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.
Answers To Set 1
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in the blanks:
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
3. Matter is anything that occupies ________ and has ______ .
4. The three ordinary states of matter are __________ ,________, and
5. Ice is water in the _______ state; water vapor is in the ________
state and running water is in the __________ state.
6. According to science, matter is composed of ________.
7. Material that is composed of only one kind of atom is called an
8. Elements chemically combine to form __________.
9. Elements and compounds found together, but not chemically combined are
called __________ .
Hydrogen is the ___________ element. It is very combustible. It is ___________
in recreational diving.
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
Nitrogen is ________________inert. Its accumulation can pose risks for the diver
known as _____________ and ______________________.
Blends of nitrogen and oxygen (Nitrox or EANx), require specialized training
since their use is____________ traditional recreational training.
Oxygen is chemically ______ reactive. Although not combustible by itself, its
presence in high concentrations ____________ risk of other substances becoming
a fire or explosion hazard.
Too little oxygen is termed ________ and too much oxygen is termed _________.
__________ 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.
Carbon dioxide is a normal body ____________ . It is a primary regulator of
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.
If the temperature of the air is below the dew point, then fog formation
If air is rapidly released from a scuba cylinder, the temperature of the air
will ______________ . This is because an ______________ expansion has occurred.
Exhalation of air on a cold winter day before an ice dive into a regulator to
insure its functioning is ___________ advised.
Air is composed of ____ % nitrogen, _____ % oxygen and _____ % "other
The five fundamental measurements are: __________ , ___________ , _____________
, ____________ , and _____________________ .
The metric system was designed to make conversion of units __________.
Most of the world uses the ___________ system; the United States uses the
___________ system of measurement.
The standard unit of length is the _________ in the English system and the
_____________ in the metric system.
Time in both metric and English is based on the _______________ .
Although not rigorously correct, divers use ___________ (English) and _________
(metric) for mass.
Mass is a property of matter characterized by _____________ ; weight is a result
of a _________ acting on that mass.
In the water, a diver's mass _________ change. The weight, however, may
Density is defined as __________ divided by the __________ .
The "key" or "fudge factor" which helps solve problems is
keeping track of -_____________.
If _________ are wrong, then the numerical solution is _____________ .
The density of fresh water is ______________ g/cc;___________ pounds/cubic foot.
The density of sea water is _______________ g/cc; __________ pounds /cubic foot.
Perhaps the easiest way to visualize and solve buoyancy problems is through the
application of "______________________."
The upward buoyant force results from the ____________ of water. The magnitude
of this force is equal to the _____________ of the ___________ displaced.
If a diver is diving with improper buoyancy, then the diver is doing too much
Moving from fresh water to seawater, the diver must ________ weight.
Moving from seawater to fresh water, the diver must ________ weight.
Objects can be lifted off the bottom by the _____________ buoyant force of air.
This is because air weighs much _______ than water.
The buoyant force of the lifting device is equal the ____________ of the
____________ of water displaced by the air in the lifting device.
The most efficient way to dive is to assume a ___________ position in the water.
Doubling the cross-sectional area of a diver increases the work of swimming by
about _________ times.
If a diver does not have neutral buoyancy, the diver's buoyancy must be either
______________ or __________________.
Energy is the ability to do ___________.
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.
Mechanical energy is the sum of _______________ and ______________ energy.
Force is a _________ or _________ . It has both _____________ and
Work is the movement of __________ over a ___________ . If no movement occurs,
then ________ work has been done.
Heat is __________ energy that is the sum of the ___________ energy of all the molecules
in a substance.
One calorie is the heat needed to raise ____ cc of water _____oC.
One BTU is the heat needed to raise ________ pound of water ______ oF.
Heat capacity is a measure of the ability of a substance to ___________ heat.
Good heat insulators should have a _____ specific heat.
The quantity that measures rate of heat loss is _______________________________
Substances like water with a high thermal capacity increase
Heat always flows from the ___________ object to the __________ object.
Insulation ____________ prevent
The most common insulating substance is __________ .
Water has a thermal capacity about _________ times the thermal capacity of dry,
still air at the same temperature.
Divers lose heat by several mechanisms. They are _____________ , ___________ ,
______________, and ___________.
In recreational diving, _______________ is the least important heat loss
_________________ and ________________ account for most recreational diving heat
Since heat loss can be accumulative, it _____ possible to suffer hypothermia in
a tropical sea.
Water is most dense at ______ oC; ________ oF.
The loss of red color in the water is explained by absorption of _________
The mnemonic for colors of the spectrum (least energetic first) is ____________.
