Diving on Gas Laws

http://edweb.sdsu.edu/edtec596/Units/Dive/gaslawsday1.html

by

Mark Sovitsky

Introduction

You have learned already that graphing is not just x's and y's, but actually a relationship between two quantities. We've even seen an example from the D = (r)(t) formula. Today, we are going to learn how this concept applies to the sport of diving.

The Task

By the end of this lesson, you will have more experience in the art of graphing relationships between quantities. You will specifically be introduced to gas laws and how they affect the diver. The major thrust of today's lesson is for you to create a graph from a real world problem and to answer questions based on what you have.

Resources

The major resources needed are graph paper, rulers and computers with internet access, as the assignment for today requires them to visit a website. Students may also need calculators, type and kind are irrelevant as graphing calculators won't necessarily help them unless they already know what they are doing.

The Process

The process we're going to use is fairly straightforward (a little long, but easy to follow).

  1. Form into groups such that there is one computer per group.
  2. Log onto the Internet and go to the site after reading these directions thoroughly.
  3. Read the page completely. Print out a copy if necessary. Answer the following questions:
    • What is the weight of one Atmosphere (1 ATM)?
    • How many feet are there in 1 ATM of water?
    • How does Absolute Pressure differ from Gauge Pressure?
  4. Remember the graph paper? Get it out and draw coordinate axes on it. Discuss the following in your groups:
    • What two quantities are we looking to study?
    • Which would you put for the x-coordinate? Which for the y?
  5. Remember how we graphed y = x - 3? We picked an x, solved for y, and plotted them as coordinates in the form (x,y). You will do the same here. For example, 1 ATM exists at sea level (0 feet), so we might plot it as (1 ATM, 0 ft.). Do this for 2 ATM, 3 ATM, and 4 ATM (REMEMBER: This is for ABSOLUTE Pressure). The article gives you the depths in feet for these. Draw a line through all the points and answer the following questions:
    • Predict the depth at 6 ATM and at 8 ATM.
    • What would you predict the pressure to be at 33,000 feet deep?
    • Can you derive the formula of the line that is represented by your graph? (Hint: think about what you have to do to get the depth given the ATM or vice-versa.)

Do not continue until you've gotten the graph right and understand what's going on. Now what we've done is great if we're given a depth that's exactly divisible by 33 feet or a number of pounds exactly divisible by 14.7 (for 1 ATM). The focus of the last part of this assignment is to find out what the pressure is at an odd depth.

  1. Repeat the procedure for Step 4 and answer the same questions.
  2. Repeat Step 5 . Remember that we are going to deal with SALT water, because that is where people usually end up diving. Plot 3 different depths with their associated pressures and answer the following:
    • Predict the pressure at 107 feet.
    • This is a key question. We know that slope = rise/run in mathematical terms. How is the slope represented in this graph?

Evaluation

You will be evaluated on the answers to the questions in The Procedure section and on your graphs. You will need to turn in the items for credit. Each question is worth 2 points and each graph is worth 10 points, for a total of 40 points. We will discuss it again tommorrow.

Conclusion

We've learned that a graph is a powerful tool that we can use to show how one quantity can affect another and how that relationship can be shown. Tommorrow, we will practice this new found knowledge with another graph.

Last updated May 21, 1997. Return to the Recreational Diving Page

Based on a template written by Bernie Dodge.