Physics Problem Set 1

Diving Myths & Realities

Dive Physics

Problem Set 1

Larry "Harris" Taylor. Ph.D.

Diving Safety Coordinator

University of Michigan

Ann Arbor, Michigan

Merely reading about dive physics and looking at some worked examples is, for most folks, insufficient to provide a true understanding of the physical principles that control our actions in the water column. Such understanding, unfortunately, only comes from doing problems. Below is a problem set, with detailed solutions, designed to test your understanding of the physical principles involved in controlling our behavior underwater.

1. We are _______________ creatures. As such, our physical abilities are optimized to function in air. This means when we enter the water, we must compensate for our lack of physical prowess by using our _______.

2. Understanding the water environment will increase your ability to have ______ !

5. Ice is water in the _______ state; water vapor is in the ________ state and running water is in the __________ state.

9. Elements and compounds found together, but not chemically combined are called __________ .

10. Hydrogen is the ___________ element. It is very combustible. It is ___________ in recreational diving.

11. Helium is an inert gas. Although not used in recreational diving, it is used in specialized applications involving __________ diving. Its advantage is _______of breathing with _______ narcotic potential than air. Its disadvantage is increased __________________ risk and a nervous disorder known as ______________ .

12. Nitrogen is ________________inert. Its accumulation can pose risks for the diver known as _____________ and ______________________.

13. Blends of nitrogen and oxygen (Nitrox or EANx), require specialized training since their use is____________ traditional recreational training.

14. Oxygen is chemically ______ reactive. Although not combustible by itself, its presence in high concentrations ____________ risk of other substances becoming a fire or explosion hazard.

15. Too little oxygen is termed ________ and too much oxygen is termed _________.

16. __________ in diving can lead to oxygen toxicity. _________-oxygen toxicity, as opposed to pulmonary toxicity can lead to ___________________ seizures which can be fatal. At recreational depths (100 fsw), this O₂ toxicity is usually _________ a problem.

17. Carbon dioxide is a normal body ____________ . It is a primary regulator of __________________.

18. If you walk into a closed space and notice a distinctive acrid taste and smell, then most likely there is a high concentration of ___________ in the air.

19. If the temperature of the air is below the dew point, then fog formation __________ occur.

20. If air is rapidly released from a scuba cylinder, the temperature of the air will ______________ . This is because an ______________ expansion has occurred.

21. Exhalation of air on a cold winter day before an ice dive into a regulator to ensure its functioning is ___________ advised.

22. Air is composed of ____ % nitrogen, _____ % oxygen and _____ % "other stuff."

23. The five fundamental measurements are: __________ , ___________ , _____________ , ____________ , and _____________________ .

25. Most of the world uses the ___________ system; the United States uses the ___________ system of measurement.

26. The standard unit of length is the _________ in the English system and the _____________ in the metric system.

28. Although not rigorously correct, divers use ___________ (English) and _________ (metric) for mass.

29. Mass is a property of matter characterized by _____________ ; weight is a result of a _________ acting on that mass.

30. In the water, a diver's mass _________ change. The weight, however, may __________.

32. The "key" or "fudge factor" which helps solve problems is keeping track of -_____________.

34. The density of fresh water is ______________ g/cc;___________ pounds/cubic foot.

35. The density of sea water is _______________ g/cc; __________ pounds /cubic foot.

36. Perhaps the easiest way to visualize and solve buoyancy problems is through the application of "______________________."

37. The upward buoyant force results from the ____________ of water. The magnitude of this force is equal to the _____________ of the ___________ displaced.

38. If a diver is diving with improper buoyancy, then the diver is doing too much _________ !

41. Objects can be lifted off the bottom by the _____________ buoyant force of air. This is because air weighs much _______ than water.

42. The buoyant force of the lifting device is equal the ____________ of the ____________ of water displaced by the air in the lifting device.

43. The most efficient way to dive is to assume a ___________ position in the water.

44. Doubling the cross-sectional area of a diver increases the work of swimming by about _________ times.

45. If a diver does not have neutral buoyancy, the diver's buoyancy must be either ______________ or __________________.

47. The light sticks used in night diving represent visible _______________energy formed as a result of the _______________ energy released by the mixing of chemicals in the tube.

49. Force is a _________ or _________ . It has both _____________ and ______________.

50. Work is the movement of __________ over a ___________ . If no movement occurs, then ________ work has been done.

51. Heat is __________ energy that is the sum of the ___________ energy of all the molecules in a substance.

54. Heat capacity is a measure of the ability of a substance to ___________ heat.

56. The quantity that measures rate of heat loss is _______________________________ .

57. Substances like water with a high thermal capacity increase ________________risk.

61. Water has a thermal capacity about _________ times the thermal capacity of dry, still air at the same temperature.

62. Divers lose heat by several mechanisms. They are _____________ , ___________ , ______________, and ___________.

63. In recreational diving, _______________ is the least important heat loss mechanism.

64. _________________ and ________________ account for most recreational diving heat loss.

