# HW#7 - Finite Difference Equations

(1) Write a spreadsheet to solve for the total head values for the problem shown below using the finite difference technique

Use a 2.5 foot square grid. Extend the grid from the centerline of the cofferdam to 40 feet downstream from the outer edge of the cofferdam. This should give you 9 rows and 21 columns in your grid. Don't forget to add an extra grid node at the location of the sheet pile for the first four rows of nodes (21 columns on the bottom half - 22 on the top half). The grid looks like this.

Lay out your spreadsheet so that you have a spreadsheet cell for each node of the grid (for each red dot). Enter an equation for the head at each node. Using the default approach in Excel, you may get an error message about a circular reference. To avoid this and to properly iterate to a solution, do the following:

** Excel 2003**: Before entering the equations, go to the *Tools/Options* dialog and select the *Calculate* tab. Turn on the iteration option and the *Manual calculate* option. Once you have the equations entered, hit the F9 button repeatedly until you converge.

**Excel 2007**: Before entering the equations, click on the Office icon (upper left corner) and select the Excel Options button. Click on the Formulas link on the left. Turn on the *Enable iteractive iteration* option and the *Manual* calculate option. Once you have the equations entered, hit the F9 button repeatedly until you converge.

**Excel 2010**: Before entering the equations, select the File|Options command. Click on the Formulas link on the left. Turn on the *Enable iteractive iteration* option and the *Manual* calculate option. Once you have the equations entered, hit the F9 button repeatedly until you converge.

(2) Add a section to your spreadsheet to compute the flow rate from your solution (assume a unit thickness in the transverse direction). To do this, compute the flux across the outgoing boundary. Using the head values at nodes on and adjacent to the nodes on the boundary to estimate the hydraulic gradient (dh/dx or dh/dy). Using this value, the appropriate contributing area, and Darcy's law, compute the flow rate. Remember to hit the F9 key to update your calculations.

### Submittal Instructions

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