Chapter 3 Solutions to Odd Numbered Problems
These solutions were provided by Dr. Todd Rayne of Hamilton
College.
3.1
What is the weight in newtons
of an object with a mass of 14.5 kg
-----------------
3.3 An object has a mass of 78.5 kg and a volume of
0.45 m3.
(A) What is its density?
(B) What is its specific weight?
(C) Is the
object more or less dense than water?
a. 
b. Specific Weight: 
c. 
-----------------
3.5. The hydraulic conductivity of a silty sand
was measured in a laboratory permeameter and found to be 3.75 3 10–5
cm/s at 25°C. What is the intrinsic permeability in cm2? Refer to
Appendix 14 for values of density and viscosity.
-----------------
3.7. A constant-head permeameter has a cross-sectional area of 78.5
cm2. The sample is 23 cm long. At a head of 3.4 cm, the permeameter discharges
50 cm3 in 38 s.
(A) What is the hydraulic conductivity in
centimeters per second and feet per day?
(B) What is the intrinsic permeability if the
hydraulic conductivity was measured at 15°C?
(C) From the hydraulic conductivity value, name
the type of soil.
a. 
b. 
c. 
-----------------
3. 9. An aquifer has a
specific yield of 0.19. During a drought period, the following average declines
in the water table were noted:
Area Size (km2) Decline
(m)
A 15 2.34
B 7.5 1.22
C 18.3 0.76
D 22.5 3.44
E 9.44 1.89
F 22.7 0.35
What was the total volume of water
represented by the decline in the water table?
and 
-----------------
3.11. A confined aquifer has a specific storage of 1.022 3 10–6
ft–1 and a thickness of 23 ft. How much water would it yield if the
water declined an average of 1.75 ft over a circular area with a radius of 418
ft?
-----------------
3.13. A confined aquifer has a specific storage of 4.033 3 10–3
m–1 and a porosity of 0.274. The compressibility of water is 4.6 3
10–10 m2/N. What is the compressibility of the aquifer
skeleton?
3.15. An aquifer has three different formations. Formation A has a
thickness of 22 ft and a hydraulic conductivity of 17.0 ft/d. Formation B has a
thickness of 3.5 ft and a conductivity of 99 ft/d. Formation C has a thickness
of 26 ft and a conductivity of 22 ft/d. Assume that each formation is isotropic
and homogeneous. Compute both the overall horizontal and vertical
conductivities.
A 17.0 22
B 99 3.5 and total 
C 22 26
3.17. Use the Hazen method to estimate the hydraulic conductivity of
the sediments graphed in Figure 3.33.
From
Equation 3-20, 
--------------------
3.19. Given the following set of data representing the hydraulic
conductivity of core samples from the same formation, perform the following:
Sample # K (m/s)
1 4.3 3 10–4
2 6.1 3 10–3
3 2.5 3 10–5
4 1.2 3 10–4
5 1.0 3 10–6
6 7.1 3 10–3
7 9.1 3 10–6
8 2.2 3 10–3
9 4.2 3 10–5
10 8.7 3 10–4
11 3.5 3 10–5
(A) Find the arithmetic mean of the data set.
(B) Find the geometric mean of the data set.
(C) Make a histogram of the data set.
(D) Make a histogram of the log transformed data.
|
Sample
# |
K
(m/s) |
ln
(K) |
|
K
bin |
ln
(K) bin |
|
1 |
4.30E-04 |
|
|
1.00E-03 |
|
|
2 |
6.10E-03 |
|
|
5.00E-04 |
|
|
3 |
2.50E-05 |
|
|
1.00E-04 |
|
|
4 |
1.20E-04 |
|
|
5.00E-05 |
|
|
5 |
1.00E-06 |
|
|
1.00E-05 |
|
|
6 |
7.10E-03 |
|
|
5.00E-06 |
|
|
7 |
9.10E-06 |
|
|
1.00E-06 |
|
|
8 |
2.20E-03 |
|
|
|
|
|
9 |
4.20E-05 |
|
|
|
|
|
10 |
8.70E-04 |
|
|
|
|
|
11 |
3.50E-05 |
|
|
|
|
|
|
|
|
|
|
|
|
sum |
1.69E-02 |
|
|
|
|
|
histogram
data for K |
|
histogram
data for ln (K) |
||
|
Bin |
Frequency |
|
Bin |
Frequency |
|
1.E-06 |
1 |
|
|
1 |
|
5.E-06 |
0 |
|
|
1 |
|
1.E-05 |
1 |
|
|
3 |
|
5.E-05 |
3 |
|
|
1 |
|
1.E-04 |
0 |
|
|
0 |
|
5.E-04 |
2 |
|
|
2 |
|
1.E-03 |
1 |
|
|
1 |
|
|
3 |
|
|
1 |
|
|
|
|
|
1 |
|
|
|
|
|
|
The histograms can be found on page 563
of the text.