Value for transmissivity is 185，location is B，flow rate is
20
Question 1: No-flow boundary conditions are implemented by: Question 2: Flow Calculation with no abstraction or recharge m2/day m/day Condition 1 flow is Condition 2 flow is Question 3: Recharge or abstraction at a node is calculated by: Question 4: Water Level and Flows for Condition 1 are: Water level at pumping/recharge node Flow accross boundary AB Flow accross boundary CD ..,..) is m3/dayFlow accross boundary BC m/dayFlow accross boundary DA m above datum m/day m/day Question 5: Water Level and Flows for Condition 2 are: Water level at pumping/recharge node (...,...) Flow accross boundary AB Flow accross boundary CD is m/day Flow accross boundary BC m3/dayFlow accross boundary DA m above datum m2/day m/day
AB (x, y) Pump A is at Node (1, 2) 10 12 KI Notes: Fixed head of 15m along A B Fixed head of 0m along D-C Figure 1: Layout of nodes for the assignment
AS stated above, it is frequently necessary the results of pumping at a known fate are included in a Here, R> O for infitration into, and R <0 for abstraction from the model. Refer to your course notes for how to solve this equation using the inite difference approach in 2 dimensions. In this assignment you will need to consider how to modity Equation 1 to represent abstraction from a uniform an isotropic aquifer using the finile difference method. HINT: Consider the dimensions of the term R in Equation 1, they are not 1.2 The problem The object of the assignment is to use commonly available spreadsheet packages (e.g. Microsoft Excel LibreOffice Calc (reeware)) to investigate the effect of changing boundary conditions to a simple rect angular isotropic and homogeneous confined aquifer. 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 diference discrimination where ΔΧ.Δυ. 100m. Your model will then be 9 nodes wide in the x-direction (extending feom node 0 to node 8 on boundaries AB and CD) and 16 nodes long in the -direction (extending from node 0 to node 15 on boundaries BC and DA) For the spread sheet to successfully iterate, circular references should be enabled In Microsoft Excel 2010+ this is done under "File-"Options-Formulas: Here you need to tick Enable iterative calculation", set"Maximum iterations to 30 000 and Maximum change to 0 0001 In LibreOfice Calc this is done under Tools "Options "LibreOffice Calc "Calculate The teraions box needs to be ticked. Set "Steps to at least 10, 000, and "Minimum change to 00001 Model the following two sets of aquifer conditions Condition 1: The problem domain (aquifer) surrounded by Dinichlet xed head) boundary conditions Use a inear a linear decrease in head from 15m to 0m along BC and AD, a fxed head of Om along boundary CD, and a fxed head of 15m along boundary AB, Year 2019 Trimester 1 Water Resources Engineering CVEN3501 Condition 2: The problem domain (aquifer) surrounded by a mix of Dirichlet and Neumann (no low) boundary conditions. Use a no-flow boundary condition (with)ross BC and AD, a foxed head of Om along boundary CD, and a fxed head of 15m along boundary AB Answer the following questions 1. Explain how you will implemnent the no-flow boundary condition using a flow equation and a spread sheet |5 marks) 2 Calculate the fow though the aquifer for Condition 1 and Condition 2 without any abstraction (5 marks) Hint: Check that the flow calculated by the spreadsheet is cormect using Darcy's Law 3. Explain how you would incorporate pumping (or recharge) from (or to) a single node representing a bore in the spreadsheet [S marks) Note that the transmissivity is given in mi/day and the rate in terms of m/day 4. Using the transmissivity, the node location and the pumping (or recharge) given on the assignment sheet, calculate the water level at the given node location and the flows across each of the 4 boundaries for Condition 1 15 marks) Note that abstraction (Q) is negative (by convention) out of the aquifer. Calculate your flows over the boundaries as postive if into the aquifer and negative t out of the aqufer 5. Using the transmissivity, the node location and the pumping (or recharge) given on the assignment sheet, calculate the water level at the given node location and the flows across each of the 4 boundaries for Condition 2 15 marks] Use the same convention for the direction of flow as in the preceding question
Now Flow Boundary Condition in 2D From no-flow condition on the boundary сх and therefore above equation can be discretised (using the central difference) as ah = hil-a-1-0 and therefore 1.1-14-1 dr2Ar The above discretization can be used on both right and left boundaries of a numerical domain. Substituting h.i, -h-j into the second order derivative approximation Ar Ar which yields h,(/4X2h,+hh,) for left boundary and h,,-( 1 / 4)( 24.ut h,j-I +A,.) for right boundary
Assignment 2: The problem The object of the assignment is to use commonly available spreadsheet packages to investigate the effect of changing boundary conditions to a simple rectangular isotropic and homogeneous confined aquifer. . You should set up an aquifer model of an area 800 m wide by 1,500 m long. Use a finite difference discrimination where ΔΧ Your model will 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) Δy 100m. .
Example: Excel spreadsheet Example Finite Difference Scheme in 2-D with Dirichlet Boundaries X coordinate coordinate 10 20 30 100 40 50 70 90 110 120 3.7 3.2 3.0 4.6 $-20 4.8 5.4 5.2 4.9 5.92 5.7 7.4 6.5 6.6 7.2 7.6 8.0 8.44 6.6 7.2 6.7 6.60 6.5 6,41 6.7 8.4 軋鉢 6.62 6.8 7.1 8.9 6.9 7.65 7.3 DIMENSIONS ARE NOT REPRESENTATIVE OF THE REAL TASK!
Assignment 2: The conditio is Condition1: The problem domain (aquifer) 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) surrounded by a mix of Dirichlet and Neumann (no flow) boundary conditions. Use a no-flow boundary condition across BC and AD, a fixed head of 0 m along boundary CD, and a fixed head of 15 m along boundary AB