Download Comparing High and Low Pressure K-Bottles for Purging: Cost Analysis and more Study Guides, Projects, Research Introduction to Business Management in PDF only on Docsity!
Project Grant Team
John S. Pazdar Peter A. Wursthorn Project Director Principal Investigator Capital Comm-Tech College Capital Comm-Tech College Hartford, Connecticut Hartford, Connecticut
This project was supported, in part, by the Patricia L. Hirschy National Science Foundation Principal Investigator Opinions expressed are those of the authors Asnuntuck Comm-Tech College and not necessarily those of the Foundation Enfield, Connecticut
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SPINOFFS
Spinoffs are relatively short learning modules inspired by the LTAs. They can be easily
implemented to support student learning in courses ranging from prealgebra through calculus.
The Spinoffs typically give students an opportunity to use mathematics in a real world context.
LTA - SPINOFF 8A Exploring Shuttle Preparations:
Crawler and VAB
LTA - SPINOFF 8B Unit Analysis
LTA - SPINOFF 8C Pressure and Volume
LTA - SPINOFF 8D At What Cost? High Versus Low Pressure
K - Bottles for the Space Shuttle
Johanna Halsey - AMATYC Writing Team Member
Dutchess Community College, New York
Virginia Lee - AMATYC Writing Team Member
Brookdale Community College, New Jersey
Michael Haddad - NASA Scientist/Engineer
Kennedy Space Center, Florida
SPINOFF 8D
At What Cost? High Versus Low Pressure K-Bottles for the Space Shuttle
Part 1 - A Different Kind Of K-Bottle
There are actually two different choices for K-bottles containing compressed air. The one
discussed so far is under a pressure of 2200 lbs/in^2. We will refer to this as the low pressure K- bottle. You can also use a high pressure K-bottle in which the air is under a pressure of 3600
lbs/in^2. The volume of each bottle is still 1.5 ft^3 , but because of the greater pressure, there is a
greater volume of air available at 14.8 lbs/in^2 in the high pressure K-bottle.
- Refer back to the LTA, Part 1, Question 1. You will need to repeat some of these calculations for this new type of bottle. First you need to determine the volume of air available at 14. lbs/in^2 in this new bottle using the equation P 1 V 1 = P 2 V 2. Once you have this volume in ft^3 , you will need to convert to cm^3. Round your answers to two decimal places.
Volume of air available at 14.8 lb/in^2 in one high pressure K-bottle = __________ cm^3
- Your goal now is to produce a formula for the number of high pressure K bottles needed for 7 days of purging at different flow rates. You should take the time to refer back to the process you used in Part 1 of the LTA for the low pressure K-bottles. Although you could repeat these steps using the three specific flow rates of 60, 100, and 120 cm^3 /sec, and then create your formula from the table, try a more general strategy using a variable flow rate, x. Create a general guideline outlining the steps you followed to determine the number of bottles ( y ) needed at a flow rate of x cm^3 /sec. Use this strategy to develop your formula directly.
Formula for the number of bottles without the 10 % “safety factor” (round to 2 decimal places): _____________
Formula for the number of bottles with the 10 % “safety factor” (use 3 decimal places):
- Use your formula with the “safety factor” to complete Table 1:
Table 1 Flow rate Whole number of bottles
60 100 120
If you compare the table for the low-pressure K-bottle (refer back to the original LTA, Part 1) and this table for the high-pressure K-bottle, you will see that you need fewer of the high pressure K- bottles for a given flow rate. You might therefore assume that it would be better to always use the high pressure K-bottles. However, it’s time to talk about money.
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Table 2 Flow rate Number of low-pressure bottles
Cost for low-pressure bottles
Number of high-pressure bottles
Cost for high-pressure bottles
Which bottle is cheaper? (L or H) 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
Consider the data produced. Using the data, decide whether there is a linear relationship between the cost of filling the K-bottles and the flow rate. Explain why or why not.
Create a new column on your table to indicate which type of bottle is cheaper to use for a given flow rate. Use L if the low pressure bottle is cheaper and H if the high pressure bottle is cheaper.
