## 01 July 2007

### the price of water

I found a link to this article in the New York Daily News which claims that in New York City, tap water costs 24 cents a gallon. This made me suspicious, because I'd always been under the impression that tap water was orders of magnitude cheaper than bottled water, and you're not going to find bottled water under, say, \$1 a gallon. Also, you don't hear about people struggling to pay their water bills. This page (which was the first source I could find) says that with water-saving fixtures, a toilet flush is 1.5 to 3.5 gallons, and a shower is 2 to 4 gallons per minute. If it costs fifty cents to a dollar to run a shower for a minute -- and what's the average shower, ten minutes? -- you know people would consider not showering.
I was curious how much water costs in Philadelphia. (I rent; my landlord pays my water bill.) Anyway, it's \$21.14 per 1000 cubic feet, or about 0.2826 cents (not dollars) per gallon, as Google's built-in calculator informed me.
And it turns out that New York City has new rates effective tomorrow; they're \$2.02 per 100 cubic feet (see page 4), or 0.2700 cents per gallon. I suspect it was 0.24 cents per gallon before the increase, and someone just thought that looked wrong, because usually when you see, say, "Candy Bars: 0.75 cents" you just assume they meant three-quarters of a dollar. The difference is a factor of 100. I bet the person responsible for this error would say "oh, it doesn't matter". Okay, I'll cut their salary by a factor of 100. Let's see how they like living on a few hundred bucks a year!
Anyway, the Philadelphia Water Department has this fact sheet which includes the question: "How can I better understand the levels of elements in my water?" They go on to define parts per million/billion/trillion. They state:

1 part per million is similar to making a line of quarters from Center City to Conshohocken, and then walking that line to find the one quarter that is flipped up heads instead of tails.

It's 15.1 miles from Broad and Walnut to Conshohocken. (Note that the Google Maps route requires one to walk on the Schuylkill Expressway, which would be unwise.) This is 956,736 inches. A U. S. quarter is 0.955 inches across, so the distance is very nearly the length of a million quarters put side-by-side.
But then they go on to say:

1 part per billion is equal to 1 green apple in a barrel containing 1 billion red apples.

Well, duh. But can you picture a barrel containing a billion red apples?
Let's say the inside of a SEPTA bus is eighty feet long, ten feet high, and ten feet across. Let's furthermore say that an apple is a four-inch sphere. Then if we fill the bus with apples, it's two hundred forty apples long, thirty apples high, and thirty apples across -- it holds 216,000 apples. So if we could fill five thousand SEPTA buses with apples, that would be a billion apples. That might be easier to picture. Except SEPTA only has 1,388 buses.. Okay, fill the busses with kiwis instead -- you can probably fit four kiwis in the space of one apple.
Finally, they say

1 part per trillion is similar to 1 inch in 16,000,000 miles or 1 penny in 10,000,000,000 dollars.

Sixteen million miles is one-sixth of the distance to the sun! However, ten billion dollars actually might be an understandable figure. The per capita income in Philadelphia was \$16,509 as of the 2000 census; the population of the city at that time was 1,517,550. The product of those is about 25 billion dollars. So a part per trillion is like finding a penny in all the money Philadelphians make in five months.
and yet... a part per trillion still is still very nearly a trillion molecules per mole, since Avogadro's number (6.02 × 1023) isn't far from a trillion trillion. A mole of water is 18 grams -- roughly a mouthful. How would people feel, knowing that there are as many molecules of [insert nasty contaminant here] in a mouthful of water as pennies made in Philadelphia in five months? (Yes, I know that I'm sweeping a lot under the rug here. My point is that a mole is a large number of large numbers.)