Hydrosystems Engineering (EACEE 3250 / 4250)
Spring 2025
Homework #4 (Due Friday, April 25th, 11:59 pm)
Homework Guidelines:
Your solutions to homework assignments will be submitted and graded through Gradescope (see the Gradescope tab on your Courseworks dashboard).
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choose to type up your calculations, in which case show all your steps and highlight your solution. Note: During the upload, Gradescope will ask you to mark which page/s each problem is on (see example here). It is important that you follow that step for grading purposes.
It is acceptable to discuss problems with your colleagues, and questions are encouraged during office hours, but all work must be done independently. Make sure to clearly show all work on each problem and that your solutions are presented in an orderly fashion. It is your responsibility to make your solutions easy to grade.
Topics/Chapters covered:
• Chapter 9: Groundwater flow, well hydraulics, superposition
• Solute and contaminant transport (notes)
Problem #1 Groundwater Flow (25 pts)
The aquifer shown in the below images has small amount of leakage R through the confining lower aquitard. In order to estimate this loss rate three observation wells are installed, as shown below. The observation wells are 500 m apart and each record the following steady head values: Well #1 h1=50.00 m, Well #2 h2=46.25 m and Well #3 h3=45.00 m.
The aquifer material is homogeneous with transmissivity T =1000 m2day-1. Estimate the loss rate R and report it in mm day-1.
Problem #2 Groundwater Flow (25 points)
The earth dam shown below is 10 m high and 20 m wide. Its thickness is 3 m. The water level in the lake sits at 9 m above the base of the dam. In the stream below the dam the water level is steady at 0.5 m above the dam base. The flow in the stream is a product of water percolation through the earth dam and is measured to be constant at 270 m3 /day.
(a) Would you consider the earth dam to abide by the properties of an unconfined or confined aquifer? Why?
(b) Determine the head profile, h(x), in this earth dam.
(c) What is the hydraulic conductivity K (m/day) of the material in the earth dam?
Problem #3 Pumping Wells & Superposition (25 pts)
A well located 100 m west of a very large lake is pumped at a rate of Q = 150 m3 day-1 (see Figure 2 below). The lake has a fixed piezometric head of 18 m. There are two observation wells nearby: well “A” is located 8 m north and 5 m east of the pumping well, and well “B” is located 50 m south and 4 m west of the pumping well. The aquifer that the well is pumping from is confined and is homogeneous and isotropic and has a storativity, S = 1.0 x 10-4 and a transmissivity, T = 50 m2 day-1.
Figure 2: Plan view of lake, pumping well, and observation wells for problem #2.
a) Estimate the piezometric head at the two observation wells 24 hours after pumping begins. You can safely assume that prior to pumping, the undisturbed piezometric surface over the domain was equal to the lake surface. Clearly document how you solve the problem.
b) Are the drawdowns at the observation wells less than, greater than, or equal to the drawdown that would exist if the aquifer were of infinite extent (i.e. no lake boundary)? Briefly explain why this is using physical arguments.
c) Additionally, show that with the solution obtained using image wells, the piezometric head at the lake remains constant at the lake boundary (as it should). Hint: in your explanation, you can do so by considering a hypothetical observation well at the boundary between the lake and the aquifer.
Problem #4 Solute/Contaminant Transport (25 pts)
The Plug and Chug Factory (P&G), located between two lakes suffers a leak in one of their toxic chemical pipes. This leak is eventually detected and sealed, but only after the chemicals had entered the homogenous confined aquifer. The Darcy flux in the aquifer is 1 m/day and the porosity of the aquifer material is 0.33. The concentration of the chemical that enters the aquifer is 100mg/L. Assume the chemical continues to leak into the aquifer undetected and that the chemicals mix through the depth of the aquifer instantaneously. Assume we have 1-D flow.
The general solution to the advection-diffusion transport equation in one dimension is defined as:
The analytical solution for this scenario using the complementary error function (erfc) is:
a) What are the two components of the overall D in the above equations? Would D likely increase or decrease if pore velocity decreased? Why?
(No calculations needed.)
b) Assuming D = 1x10-4 m2/s, plot the concentration profiles (in a software of your choosing, such as Excel or Matlab) for the following times and for each time indicate if the spill has been detected:
i. t=10 days
ii. t=30 days
iii. t=50 days
iv. t=100days
Combine your profiles on one plot, if possible,for ease of comparison.
c) The health department believes that concentrations of the chemical greater than 10mg/L is dangerous for consumption.
i. Calculate or estimate the time at which the concentration in Well B becomes greater than 10mg/L.