CVEN3501 - Water Resources Engineering - Engineering Assignment Help

Assignment Task

The Problem
The objective of the assignment is to use the spreadsheet package Microsoft Excel to investigate the effect of changing boundary conditions to a simple rectangular isotropic and homogeneous confined aquifer with and without a groundwater pumping bore abstracting or injecting water. The assignment is based on the analysis of Frank and Reilly (1987).
You should set up an aquifer model of an area 800 m wide (AB and CD) by 1,500 m long (BC and DA). Use a finite difference discrimination where ?x = ?y = 100 m. Your model will then be 9 nodes wide in the x-direction (extending from node 0 to node 8 on boundaries AB and CD) and 16 nodes long in the y-direction (extending from node 0 to node 15 on boundaries BC and DA). Each student will have a unique set of data for the transmissivity (T [m2 /day]), Pumping rate (Q [m3/day]) and a letter (A to L) representing the bore location. Find your data in the excel sheet on Moodle (CVEN3501 Assignment 2 individual values 2021.xlsx). Figure 1 shows how the bore location letter corresponds to a node in the numerical scheme. For the spread sheet to successfully iterate, circular references should be enabled. In Microsoft Excel 2010+ this is done under the menus: ”File” - ”Options” - ”Formulas”, where you need to tick ”Enable iterative calculation”, set ”Maximum iterations” to 30,000 and ”Maximum change” to 0.0001.

Model the following two sets of aquifer conditions:
Condition 1: The problem domain (aquifer) is surrounded by Dirichlet (fixed head) boundary conditions. Use a linear decrease in head from 15 m to 0 m along BC and AD, a fixed head of 0 m along boundary CD, and a fixed head of 15 m along boundary AB.
Condition 2: The problem domain (aquifer) is surrounded by a mix of Dirichlet and Neumann (no flow) boundary conditions. Use a no-flow boundary condition (with ∂h/∂x = 0) across BC and AD, a fixed head of 0 m along boundary CD, and a fixed head of 15 m along boundary AB.

Provide the answers for the following questions in Moodle:
1. On Moodle, pick the equation which best represent a Dirichlet boundary condition.

2. Pick the equation which best represent a no-flow boundary condition in a discretised scheme. 
3. Pick the equation which best represent the implementation of a pumping bore at a single node in a numerical scheme.
4. Calculate the flow though the aquifer for Condition 1 without any abstraction. Hint: Check that the flow calculated by the spreadsheet is correct using Darcy’s Law.
5. Calculate the flow though the aquifer for Condition 2 without any abstraction. Hint: Check that the flow calculated by the spreadsheet is correct using Darcy’s Law.
6. Using your unique values of the transmissivity, the bore node location and the abstraction or injection rate, calculate the water level (relative to the datum) at the given node location and the flows across each of the 4 boundaries, as determined by the model, for Condition 1. Note that abstraction (Q) is negative (by convention) out of the aquifer. Calculate your flows over the boundaries as positive if into the aquifer and negative if out of the aquifer. 

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