constant for
hydrolysis using Eq. (2.89):
41. A decrease in soil water content in the vadose zone will:
a. decrease hydraulic conductivity;
42. a. Use the form of the Thiem equation shown in Eq. (3.8b) to estimate
the aquifer transmissivity:
e104 SOLUTIONS MANUAL ONLINE
43. a. Hydraulic conductivity is a measure of specific discharge per unit
of elevational gradient, which depends on the acceleration due to
b. If C
T
cannot be greater than 10
4
Min the treated water, and ionic
species can be removed from the water during treatment, then the
e105CHAPTER 3 SOLUTIONS
44. a. From Table 1.3, the vapor pressure of toluene is 3.7 10
2
atm. The
concentration of toluene vapor at the water table can be estimated
from Eq. (1.25):
b. From Table 1.3, the density of toluene is 0.87 g/cm
3
, and the
molecular weight is 92 g/mol. Thus, the amount of toluene per
unit area of water table is:
45. a. From Eq. (3.2),
b. From Eq. (3.8c),
e106 SOLUTIONS MANUAL ONLINE
c. Assuming that the well is not being pumped, water containing
dissolved fuel would travel according to the natural hydraulic
gradient, with the fuel’s transport slowed by retardation. From
Eq. (3.26),
46. a. An ideal tracer, which is nonsorbing, travels at the seepage
velocity:
b. The peak containing 68% of the mass is 3.4 sec wide; this
corresponds to a spatial width of (3.4 sec) (1.5 cm/sec) ¼5.1 cm.
This width encompasses one standard deviation on either side of
c. The effective molecular diffusion coefficient is approximately
d. Acetate is retarded:
47. a. For drawdown/mounding of 30 cm at a radius of 15 ffiffiffi
2
pm, what is
the required value of Q
w
, the flow rate of the well? From Eq. (3.8b):
e107CHAPTER 3 SOLUTIONS
b. From Eq. (3.8c):
48. a. From Eq. (1.21),
b. From Eq. (2.88),
c. For pH 6.7,
49.
a. Summing the cation concentrations gives 7.3 meq/liter, as does
summing the anion concentrations. Therefore, it does not appear
b. If this water is in equilibrium with air, [H2CO3]10
4.9
M.
Ion Conc. (mg/liter) MW (g/mol) Conc. (mol/liter) Conc. (meq/liter)
Ca
2þ
110 40 2.7510
3
5.5
e108 SOLUTIONS MANUAL ONLINE
c. New C
T
¼2(6.4610
3
Mþ10
4.9
M)¼1.310
2
M
T
50. a. From Eq. (3.8c):
b. The slope of the water table due to the cone of depression can be
calculated using Eq. (3.7b); multiplying by Kgives specific
e109CHAPTER 3 SOLUTIONS
c. Log K
ow
for TCE is 2.42 from Table 1.3. Using the approximation
51. a. From Eq. (3.2):
b. Bromide moves at a speed equal to:
c. Dissolved toluene will be retarded. Log K
ow
for toluene is 2.69
52. From Eq. (2.71a):
e110 SOLUTIONS MANUAL ONLINE
