Seepage under a Dam by Flow Nets

Given the elevation and the hydraulic conductivity under a dam, this Demonstration computes the discharge (per meter) that is perpendicular to the flow nets.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The rate of flow (or seepage) of water under a dam is obtained by solving the equation of flow, which has the form of Laplace's equation. The analytical solution of Laplace's equation in Cartesian coordinates in two dimensions for a given set of boundary conditions results in two sets of solutions: , which represents the streamlines (or flow lines), and , which represents the equipotentials. The equipotentials and streamlines are mutually orthogonal. The seepage may be calculated graphically [1]. The same results are obtained when these two equations are linearized and plotted to form a simple mesh of equal squares, as shown. Horizontal lines are streamlines where the water discharges from higher to lower elevations. When the graphical method is employed, there is seldom any need to have more than six or seven channels of streamlines. While each streamline carries the same flow, the equipotential lines are characterized by different values of the head. The equation for the flow nets is the special solution of Darcy's law. Vertical lines or equipotential lines represent potential differences in each channel. When equipotential lines are drawn, it is not usually necessary to draw more than 18 channels.
[1] R. A. Freeze and J. A. Cherry, Ground Water, Englewood Cliffs, NJ: Prentice–Hall, 1979.
[2] P. B. Bedient, W. C. Huber, and B. E. Vieux, Hydrology and Floodplain Analysis, Englewood Cliffs, NJ: Prentice–Hall, 2007.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+