Overview

The "Pi in the Sky" math challenge gives students a chance to take part in recent discoveries and upcoming celestial events, all while using math and pi just like NASA scientists and engineers. In this problem from the ninth set, students use the mathematical constant pi to calculate the water output from a dam to assess its potential environmental impact.

Materials

Pi in the Sky 9: Dam Deduction worksheet – download PDF

Pi in the Sky 9: Dam Deduction answer key – download PDF (also available as a text-only doc)

Background

This animation shows the collection of data over the state of Florida, which is rich with rivers, lakes and wetlands. Credits: NASA/JPL-Caltech | + Expand image

Dam Deduction

The Surface Water and Ocean Topography, or SWOT mission will conduct NASA's first global survey of Earth's surface water. SWOT’s state-of-the-art radar will measure the elevation of water in major lakes, rivers, wetlands, and reservoirs while revealing unprecedented detail on the ocean surface. This data will help scientists track how these bodies of water are changing over time and improve weather and climate models. In Dam Deduction, students learn how data from SWOT can be used to assess the environmental impact of dams. Students then use pi to do their own analysis, finding the powered output of a dam based on the water height of its reservoir and inferring potential impacts of this quick-flowing water.

• 
  Teachable Moments: Pi Goes to Infinity and Beyond in NASA Challenge

  Learn more about about pi, the history of Pi Day before, and the science behind the 2022 NASA Pi Day Challenge.

Procedures

Dam Deduction

Water exiting a hydropower dam is called non-powered or powered outflow. Non-powered outflow exits via a spillway, on top of the dam. Powered outflow, which is used to generate electricity, travels through penstocks, pipes at the bottom of a dam. Powered outflow is usually colder and travels at a higher velocity, so it can disturb sediments, temperatures, and water quality of downstream rivers, especially when it’s a high percentage of the total outflow.

The SWOT mission, a satellite designed to survey all of Earth’s surface water, including lakes, rivers, oceans, and reservoirs, can help scientists better analyze these impacts.

A dam has 3 penstocks with diameters of 6.2 meters and a measured total outflow of 1,350 m³/s. If SWOT measured the reservoir’s water depth (H) at 100 m above the penstocks, compute the velocity (m/s) of the powered outflow using V=√(2gH).

What is the powered outflow if 1 penstock is open?

Is this a high or low percentage of the total outflow?

What can this tell you about the potential environmental impacts?

› Learn more about the SWOT mission

Image credit: NASA/JPL-Caltech | + Expand image

Assessment

Image credit: NASA/JPL-Caltech | + Expand image

› Download text-only answer key (doc)

Extensions

Participate

Join the conversation and share your Pi Day Challenge answers with @NASAJPL_Edu on social media using the hashtag #NASAPiDayChallenge

• 
  Pi Day Challenge Lessons

  Here's everything you need to bring the NASA Pi Day Challenge into the classroom.

  Grades 4-12

  Time Varies

• 
  Slideshow: NASA Pi Day Challenge

  The entire NASA Pi Day Challenge collection can be found in one, handy slideshow for students.

  Grades 4-12

  Time Varies

• 
  Pi Day: What's Going 'Round

  Tell us what you're up to this Pi Day and share your stories and photos with NASA.

Blogs and Features

• 
  How Many Decimals of Pi Do We Really Need?

  While you may have memorized more than 70,000 digits of pi, world record holders, a JPL engineer explains why you really only need a tiny fraction of that for most calculations.

• 
  Slideshow: 18 Ways NASA Uses Pi

  Whether it's sending spacecraft to other planets, driving rovers on Mars, finding out what planets are made of or how deep alien oceans are, pi takes us far at NASA. Find out how pi helps us explore space.

Related Lessons for Educators

• 
  Tracking Water Using NASA Satellite Data

  Using real data from NASA’s GRACE satellites, students will track water mass changes in the U.S.

  Grades 4-8

  Time 30 min to 1 hour

• 
  Modeling the Water Budget

  Students use a spreadsheet model to understand droughts and the movement of water in the water cycle.

  Grades 5-8

  Time 30 min to 1 hour

Related Activities for Students

• 
  NASA's Earth Minute: Mission to Earth?

  NASA doesn't just explore outer space! It studies Earth, too, with a fleet of spacecraft and scientists far and wide.

  Type Video

  Subject Science

Multimedia

• 

  Downloads

  Can't get enough pi? Download this year's NASA Pi Day Challenge graphics, including mobile phone and desktop backgrounds:

  • Pi in the Sky 9 Poster (PDF, 11.2 MB)
  • Lunar Flashlight Background: Phone | Desktop
  • Mars InSight Lander Background: Phone | Desktop
  • SWOT Mission Background: Phone | Desktop
  • TESS Mission - Downlink Background: Phone | Desktop
  • TESS Mission - Science Background (not pictured): Phone | Desktop
  • Medley Background (not pictured): Phone | Desktop
• 
  Infographic: Planet Pi

  This poster shows some of the ways NASA scientists and engineers use the mathematical constant pi (3.14) and includes common pi formulas.

Recursos en español

• 
  18 Maneras en Que la NASA Usa Pi

  Pi nos lleva lejos en la NASA. Estas son solo algunas de las formas en que pi nos ayuda a explorar el espacio.

Facts and Figures

• Earth

Missions and Instruments

• SWOT Mission

Websites

• NASA Climate