The scattering of light as it moves through water is called ________________ .
___________ refers to the amount of particulate matter in the water.
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.
Sound _________ a reliable direction clue underwater.
Pressure is the result of a ________ acting across an __________ .
The ___________________ measures
The diameter of the barometer tube is _______ important. The mercury in the tube
is held up by ____________________________.
The more dense the fluid in a barometer, the _______________ the tube has to be.
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.
The name given for the pressure exerted by the column of water affecting the
diver is ____________ pressure.
The name given for the pressure exerted by the sum of hydrostatic and
atmospheric pressures i.e _________________ or ______________ pressure.
Depth gauges measure _____________ , not __________ !
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.
Diving at altitude with sea level gauges and procedures ____________ risk to DCS.
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___________________ .
If the temperature of a gas decreases, the amount of air available to the diver
If the temperature of a gas increases, the pressure _________________.
If pressure on a gas increases, the volume _________________ and the density
On ascent, the volume of air _________________
The change of volume associated with a change in depth is greatest
Estimating gas consumption at depth assumes breathing volume is
____________regardless of depth.
The "average diver" consumes ____
cubic foot; _________ liters per minute on the surface.
Air consumption __________ as depth increases.
If the absolute pressure on the diver doubles, then air consumption
Since air consumption factors ____________ include ascent or safety stop values,
divers ___________ add safety margins to their calculations.
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.
The total pressure exerted by a mixture of gases is the _____ of the pressures
of the individual components.
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.
As a diver descends, the amount of all gases dissolved in tissues _____________.
Henry's Law relates the amount of gas that will dissolve at depth. It says
nothing about the _________ of obtaining equilibrium.
Knowledgeable, physically fit divers have more
Part B: Names
1. _________________ , a Greek natural philosopher developed buoyancy
2. The ________________________ Effect describes temperature drop during
3. ____________________________ developed the first reliable thermometer.
4. __________________________ developed a scale based on 100 degrees
between the boiling and freezing points of water.
5. The Absolute Fahrenheit scale is the ___________ scale.
6. The Absolute Celsius scale is the __________ scale.
7. The principles of classical physics were described by
__________________ in PRINCIPIA.
8. The Greek philosopher, _______________, said "Nature abhors a
9. _______________________ developed the barometer and the concept of
______________________ studied the relationship between volume and absolute temperature.
______________________ measured temperature with a gas pressure thermometer.
_____________________ studied the relationship between absolute temperature and
pressure by taking measurements while ascending in a hot-air balloon.
______________________ measured the change in volume associated with differences
in absolute pressure.
_____________________ explained the result of total pressure increases when
gases were mixed.
____________________ examined the relationship between partial pressure and gas
____________________ said, "Dive with your brains, not your back!"
C: Unit Conversions
1. The English rod is 16.5 feet. Convert this to meters.
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.
4. A car has a gasoline tank capacity of 56 liters. Convert this to
5. One type of metric scuba cylinder is 2400 liters. Convert this to
6. A scuba cylinder has a volume of 50 cubic feet. Convert this to
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?
8. The dive charter has a depth limit of 100 feet. Convert this to
9. What is the absolute Rankine equivalent of 78 oF?
What is the Kelvin equivalent of 100 oC?
D: Numerical Problems
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
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
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
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?
What is the hydrostatic, absolute, and ambient pressure in atmospheres and bars
for 12 msw?
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?
A scuba cylinder delivers 2000 liters of air at 25 oC. What volume is
available at 18 oC?
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?
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?
A diver has 80 cubic feet of air available at the surface. How much air is
available at 48 fsw?
A diver has 2000 liters available in a scuba cylinder at the surface. How much
air does the diver have at 18 msw?
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?
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?
A diver's air supply lasts 22 minutes at 84 fsw. How long will it last at 18 fsw?
A diver's air supply lasts 30 minutes at 24 msw. How long will the same cylinder
last at 9 msw?
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?
A diver consumes 60 bar in 3 minutes at 5 msw. What is this divers absolute air
consumption and SAC rate?
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?
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?
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.
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.
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?
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.
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?
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?
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?
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?
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?
Answers To Set 1
Go To Site Page: Home About "Harris" Articles War Stories Biblios Editorials Links Site Map Fini
"Harris" Taylor, Ph.D. is a biochemist and Diving Safety Coordinator
at the University of Michigan. He has authored more than 100 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.
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Use of these articles for personal or organizational profit is specifically denied.
These articles may be used for not-for-profit diving education