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Ground water hydrology problems

Group Four
1. A well in a water-table aquifer was pumped at a rate of 873 m3 min−1. Drawdown
was measured in a fully penetrating observation well located 90 m away. The
following data (Table below) were obtained:
Find the transmissivity, storativity, and specific yield of the aquifer.
2. In an aquifer, Kxx = 100 m/day, Kyy = 10 m/day, and Kxy can be ignored. Where
the x and y axes are along the east/west and north/south directions, receptivity.
Groundwater flows toward east direction in this aquifer. The development of a
new well field will cause the mean head gradient to shift from the east to
southeast. Compare the specific discharge in the direction of the head gradient
for a gradient of 0.01 in the east direction with the specific discharge in the
direction of the head gradient of 0.01 in the southeast direction. In either of these
cases, does the groundwater flow have the direction of the head gradient?
3. A confined aquifer has a length of 1000 m, transmissivity of 500 m 2/day, and
storage coefficient of 0.0002. The head is initially uniform at 20 m. The head
increases to 50 m at the inlet boundary and to 40 m at the outlet boundary. Solve
the one-dimensional transient groundwater flow equation using: (a) Explicit finite
difference method (b) Implicit finite difference method
4. For two-dimensional flow in an aquifer having a length of 1000 m and width of
800 m, find out the head at different points. The properties of the aquifer, initial
conditions, and boundary conditions are given below.
Transmissivity in x-direction = 500 m2/day
Transmissivity in y-direction = 700 m2/day
Storativity in x-direction = 0.0002
Storativity in y-direction = 0.0002
Initial condition: h = 60 m, t = 0, 0 ≤ x ≤ 1000 m, 0 ≤ y ≤ 800 m
Boundary conditions: h=100m, t ≥ 0, 0 ≤ x ≤ 1000 m, y=0
h=80m, t ≥ 0 , 0 ≤ x ≤ 1000 m, y=800
h=70m, t ≥ 0 , 0 ≤ y ≤ 800, x=0
h=90m, t ≥ 0 , 0 ≤ y ≤ 800, x=100
5. A sample of silty sand has a volume of 215 cm3. It has weight of 514.7 g. After
saturating the sample is weighed 594.2 g. The sample is then drained by gravity
until it reaches a constant weight of 483.4 g. Finally, the sample is dried in oven
for ten hours and it reaches the weight 452.1 g. Assuming the density of water is
1 g/cm3, compute the following: (a) Water content of the sample. (b) Volumetric
water content of the sample. (c) Saturation ratio of the sample. (d) Porosity (e)
Specific yield (f) Specific retention (g) Dry bulk density
6. Consider two strata of the same soil material that lie between two channels. The
first stratum is confined and the second one is unconfined, and the water surface
elevations in the channels are 30 m and 15 m above the bottom of the unconfined
aquifer. What is the thickness of the confined aquifer for which a) The discharge
through both strata are equal? b) The discharge through the confined aquifer is
half as compared to the unconfined aquifer?
7. A well fully penetrates a 30-m thick confined aquifer. After a long period of
pumping at a constant rate of 0.07 m3/s, the drawdowns at distances of 40 m and
120 m from the well were observed to be 3 in and 1.5 m, respectively. Determine
the hydraulic conductivity and the transmissibility. What type of unconsolidated
deposit would you expect this to be?
8. A new borewell is to be installed in a regionally confined aquifer with a
transmissivity of 150m2 d−1 and a storativity of 0.0005. The planned pumping rate
is 1.5 m3 min−1. As there are several nearby wells tapping the same aquifer, it is
required to know if the new well will interfere significantly with these wells:
(a) Compute the theoretical drawdown caused by the new well after 30 days of
continuous pumping at the following distances: 10, 50, 150, 250, 500, 1000,
3000, and 6000 m.
(b) Plot distance-drawdown data on semi-log paper.
(c) If the pumping well has a radius of 0.3 m, and the observed drawdown in the
pumping well is 39 m, what is the efficiency of the well?
(d) If the aquifer is not fully confined but is overlain by a 4mthick confining layer
with a vertical hydraulic conductivity of 0.04md−1,what would be the drawdown
after 30 days of pumping at 1.5 m3 min−1 at the indicated distances, neglecting
storativity of the aquifer?
(e) For the new well and aquifer system, plot the drawdown at a distance of 6 m at
the following times: 1, 2, 5, 10, 15, 30, and 60 min; 2, 5, and 12 hr; and 1, 5, 10,
20, and 30 days.