65. Since heat loss can be accumulative, it _____ possible to suffer hypothermia in a tropical sea.

67. The loss of red color in the water is explained by absorption of _________ energy light.

68. The mnemonic for colors of the spectrum (least energetic first) is ____________.

69. The scattering of light as it moves through water is called ________________ .

71. The air - water interface can act as a lens. This is termed _______________ .

72. Light loss may be increased near dusk as light is _________________ from the water surface.

76. The diameter of the barometer tube is _______ important. The mercury in the tube is held up by ____________________________.

77. The more dense the fluid in a barometer, the _______________ the tube has to be.

78. One atmosphere of pressure corresponds to _____ inches of water, ________ mm Hg, _____ fsw, ____ ffw, _____ msw, ____ mfw, _______ psi, and _____ bar. In the metric system, ______ msw = 1 bar.

79. The name given for the pressure exerted by the column of water affecting the diver is ____________ pressure.

80. The name given for the pressure exerted by the sum of hydrostatic and atmospheric pressures i.e _________________ or ______________ pressure.

82. At high altitude, the actual depth is ______________ than the depth indicated by the sea level calibrated depth gauge; the decompression equivalent sea level depth is ____________ than the sea level calibrated gauge indicates; the ascent rate should be _________ than the ascent from depth while diving at sea level.

83. Diving at altitude with sea level gauges and procedures ____________ risk to DCS.

84. Gas pressure can be thought of as collisions of gas molecules with the walls of the container. If the temperature of the gas increases, the number of collisions _________________ and the pressure___________________ .

85. If the temperature of a gas decreases, the amount of air available to the diver ________________ .

87. If pressure on a gas increases, the volume _________________ and the density ________________ .

89. The change of volume associated with a change in depth is greatest _________________________________________ .

90. Estimating gas consumption at depth assumes breathing volume is ____________regardless of depth.

91. The "average diver" consumes ____ cubic foot; _________ liters per minute on the surface.

93. If the absolute pressure on the diver doubles, then air consumption ____________.

94. Since air consumption factors ____________ include ascent or safety stop values, divers ___________ add safety margins to their calculations.

95. The primary difference between a real and ideal gas is that an ideal gas molecule occupies __________ volume. Real-type gas calculations are ______ necessary for recreational diving. They are a consideration when _________gases other than air.

96. The total pressure exerted by a mixture of gases is the _____ of the pressures of the individual components.

97. An eighty cubic foot cylinder contains 2 ata pressure of nitrogen gas. If 1 ata of another gas were added, the pressure exerted by the nitrogen would be ___ ata and the pressure of the total mix would be _____ ata.

98. As a diver descends, the amount of all gases dissolved in tissues _____________.

99. Henry's Law relates the amount of gas that will dissolve at depth. It says nothing about the _________ of obtaining equilibrium.

1. _________________ , a Greek natural philosopher developed buoyancy principles.

2. The ________________________ Effect describes temperature drop during adiabatic expansions.

4. __________________________ developed a scale based on 100 degrees between the boiling and freezing points of water.

7. The principles of classical physics were described by __________________ in PRINCIPIA.

9. _______________________ developed the barometer and the concept of atmospheric pressure.

10. ______________________ studied the relationship between volume and absolute temperature.

11. ______________________ measured temperature with a gas pressure thermometer.

12. _____________________ studied the relationship between absolute temperature and pressure by taking measurements while ascending in a hot-air balloon.

13. ______________________ measured the change in volume associated with differences in absolute pressure.

14. _____________________ explained the result of total pressure increases when gases were mixed.

15. ____________________ examined the relationship between partial pressure and gas in solution.

2. The meter was originally defined as 1/10,000,000 of the distance from the earth's equator to the north pole. Convert 10,000,000 m to miles.

3. The St. Clair river serves as a border between the United States and Canada. The current there is so intense that fisherman use as much as three pounds per line to keep the current from moving their fishing tackle. Convert 3 pounds to grams.

5. One type of metric scuba cylinder is 2400 liters. Convert this to cubic feet.

7. One measure of oxygen tolerance is the amount of oxygen exposure obtained per minute. If it is safe to accumulate 1 unit per minute, what is the maximum number of units that could be accumulated in a 24 hr period?

1. An object has a volume of 9 cubic feet. Its mass is 6 pounds. Calculate the density.

2. An object has a mass of 3 kg. Its volume is 16 liters. Determine the density.

3. An object has a density of 50.6 lb/cubic foot. How far will it be submerged in seawater?

4. An object has a density of 0.678 g/cc. How much will be submerged in fresh water?

5. A diver weighs 157 pounds in diving gear. This diver has a volume of 2.8 cubic feet. How much lead will this diver need to dive in sea water and fresh water?

