Physics of the Everyday

Breaking news! — The Baltimore Sun, CNN, Fox, and others are reporting that Baltimore's streams are tainted by amphetamine — a nervous system stimulant that is used in recreational settings and also is prescribed to treat the symptoms of attention-deficit disorder. Experts blame a leaky sewer system; reporters infer illicit users are dumping drugs down the toilet. In its article "Your Drain On Drugs," CNN reports that six Baltimore County streams tested positive for amphetamine.

Is amphetamine in the water supply a potential health hazard, or is this story a product of a supercharged news cycle desperate for views, likes and clicks? As we explore this eye-popping story, we will introduce the so-called back-of-envelope style of calculating that you will encounter often in this course, which emphasizes general number sense rather than precision.

Water Contamination


The CNN article refers to a research study that measured drug contaminants in Baltimore’s surface water. The researchers found that the most contaminated stream contained 630 ng/L\SI[per-mode=symbol]{630}{\nano\gram\per\liter} of amphetamine. In this quiz, we will interpret the researchers' measurement and weigh whether it poses a health risk.

This measurement is a concentration rate that tells us a 11-liter volume of water contains 630630 nanograms of amphetamine. This is a pretty small mass, but if your dog drank from the stream, would it be large enough to have an ill effect?

Answering this question depends on how small a nanogram is. It turns out that one gram (about the mass of a small paperclip) is 11 billion (1000000000)(\num{1000000000}) times larger than 11 nanogram.

To get a feel for this difference in scale, which of the choices is about a billion times larger than a paperclip?

Water Contamination


Baltimore water contains a small amount of amphetamine, 630 ng,\SI{630}{\nano\gram}, in each liter they sampled, according to the research study.

A liter is just one of several different units of volume the researchers could have selected to take their samples. Another common unit is a milliliter, which is 10001000 times smaller than a liter.

If you sampled water with an amphetamine concentration of 630 ng/L,\SI[per-mode=symbol]{630}{\nano\gram\per\liter}, how much amphetamine would be in a 1 mL\SI{1}{\milli\liter} sample?

Water Contamination


In 1 L\SI{1}{\liter} of water, the researchers measured 630 ng\SI{630}{\nano\gram} of amphetamine. This is an unthinkably small mass, so let's put this concentration in terms we can picture.

A typical, therapeutic dose of amphetamine is 10 mg.\SI{10}{\milli\gram}. Imagine you crushed up this amount and dissolved it into a volume of water so that it contains the same concentration the researchers measured. How much water is in the volume?

Note: There are 1000000 ng\SI{1000000}{\nano\gram} in 1 mg.\SI{1}{\milli\gram}.

Water Contamination


Perhaps we can find some comfort in the answer to the last question. The concentration rate of amphetamine needed to induce a physiological response in a human is about 10 mg\SI{10}{\milli\gram} dissolved in 5 L\SI{5}{\liter} of blood, and 630 ng/L\SI[per-mode=symbol]{630}{\nano\gram\per\liter} is nowhere close to this critical concentration.

But the question still stands: short of people accidentally spilling their amphetamine prescriptions into streams, how does any amount of amphetamine contaminate the surface water?

Another way for amphetamine to enter the environment is through wastewater. The body doesn't fully metabolize a full dose of amphetamine; in fact, for each person who takes amphetamine, about 50%50\% of every dose is excreted in urine. Baltimore is a city of 700000\num{700000} people where about 15%15\% of the population takes a daily 10 mg\SI{10}{\milli\gram} average dose of amphetamine.

Estimate the mass of amphetamine that enters Baltimore's wastewater each day.

Water Contamination


Cities the size of Baltimore are laid out so that all wastewater flows to a central treatment facility where solids are removed, and the water is filtered so that it can re-enter the water cycle.

Baltimore treats 900×106 L\SI{900e6}{\liter} per day. Using the mass from the previous question, how does the concentration of amphetamine in wastewater compare to the concentration in Baltimore's streams 630 ng/L?\SI[per-mode=symbol]{630}{\nano\gram\per\liter}?

Water Contamination


Perhaps surprisingly, we’ve estimated that the concentration of amphetamine the researchers measured in the surface water is roughly the same concentration we would expect in raw sewage.

Of course, this may be just a coincidence. On the other hand, exposure to raw sewage is a known health risk. Regardless, using simple estimates, we've shown in this quiz that amphetamine contamination at a concentration of 630 ng/L\SI[per-mode=symbol]{630}{\nano\gram\per\liter} would probably be pretty low on your list of concerns. The risk of severe bacterial infection would be a more viable risk.

Nonetheless, other smaller organisms, like algae, may be affected by this concentration of amphetamine. In this quiz, we used some basic quantitative tools (back-of-envelope calculation, rates, percentages, and units of measurement) to focus on the health risk for humans. The reporting hype didn't measure up to the actual risk, but you could use these same tools to gauge the effect on other species.

Water Contamination


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