Names: Partner #1 ___________________________________________
Partner #2 ___________________________________________
The Big Squeeze: A Study in Pressure Calculations
Cetacean biologists are working closely with biomedical companies in researching how sperm whales can
dive at depths reaching up to 3000 feet. Of interest are the compressed lungs of sperm whales in which the
alveoli do not adhere to one another upon decent. Scientists hope to apply the knowledge of sperm whale
diving physiology to human medical applications. The hope is that this research will assist medical personnel
in treating a variety of respiratory disorders in humans. In order to do so scientists need to understand both
the volume and surface area changes that result when a sperm whale free dives to great depths. By using
Boyle’s Law and surface area calculations you will construct base line data plots of volume and surface area of
a sperm whale’s lung on descent.
Note: For this activity we are assuming that the whale’s lung is a sphere for ease of calculation.
Pressure and Volume Plotted Calculations Based on a Simulated Dive to 3000 Feet
1. Use the pressure calculations to determine the pressure in BAR/ATA and PSI for the following depths
that the sperm whale will descend to.
Calculations: Use the following equations to determine your pressure in both BAR/ATA and P.S.I.
a. Determine depth in feet. (Depth in feet ÷ 33) + 1 = Pressure in BAR/ATA
Note: Add 1 for the 1 atmosphere of pressure of air above the water. The calculations you are doing are for
total pressure. Example: A depth of 500 feet would have a BAR/ATA calculated as (500 feet
÷ 33) + 1 = 15.2 BAR/ATA
b. Each BAR/ATA is equal to 14.7 P.S.I. To convert BAR/ATA into P.S.I. multiply the BAR/ATA
you obtained by 14.7 to obtain the pressure in P.S.I. units. Example: Using the 15.2 BAR/ATA
pressure in the above example, convert it to P.S.I. units. (15.2 BAR/ATA) x (14.7 P.S.I.) = 222.7
P.S.I.
Note: You are actually multiplying by 14.7 P.S.I. / 1 BAR/ATA. That way when you multiply the
BAR/ATA units will cancel.
2. Graph the pressure in BAR/ATA against the depths for the data you have obtained in Table 1.
3. Use the BAR/ATA pressures at the various depths to calculate the volume of the lung the sperm
whale will have as it dives.
This calculation involves Boyle’s gas law.
Boyle’s Law Summary
P1xV1 = P2xV2
P1 = Pressure at beginning or start
V1 = Volume at beginning or start
P2 = Pressure at completion or end
V2 = Volume at completion or end
Algebra Notes: You will need to algebraically reconfigure the equation to solve for V 2. You also need to
make sure that whatever units you use on one side of the equation are the same units you use on the other.
4. Graph the depth versus volume of the data you have obtained in Table 2.
5. Using the lung volumes calculated above in procedure three, calculate the sperm whale’s
overall lung surface area to corresponding depths on Table 3. You will need to use the algebraic
expression:
Surface Area = 4π r2 and Volume = 4π r3
3
Hints for calculating overall lung surface area:
Step 1. Calculate the radius using the volume equation for each depth provided. *Use the volumes you
obtained in procedure three above. The equation should be – cubed root of (Volume x ? / 1) =
Example: A volume of 100 liters is the same as saying 100,000 cm 3
100,000 cm3 = 4π r3
3
solve for r (the radius) = 28.8 cm radius
Step 2. You will need to take the radius obtained with the above series of steps to determine the surface
area of the sphere. The equation should be – Surface Area = 4π r2
Example: Using the volume of 100 liters and the radius calculated for it’s sphere that was determined in
the above example enter the radius in the equation above as shown below.
Surface Area = 4 π (28. 8) 2
Area = 10423.05 cm2 or 1.04 m2
6. Graph the depth of the water versus the surface area of the sperm whale’s lungs.
Observation statements:
1. How does the plotted line of Graph 3 differ from that of the other two graphs before it (the depth vs. pressure and
depth vs. volume graphs)?
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2. How does the depth-pressure graph differ from that of the pressure-volume relationship?
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3. Upon diving what did you observe happen to the surface area of the sperm whale’s lung? How was it different
than the curve plotted for the volume?
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Analysis and Calculations
1. Calculate the total pressure in atmospheres and PSI experienced at a depth of 250 feet, which is the depth limit of very
experienced scuba divers using unconventional scuba diving equipment.
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2. Calculate the total pressure in atmospheres and PSI experienced on the ocean basin (abyssal plains) at an average
depth of 15,000 feet.
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3. Calculate the total pressure in atmospheres and PSI experienced at 36,000 feet in the Challenger Deep within the
Marianas Trench.
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4. You are in a submersible and you are observing a pressure of 100 atmospheres on the pressure gauge. Calculate your
depth.
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5. Assuming that a sperm whale has a total surface area of 500,000 square inches. What would be the total weight of
water in pounds on the sperm whales body at a depth of 500 feet? Why is the whale not crushed?
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6. What is the best 3-dimensional shape to be if you want to be able to withstand tremendous pressures? Explain.
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7. The Alvin has a 5-foot diameter sphere in which three people can survive the crushing pressures experienced at 16,000
feet. If the Alvin actually dove to 16,000 feet, what would be the total pressure on the hull of the sphere? HINT: The area of
a sphere = 4 π r2
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8. Provide an explanation as to why deep-water marine organisms have very compressed bodies with no gas
chambers.
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9. What is the problem with having any gas chambers in an organism’s body if they dive to great depths?
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10. Where are the gas chambers of your body located?
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11. An adult human has a lung capacity of approximately 5 liters when a full breath of air is taken. If you go
snorkeling in the Florida Keys and free dive to a depth of 20 feet what will your lung volume be? Use Boyle’s Law.
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12. When a scuba diver is breathing at a depth of 90 feet his/her lung capacity is the same as it would be at the
surface. So, if you have an adult human scuba diver with a lung volume of 5 liters that is diving a reef at a depth of 90
feet who suddenly comes to the surface before he can breath out the excess air, what will the resulting lung volume
be?
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13. A submarine is going down to the Titanic at a depth of 13,000 feet and will be collecting some artifacts from the
vessel. The artifacts are placed in a basket in which a balloon is attached and is inflated to bring the items back to the
surface. The volume of the balloon is 1 liter at the Titanic site. What will the balloon’s volume be when it reaches the
surface?
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14. Why would a scuba diver want to exhale on the way up to the surface if he is forced to ascend to the surface?
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