How Much Water is That?

lakemead.jpg

Lake Mead

It all started with a phone call from my Dad.  He had heard on the news that the water level of Lake Mead had decreased 100 feet and asked me, as the resident mathematician in the family, "How much water is that? "

LakeMead drop.jpg

I admit, I LOVE it when that happens!

What do I love specifically?  Well, I love that my Dad has every confidence that I can figure out whatever type of math problem he can throw at me.  I also love that it's the perfect math question because it's prompted from real life, answering it leads to even more questions, and answering it requires answering a bunch of other questions first.  Such potential for learning new stuff!

In the conversation with Dad I mentioned all of this in the form of some of my comments and ponderings:

Me:  "hmmm, I'd need to know the area or the dimensions of the lake..."

Dad:  "Yep."

Me:  "My guestimate is that it's a huge amount of water.  What's your guess?"

Dad:  "5 trillion gallons."

Me:  *laughing* (mostly because it's hard to even think about that much water and I figured he just picked a huge number out of the air)

Little did I know how close (relatively speaking) Dad's estimate was!

I've had the good fortune to visit Lake Mead so I had some personal experience from which to begin my problem solving (which is always a plus).  However, I am by no means an expert and had no idea of the size of the lake so I started with some initial research (sites referenced below).  Here's a bit of what I learned:

  • When filled to capacity, Lake Mead is the largest reservoir of fresh water in the United States.
  • The lake measures 532 ft at its deepest point.
  • There's a sunken B-29 aircraft & 2 smaller aircraft at the bottom of the lake!
  • The area of the lake is about 247 sq. mi.
  • The surface elevation reached a record low of 1081 ft on July 10, 2014 (the max is 1229 ft and throughout the 80's it was around 1200 ft).  This was the data point which the news broadcast focused on as that's roughly 100 ft difference.
  • The volume of huge reservoirs like Lake Mead is measured in a unit called an "acre-foot" (ac-ft or AF).  1 ac-ft is approximately equal to 325,851 gallons!  
  • At maximum capacity, Lake Mead holds about 23,134,000 ac-ft of water.  On June 26, 2014, the capacity was approximately 10,313,200 ac-ft.
350px-Acre foot.svg.png

I'd already learned something and had only begun solving the problem!  Three degrees in mathematics and I'd never heard of the unit of measure: acre-foot!  When I spoke with Dad later, he'd also never heard of it.  For those of you who, like me & Dad, are curious about what that is (and what it looks like), here's a visual.  As an aside, I also didn't know that an acre is defined as "a chain by a furlong" (talk about non-standard units of measurement!).  In math, that's 66 ft x 660 ft.

As a rule of thumb in U.S. water management, one acre-foot is taken to be the planned water usage of a suburban family household, annually. One acre-foot/year is approximately 893 gallons per day.

Isn't that quote amazing?  I imagine that people in other parts of the world, where water is a much more precious commodity than we treat it in the U.S., would be appalled by that figure.

For those of you who are as fascinated by this unit and want more data, here's the site for you:  Lake Mead daily water levels measured in ac-ft, updated daily!  Isn't technology grand?

There are many sites that have been tracking data at Lake Mead and many wonderful graphics that you could use with students.  Here are a few of them.  The references section has links where all of these came from as well as links to more data you could use in class.  Just think of the fabulous graphing calculator lessons you could create with this!

lakemead graph.jpg

So much data!

Lake Mead Water Levels.png

We all have heard about droughts on the news.  But water is taken for granted so much here in the United States that I doubt you or your students have really given it much thought.  Here's a quote that may raise some awareness for us all:

During WY 2014, water storage has risen by 10,067,410 AF yet total outflows have exceeded total inflows by 4,337,006 AF.

Visually, the water level graphic is startling:

water levels graph.png

So, have you calculated the answer to Dad's question yet?

conversion.jpg

My Dad's guess was 5 trillion gallons and the answer is over 4 trillion gallons!  Absolutely amazing!

As always, I'd love to hear from you.  

References:

Link for opening graphic of Lake Mead 

Link for water level graphic

National Park Service link for Lake Mead

Link for various data on Lake Mead (weather, water levels, etc.)

Link for education video and podcast on the sunken B-29

Link for information on the acre-foot

Link for Lake Mead tracker graphic

Link for water levels graph

Link for the Lake Mead water database

Link for Lake Mead surface elevation data

Really excellent PDF water conversion table

Fabulous ac-ft <--> gal conversion calculator

Video of recent NBC news story about Lake Mead and water shortages, drought

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The Solver Blog

Author:  Dr. Diana S. Perdue

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