# HW#4 - Analytical Solution to Profile Model

In class we discussed the Dupuit problem with an infiltration term (e):

Derive an equation for h in terms of x. Start with **h**^{2} = -(e/k)x^{2} + C1x + C2 and insert the left and right boundary conditions and solve for C1 and C2. Solve the resulting equation for h.

Once you have found your equation, click here to download a copy of the spreadsheet we solved in class.

Use the given equation for q and the equation you derived for h to fill in the table illustrating how h and q vary with x when infiltration (e) is used. As you fill in the table, the chart on the right will automatically update.

### Submittal Instructions

Put your derivation in a word document using Equation Editor. Put your word document and your spreadsheet into a single zip archive. Upload your zip archive via Learning Suite.