A math problem dealing with center pivots and water usage.

Notice the small pivot and pivot that rotates less than 360 Degrees

There are some great mathematics problems in agriculture.   I will be constructing problems throughout the year and placing them on this site.  A center pivot is a device used to water crops.  The pivot itself is the radius of a circle.  They come in many sizes.   The image from Google Earth shows several center pivots west of our small community.  This image is ripe for exploration.  What kind of questions could we ask here?  How many acres per field?  How many acres are in the “white ring” located in about the center of the image.  How many acres are left outside the circle yet inside the square field?

In the problem below I filmed a pivot at its top speed.  I am standing on the outside set of wheels for the pivot.   The video at the bottom of this post is not the most exciting video footage ever shot, but it makes a great math problem, and asks a relevant question.  How many passes will the pivot have to make to use up all 13 acre-inches of water?  But there are a number of questions that could be asked here.  Knowing the speed of the outside set of wheels, how fast would any of the inside wheels be traveling? How much fuel will we have to buy to pump this much water? How much fuel would we have to buy to pump 1 acre-inch of water on the entire field?  What does that make 1 inch of rain worth?   How many swimming pools would it fill?  There are hundreds of ways to take this problem.  So here is the problem and I hope that it is useful.  It is 17MB so it takes some time to load.  Also I have to place all videos in Quicktime (MP4), so downloading it may be a problem for some although you could down load it and convert it to another format to run in a windows machine or just put Quicktime player on your machine.

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