Pi Day! Yum. Yum. (And the math is awesome, too!)

Denver Water loves pie and also pi, which gets used every day around here.

March 13, 2019 | By: Jessica Kirk

If I had a nickel for every time I heard a high school classmate say, “I don’t understand why I have to study geometry, I’m never going to use that stuff in real life,” I’d be a wealthy woman today.

Especially when you consider how that nickel would have grown due to the compound interest accrued over the many years since my high school graduation.

But this not a story about exponential functions (like compound interest), this is a story about pi, that irrational, infinite number we celebrate every year on March 14, or Pi Day. That’s when the date, 3-14, looks like 3.14, the first three digits in math’s most famous number.

Pi is the ratio of the circumference of a circle to its diameter.

At Denver Water, pi is embedded in the work done every day to get water from the mountain streams to city taps, from figuring out the best size of the pipe needed to deliver water to designing a round storage tank.

People holding flashlights walk through a huge pipe that looks like a tunnel.
How big is a conduit that’s 108 inches in diameter, or 9 feet? Big enough for people to walk through during inspections, which involve significant planning and safety processes. Here’s a story about this pipe’s most recent inspection: On assignment: My underground pipe quest. Photo credit: Denver Water.

 

As a Greek letter, pi looks like π. Using digits, it starts out like this: 3.14159.

But that’s the short version. Pi has been calculated to more than 1 trillion digits beyond the decimal point. As what’s called an irrational and transcendental number, it will continue infinitely without repetition or pattern.

So, in honor of the mighty Greek symbol π here are some examples of how pi is used at Denver Water.

Determining the area of a pipe

Denver Water uses pi to calculate the cross-sectional area of the pipes in its system.

A cross section is the shape you get when you cut straight through an object. So, the cross section of a round pipe is a circle. The formula to determine the area of a circle is A=πr².

Knowing the area of a pipe in our system is fundamental to determining how much water a pipe can deliver.

One finger hold a tape measure.
Denver Water operators use diameter tape measures, like the one pictured above, to easily determine the diameter of a pipe (the distance from one side to the other side of the circle, passing through the center) based on the pipe’s circumference (the measurement around the outside of the circle). Photo credit: Denver Water.

Determining the delivery capacity of a pipe

Pi is also used to calculate the delivery capacity of each pipe in our system, or how much water can pass through a pipe.

Denver Water follows engineering standards that set the maximum velocity — the speed at which water moves — for pipes based on diameter. This formula is also pi based: Q=AV=πr²V (V is velocity).

Additionally, Denver Water uses this calculation to estimate how much water is used during hydrant flushing operations, which are done to eliminate stagnant water and maintain high water quality standards, and how much water has spilled if a pipe breaks.

Table of numbers with pipe sizes ranging from .75 inches to 108 inches.
This chart shows the delivery capacity of pipes in Denver Water’s system based on their size, or diameter. For instance, if the utility needs to deliver 280 million gallons per day, then the 108-inch pipe is the size that’s best for that purpose. But if a building only needs a maximum of 3,520 gallons per minute, then the 12-inch pipe is the best one for that job. Photo credit: Denver Water.

 

Determining storage tank volume

Denver Water also uses pi to calculate the volume of the circular storage tanks in our distribution system.

The volume of a round storage tank is calculated by taking the area of the circle multiplied by the height of the tank. The equation for this is V=πr²h (V stands for volume and h stands for height). Storage tanks in Denver Water’s system range from 167.5 feet in diameter to 370 feet.

An image, taken by a drone flying above the construction site, shows concrete being poured onto what will be a round storage tank.
Denver Water historically has had many rectangular storage tanks, but as they age those tanks are being replaced with circular tanks. Circular tanks, like the one pictured here under construction at our Hillcrest storage facility near East Quincy Avenue and Interstate 25, have structural advantages over other shapes and also are a better environment for maintaining water quality. Photo credit: Denver Water.

 

Whether you participate in Pi Day celebrations with pie baking contests or reciting digits of pi from memory, we hope you also raise a glass of water to the power of pi in our daily lives.

And maybe, while you’re at it, calculate the cross-sectional area and volume of the glass in your hand.

And to high school students everywhere, know that what you learn today is indeed useful in real life, particularly in exciting and fulfilling careers in water operations like Denver Water.

black pipes are stacked 7 rows high, with wood blocks between them.
These 12-inch-diameter pipes are used throughout Denver Water’s system. These pipes deliver up to 3,524 gallons per minute. Photo credit: Denver Water.

3 thoughts on “Pi Day! Yum. Yum. (And the math is awesome, too!)”

  1. Dear Jessica,
    Thanks for reminding us of the importance of mathematics in our everyday lives.
    Sincerely,
    John Hokanson

Post a Comment

Your email address will not be published. Required fields are marked *