The Theis Equation and Flow

Mathematics is remarkably effective in describing the physical world in part due to isomorphisms, relationships between concepts that reveal a similar underlying structure. In 1935 Charles Vernon Theis was working on groundwater flow, a subject with little mathematical treatment at the time. He thought that perhaps a well tapping a confined aquifer could be described using the same mathematics as the heat flow of a thin wire drawing heat from a large plate, as this work was better established. With a little bit of help from C. I. Lubin and considering how parameters describing underground water flow could be compared to those describing heat flow in solid materials, he developed the Theis equation which is used to this day to model the response of a confined aquifer to pumping over time.

I developed a small program which allows visualization of the potentiometric surface of a confined aquifer subject to pumping using Processing. This particular example uses aquifer and pumping parameters from a Geo-Slope whitepaper.

The source code may be downloaded here. All values including aquifer, pumping, visualization, and numerical parameters may be varied to apply to a wide variety of situations. The exponential integral (or “well function”) is calculated using a numerical approximation accurate to at least 1 part in 10,000,000 .

Waterloo Engineering Welcoming Committee

I graduated Waterloo Engineering in 2007. I now work at the Canadian Space Agency on my Master’s degree. Some new co-op students have arrived, and among them is Steve, a fellow Waterloo student in second year Mechatronics. He had a great little story for me.

First, some context. The University of Waterloo (UW) is known as an engineering school, and tends to have an abundance of male students as a result. In contrast, Wilfrid Laurier University (WLU) is known as an arts school, and tends to have an abudance of attractive women as a result. The two schools are quite close together, perhaps a five minute walk from campus to campus.

It’s September, and that means that a fresh new crop of students has arrived on both campuses, more than likely with parents in tow. I can only imagine the face of a nervous father, dropping his little princess off where she’ll live away from home for the first time, only to see this massive banner on an overpass above the biggest highway leading to both UW and WLU…

Poor bastards. I hope your daughter didn’t blush.