6. A diver in scuba gear has a mass of 70 kg has a volume of 80 liters. How much lead will this diver need in fresh and sea water?

7. A diver in scuba gear weighs 196 pounds. This diver needs 22 pounds to dive in sea water. How much lead does this diver need for fresh water?

8. A diver in scuba gear weighs 73 kg. This diver uses 6 kg of lead in fresh water. How much lead is needed to dive in sea water?

9. What is the hydrostatic, absolute, and ambient pressure in psi and atmospheres for 46 fsw?

10. What is the hydrostatic, absolute, and ambient pressure in atmospheres and bars for 12 msw?

11. If a scuba cylinder is capable of delivering 36 cubic feet of air to the diver at 78 ^oF, what volume will the cylinder deliver at 40 ^oF?

12. A scuba cylinder delivers 2000 liters of air at 25 ^oC. What volume is available at 18 ^oC?

13. What is the gauge pressure in a scuba cylinder that has a pressure of 3000 psig at 75 ^oF that has been heated to 126 ^oF?

14. What is the gauge pressure of a scuba cylinder that has a gauge pressure of 200 bar at 25 ^oC that has been heated to 42 ^oC?

15. A diver has 80 cubic feet of air available at the surface. How much air is available at 48 fsw?

16. A diver has 2000 liters available in a scuba cylinder at the surface. How much air does the diver have at 18 msw?

17. If a scuba cylinder delivers 71.2 cubic feet at 78 ^oF on the surface, how much air will it deliver at 58 feet of cold fresh water at 50 ^oF?

18. A scuba cylinder delivers 2400 liters on the surface at 25 ^oC. What volume of air will the cylinder deliver at 22 m of fresh water at 5 ^oC?

19. A diver's air supply lasts 22 minutes at 84 fsw. How long will it last at 18 fsw?

20. A diver's air supply lasts 30 minutes at 24 msw. How long will the same cylinder last at 9 msw?

21. A diver consumes 125 psig in two minutes at 38 ffw. What is this divers absolute air consumption in terms of pressure and what is this diver's SAC rate?

22. A diver consumes 60 bar in 3 minutes at 5 msw. What is this divers absolute air consumption and SAC rate?

23. A diver has an absolute air consumption of 40 psig/ata-min. The diver wishes to begin ascent at 1000 psig. Assuming the diver reaches depth with 2900 psig, how long can the diver remain at 45 fsw before beginning ascent?

24. A diver has an absolute air consumption of 2.0 bar/ata-min. Assuming the diver reaches depth with a gauge reading of 200 bar and will begin ascent at 70 bar, how long will the diver be able to remain at 20 msw?

25. A diver has an absolute air consumption of 25 psig/ata-min. Convert this to an absolute volume consumption with the knowledge that this consumption factor was determined with a cylinder holding 71.55 cubic feet at 2475 psig.

26. A diver has an absolute air consumption of 2.0 bar/ata-min. Convert this to an absolute volume consumption with the knowledge that this factor was determined using a cylinder holding 2000 liters at 200 bar.

27. A diver has an absolute volume consumption of 0.72 cubic feet /ata-min. Will a single "80" be sufficient for this diver to dive 25 minutes at 90 fsw?

28. A diver has an absolute volume consumption of 20 liters /ata-min. Will this diver be able to dive to 24 msw for 45 minutes with a 2000 liter scuba cylinder.

29. A diver has an absolute volume consumption factor of 0.72 cubic feet /ata-min. How long will it take to consume 40 cubic feet at 36 feet of fresh water?

30. A diver has an absolute volume consumption rate of 20 liters /ata-min. How long will it take this diver to consume 1200 liters at a depth of 18 mfw?

31. What is the absolute pressure consumption factor (psig/ata-min) for a diver whose absolute volume consumption factor is 0.72 cubic feet per ata-min using a cylinder that has a capacity of 50.43 cubic feet at 3000 psig?

32. What is the absolute pressure consumption factor (bar/ata-min) of a diver whose absolute volume consumption is 20 liters/ata-min using a cylinder that is rated at 2000 liters at 200 bar?

33. A cylinder contains 21% O₂ at 3000 psig. The cylinder is then taken to 66 fsw (20 msw; 4 ata). What is the percentage of oxygen in the cylinder and what is the partial pressure (in ata) of oxygen and nitrogen at that depth?

Larry "Harris" Taylor, Ph.D. is a biochemist and Diving Safety Coordinator at the University of Michigan. He has authored more than 200 scuba related articles. His personal dive library (See Alert Diver, Mar/Apr, 1997, p. 54) is considered one of the best recreational sources of information In North America.

Use of these articles for personal or organizational profit is specifically denied.