Exercise - Analytical Solutions

Part 1 - Dupuit Problem

Consider the following profile representing the classic Dupuit problem with a rectangular cross-section:

The flow through the section is given by:

\(Q = K \dfrac{\left(H_o^2 - H_D^2\right)}{2D}\)

And the head (h) as a function of x is given by:

\(h = \sqrt{\dfrac{\left(H_D^2 - H_o^2\right)}{D} x + H_o^2}\)

Assume following parameters:

Calculate the flow rate (Q) and generated a plot of the head (h) as a function of x for the parameter values given above.

Excel starter file: dupuit.xlsx

Excel solution: dupuit_KEY.xlsx

Python starter file:

Python solution:

Consider the following profile representing the flow through an earth dam:

The flow through the section is given by:

\(q = k L \tan(\alpha) \sin(\alpha)\)

where:

\(L = \dfrac{d}{cos(\alpha)}-\sqrt{\dfrac{d^2}{cos^2(\alpha)}-\dfrac{H^2}{sin^2(\alpha)}}\)

Solve for the flow rate (q) using the set of parameters contained in the following Excel file.

Excel starter file: earthdam.xlsx