BotEC: The Grand Canyon's Rate of Erosion
Some geologic processes, like volcanism and earthquakes, occur intermittently but can cause significant and sometimes catastrophic change very quickly. Others, like weathering, act continuously but gradually, in fact, imperceptibly slow. Regardless of how they operate, geologic processes, acting over long periods of time (thousands and millions of years) will produce significant change in the earth's surface.
If you were to occasionally visit the Grand Canyon over a period of many years, you would most likely notice no change. Even the details in the walls would probably seem frozen forever. Yet the Colorado River is continuously, albeit very slowly, cutting into and eroding the Colorado Plateau. The Grand Canyon is gradually being deepened and enlarged.
Some geologists are finding evidence that suggests that this mile deep canyon may have been cut with the last 4 million years. Assuming a uniform rate of erosion and without considering canyon widening due to slop retreat, calculate how much (in millimeters per year) the Colorado River would have to downcut per year to form this mile-deep canyon in 4 million years.
References and Resources
This SERC page describes the use of Back of the Envelope Calculations
The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.