Review the work you have done so far. Then suppose you are the engineer in charge of this comparison. Brainstorm in your groups on how you would respond if someone asked whether you should always use the high pressure K-bottles. Think about how you might decide what kind of bottle to use and what rationale you would give to support your decision. Think about what factors in addition to cost might affect your decision as to what type of bottles to use.
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- After your group discussion, write a brief memo to your supervisor outlining the results of your investigation, and the decisions you would make as well as the rationale for these decisions. One way to know if you have written a clear memo is to read it to someone who has not worked through this entire problem. There must be enough information presented in the memo so that the person can understand the objective of your project as well as the results of your analysis. Although the process you went through is important, you should not include all of the details. Rather, present the major points, equations, and how you use the information in the table to make decisions.
Part 3 - More Compartments
Some orbiting spacecraft could carry several different instruments that need to be purged. Depending upon the nature and function of the instrument, each instrument may need to be isolated in its own compartment. (The radiation given off by one instrument may be enough to affect the operation of another instrument.) Suppose that there are two instruments, each housed in separate
compartments, with each requiring the same flow rate of 50 cm^3 /sec for purging.
Let’s first talk about the physical scenario. The simplest way to set this up is to have a single hose coming from the K-bottles, and a T-connector at the end of the hose with one end going to each compartment. As long as all hoses are the same diameter, we can assume that each compartment will receive half of the flow rate coming through the main tube. Create a sketch depicting this scenario.
- What flow rate is required through the main tube in order for each compartment to receive a
flow rate of 50 cm^3 /sec?
Total flow rate = _____________
- Since you now know the total required flow rate through the main tube, assuming that we purge for 7 days, determine from the table you created in Part 2 the number of each type of K- bottle needed.
Number of K-bottles needed to purge two compartments at a rate of 50 cm^3 /sec each
of Low Pressure bottles ________ # of High Pressure bottles _________
Let’s now assume that the two instruments need different flow rates for purging. One instrument
requires 70 cm^3 /sec, while the other needs 100 cm^3 /sec. We need a way to change the flow into each separate compartment. We can accomplish this by inserting a flow regulator into the hosing that leads from the main tube to the instrument requiring the smaller flow rate. This flow
regulator will ensure that only 70 cm^3 /sec flows to that compartment. The remaining air must therefore flow into the other compartment.
- What flow rate is required through the main tube in order for each compartment to receive the appropriate flow rate?
Total flow rate required = _____________
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- Use your Table 2 from Part 2 of this investigation and the information in Table 3 to help set up Table 4. The interior numbers represent the number of low pressure bottles needed, followed by the cost of filling these bottles. Table 4 Flow Rate for Compartment 1Flow Rate for Compartment 1Flow Rate for Compartment 1Flow Rate for Compartment 1 50 60 70 80 90 100 30 \ \ \ \ \
Flow Rate 40 \ \ \ \ \
for 50 \ \ \ \ \
Compartment 2 60 \ \ \ \ \
70 \ \ \ \ \
80 \ \ \ \ \ \
The numbers within Table 4 represent: _________________________________________
Remember, you cannot attach more than 12 bottles to the manifold on the crawler. What implications does this have for your table? Are all cells in the table valid? Why or why not?
- Fill in Table 5 using the information on the high pressure bottles.
Table 5 Flow Rate for Compartment 1Flow Rate for Compartment 1Flow Rate for Compartment 1Flow Rate for Compartment 1 50 60 70 80 90 100 30 \ \ \ \ \
Flow Rate 40 \ \ \ \ \
for 50 \ \ \ \ \
Compartment 2 60 \ \ \ \ \
70 \ \ \ \ \
80 \ \ \ \ \ \
The numbers within Table 5 represent ________________________________________
- After reviewing the work you have done so far, brainstorm with your group members on what ideas and highlights you would want to emphasize if you were to present a report to a team of scientists and administrators. Make sure you consider options other than the lowest and highest cost. What information in the tables would you want to highlight? How would you summarize the results in the tables? What suggestions would you make in terms of the type of K-bottle to be used? How would you explain and defend these suggestions?
10)Finally, use the ideas generated in your brainstorming session to write a report to the team of scientists and administrators. Your report should contain a clear description of how you approached the problem, what information is evident from your tables, and your suggestions for how they can use the tables to make their final decision on what type of K-bottles to use.
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