Showing posts with label Numbers. Show all posts
Showing posts with label Numbers. Show all posts

Monday, December 10, 2012

Why pipes freeze when the hose is attached.

Why pipes freeze when the hose is attached.

November in Kansas was unseasonably warm. Most days the temperature rose into the sixties, sometimes even into the seventies. People walked around in shorts, t-shirts, and tennies saying things like, "If this is Global Warming, I'm all for it," or "Living in L.A.." Even into the first week of December, it seemed as if summer had lingered a bit too long.

Perhaps, to Al Gore's relief, the weather finally turned cold. The temperature last night dipped down into the low teens and for the first time, and the weatherman was using the words "frigid" and "wind chill".

The Old Man's wife came home late last night. Dressed in pajamas and shoeless, he was ordered out of the house and told to unhook the hose from the faucet.  "If you don't, the pipes will surely freeze," she said knowingly.

The Old Man is a skeptic, not a cynic, mind you, just a skeptic. There is a difference. So, he said, "Can't be!" It was not just because he did not want to go out in the chilly night air and wrestle with two hoses, it was because he truly didn't think water could freeze all the way to the interior pipes of the house and burst.

After minding the wife and disconnecting the hoses, the skeptic went to Googe for an answer. Not surprising was that everyone repeated the mantra that one has to disconnect a hose or a pipe will freeze and burst. What was surprising was that no one explained why.

Was it just an Urban Myth cooked up by wives to get their husbands out of bed and out in the cold?

Water is one of those molecules that has an unusual property. Freeze most things and they contract. Any guy standing out in the cold North Wind notices this phenomenon with parts of his body. Not so with water, freeze it and the molecules form a pattern that actually increases the volume of a given mass. This is why ice cubes float, why pot holes show up, why icebergs sink ships, and why, if the polar ice caps melted, Florida would be under water.

The skeptical Old Man googled the volume of ice compared to water. It turns out that ice has about one-tenth more volume than water. Here's what the chemistry experts at Elmhurst College say:

Elmhurst College, Illinois

Which is more dense - Ice or Liquid Water?
"The increase in volume of ice is about 9%. This increase causes enough force to break most rigid containers. This is the same force, repeated on a daily basis, that creates "pot holes" in the roads in the winter time."
Of course, the Old Man's wife knew already that the Old Man was denser than both water and ice. The Old Man needed proof. How could a hose, turned off at the faucet, have enough water to expand and reach inside the house, bursting pipes and making plumbers all over the America rich? Scientific fact or nefarious housewives' plot.

Let's think about it. Take a 50 foot hose that attaches to a faucet 2 feet off the ground. Turn the water off at the faucet and one would expect that, all things being equal, the water in the hose would drain out if it was on a down hill incline. But, if the hose was attached to a sprinkler or a nozzle or if the hose was on an uphill incline, then one would expect the hose to be chock full of water. This is something the Old Man verified as he unscrewed the hoses from the faucets.

Now, the Old Man could calculate the volume of the hose, but it the answer comes out the same if we just use the length of the hose as a measurement. Assuming, for argument sake that 2 feet of hose is empty (the distance from faucet to ground) that leaves 48 feet full of liquid water.

That is a hose that is 96% full of water, or more than enough to burst anyone's pipe.

Now the Old Man was out to dinner the other night when his wife gave him some bubble gum with the following message on the package, "Let's just assume I am right."

Following this advice would have saved the Old Man some time and worry.

Sunday, September 23, 2012

Numbers

While driving I-35 through the Kansas Flint Hills yesterday, I got to thinking about numbers. More specifically, I guess, I was thinking about how we measure distance. Highways are measured in straight lines even though we don't travel that way. It is really a combination of curves, rises and falls. No one travels as the crow flies, but still we measure that way.

Off of I-35. near Garnett, Kansas, a straight road

For the most part, the highway is measured in miles and feet. Inches are left to shorter items that we hold in our hand. But, miles and feet are not a universal measurement. In Europe and most of the world the kilometer and meter are used. This is because meters are a more precise form of measurement when it comes to computers and calculators. Kilometers and meters are based on the numbering system of ten. You can thank Napoleon for this revolutionary change. But remember the Greeks and Romans were counting in units of ten long before Napoleon resurrected their system.

But what are miles and feet based on?

Back in the Merry England of the Middle Ages, and Europe for that matter, no one kept rulers in their pocket. If you had to measure something, then the measuring stick was a body part. The foot is an easy one, for it is the length of a man's foot, give or take. The inch was the width of a thumb.

How about the mile?

The mile is a left-over of the Roman Empire's rule over Britain. The Romans had a measurement known as mille passuum, or a thousand paces. A pace (don't be confused, today a pace is generally considered as one step) was two strides, the distance from when the heel of one foot was lifted off the ground until it was placed back on the ground. This was about five Roman feet. The Roman soldier, like contemporary ones on parade, would count off until reaching a thousand paces. The Latin word for a thousand is mille, which becomes mile.

Hui! Or Latin for wow!

The Romans left mile markers throughout the Empire, so that they would always know where they were. Next time you are breezing down the highway look to the side and you will see highway markers in miles. Bridges have a similar mile marking. This way the Highway Patrol can note where you are if a break-down occurs.

But wait, why 5,280 feet?

The British farmer was not going to count up to 5,000. He would get lost in counting along the was. Instead, a shorter measurement was needed. One that aided one in getting to the magic mile. If you have ever counted the cards in a deck of 52, then you know it is sometimes best to stack them in piles of ten, so as to not mess up your count. The Chinese abacus has counters of five an ten that help the counter to add to higher numbers.

The Old Man is tired of plowing, Credit: © Bob Langrish.

Now, back to the ancient British farmer. This measurement was the furlong. The furlong was the distance a plow horse could plow a straight line on a farmers field before getting tired. This distance was agreed by all sensible people to be 660 feet. That number is convenient because it has as common factors the numbers 3, 4, 5, 10, and 12. It was easy from this distance to jump to a mile consisting of eight furlongs, or 5,280 feet. Today, the furlong has for the most part disappeared except on the race track where the measurement is still used.

Other body parts have been used by ancient civilizations for measurement. The Hebrews, Greeks and Egyptians used the cubit or length of the forearm. Noah's ark was measured at 300 cubits long, 50 wide, and 30 high. The cubit is similar to the yard, the distance from nose to extended arm, which was a useful way for merchants to measure rope or cloth. Finally, there is the hand which was the width of the hand or about four thumbs wide. Full-grown horses often measure about fifteen or sixteen hands, but it is hard to imagine that a horse would stand still while the farmer placed his hands along the horse that many times.

Hope this helps.