Abstract

Citation

Researchers should cite this work as follows:

• Hallare, M., Lamb, C. (2022). 1-165-FlushToilet-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/KX0G-8N50

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Article Context

Description

The students derive the solution to the model, use least squares method to estimate the parameters, and investigate another technological innovation using the method outlined here.

To flush, or not to flush? That is not the question. The question is, how does one use differential equations to model the spread of toilet flushing as a technological innovation in the United States?

Various historical sources credit Sir John Harington, godson of Queen Elizabeth I, in designing the first flushable toilet in 1596.

His design contained the two components of the modern toilet: a valve to flush out the water and a wash-down system to empty the bowl. His design, however, failed to eliminate the foul smell. More than two hundred years after, Alexander Cumming, a Scottish mathematician and inventor, improved Harington's design by inventing the S-trap that retained water permanently in the waste pipe and prevented the foul smell from escaping.

The spread of Cumming's S-trap design was slow. When the Great Stink in Central London happened in the summer of 1858, the legislators of the Houses of Parliament pushed to require the S-trap as part of the sewage system.

The Houses of Parliament was located along the River Thames, which was practically an open sewer at that time. Indeed, government legislation has the power to accelerate the diffusion of technological innovations and in this case, it used its power to control the diffusion of the stink.

In America, flush toilets were introduced in the homes of the wealthy in the 1860's. Up until the 1980's, only 98 percent of American households have access to flush toilets. Table ref{tab:FlushToiletData} below summarizes the data on how this technological innovation spread in the United States: