After dinner last Sunday and my 'MEC Was a Hard-Ass' post , former student Dan Wendell dug out this one-pager I distributed in my Geology 783 Groundwater Hydraulics course almost 30 years ago:
I was actually amazed to read it. What Dan recalled was the quote that I have at the bottom of this post. It's nothing new; I suspect many science and engineering professors had repeated it years before I said it. Why I said it was simple: an applied mathematics professor (David Lomen, I believe - one of the best instructors I had at any level) had said it to me years earlier. As for its relevance to hydrogeology I had to discover that for myself. I read it in a book.
So how is the quote relevant? I need to tell a story.
The best-known water well hydraulics equation is arguably the Theis equation, promulgated by C.V. Theis in 1935. It was an advance because until then, hydrogeologists had to be content with applying steady-state equations (no water level changes in time) such as the Thiem equation to water well hydraulics situations: trying to relate the drop in well water levels to pumping rates and aquifer properties. The problem was that steady-state conditions were generally not the rule and well water levels changed (declined) with time.
The Theis equation allowed you to use transient changes in well water levels to discern aquifer properties - both transmissive and storage properties. The latter could not be derived from steady-state analysis. So it was a big deal - you could now do something called an aquifer (or 'pump') test to detemine aquifer properties. The rest in hydrogeological history, in more ways than the proliferation of aquifer tests.
Theis actually developed his approach by making an analogy between groundwater flow in a confined aquifer and heat conduction in an infinite slab. He asked a friend, mathematics professor Clarence Lubin, to help him with the mathematics. He offered Lubin co-authorship, but Lubin politely declined, essentially saying that the math in the paper was no big deal and he wouldn't benefit by being listed as a co-author.
The heat conduction analogy led to a plethora of well hydraulics (and related) equations for a variety of aquifer conditions. I recall it very well; for a time, the most important book on my shelf was Conduction of Heat in Solids by H.S. Carslaw & J.C. Jaeger. I used this book in Geology 783.
This excellent USGS publication of Theis' career is worth perusing; the section about the devlopment of the Theis equation starts around page 49.
As usual, I've digressed. I was trying to explain the importance of the quote Dan unearthed. The Theis equation discussion is important because one of the assumptions Theis makes is that the aquifer (just like the 'slab' in the heat conduction equation) is of infinite extent. We all know that's a fictional construct. But in the real world it is reasonable if your well is far enough from boundaries (faults, impermeable barriers, water bodies, etc.) such that the well's cone of depression does not intercept any. That assumption also implies that at an infinite distance from the well, the water level decline is zero. That makes the solution tractable.
I'm embarrassed that I must rely on former students to ferret out this material. I do have several looseleaf binders in my office but I have not cracked them open for many years. Maybe I should.
I should also return to teaching a course like Geology 783, which I have not taught since 1988. Biy, did I learn a lot from that course.
Interesting footnote: while I was at the University of New Mexico, Theis' old USGS office was just down the hall from me - Northrop Hall 226.
"If you know the IC & BC [initial conditions and boundary conditions] of the governing PDE [partial differential equation] and what they mean in the real world,you will be a better scientist/engineer. Trust me." - Yours truly, from my Geology 783 Course Information (1985) - thanks to Daniel Wendell