SMS-491: Integrative marine sciences.
Review questions for final exam:
1. How many liters are there in a cubic meter (1 liter = 1000cm3)?
Answer: 1000liter/m3
2. A boat is sailing at 7 knots. How fast is it in m/s (1 nautical mile = 1853 m, 1 knot = 1
nautical mi h-1)?
Answer: 7x1853m/3600s~3.5m/s
3. The ocean's volume is approximately 328,000,000 cubic miles of salt water. What is
the ocean's volume in cubic kilometers (1 mi =1.6093 km)?
Answer: 328000000mi3x(1.6093km/mi)3=1,367,051,505.6km3
4. A whale swims at a constant speed while feeding on plankton.
a. How many cubic meters of water enter the open mouth (2m2 area) of the whale each
minute as it swims through the water at 2 m s-1?
Answer: 2m2 x 2m/s x 60s/min=240m3/min.
b. How many plankton can the whale ingest per second if the plankton concentration is
5000 per m3?
Answer: 2m2 x 2m/s x 5000 m-3=20,000s-1
c. A whale ingests 500,000 calories per day. How many are ingested per second?
Answer: 500000cal/day x 1/(60x60x24) day/s = 5.8cal/s
5. The Barringer Crater in Arizona was formed 30,000 years ago by a spherical meteorite
of diameter 60 m and mass 106 tonnes (one tonne = 1000 kg) traveling at 15 km s-1 when
it hit the ground.
a. What was the mean density of the meteorite?
Answer: 109Kg/ {4/3 π x(60m/2)3} = 8846Kg/m3
b. If one ton of explosive TNT is equivalent to five billion joules, how many tons of
TNT would have the same impact as the meteorite?
Answer: Meteorite energy upon impact: mv2/2= 109Kgx15000m/s=15x1012J{Kg m/s}
Æ15x1012J/5 x109J=3000tons of TNT
6. A log floats on water (ρ =1000 kg m-3) with 1/3 of its volume outside the water. What
is the density of the log?
Answer (Archimedes’s principle): 2/3V*1000kg/m3=V*ρwoodÆ*ρwood=666 kg/m3
7. What are the forces acting on a settling particle?
Answer: gravity down, buoyancy up and friction in the opposite direction to its motion.
8. Name three differences and three similarities between sound and light.
Answer: Differences: 1. light propagates in void sound doesn’t. 2. Sounds travels faster in
water than air, light is faster in air. 3. Different wavelength range (nm for light vs. mm
and up for sound).
Similarities: 1. Both travels as wave, 2. Both used by organisms to sense their
environment, 3. Both change speed as they path between different media.
9. How is the wave frequency related to its wavelength and its phase speed?
Answer: phase speed=wavelength x frequency Æ frequency=phase speed/wavelength.
10. Name a swimming technique that works well at high Re but that will fail at low Re.
Why does it not work at low Re?
Answer: Axial undulatory propulsion. Does not work in low Re because it is reversible.
11. A bacteria (L~10-6m) swims in water (ν~10-6m2/s) and a velocity of U~30x 10-6m/s.
1. What is the Reynolds number of the swimming?
Answer: Re=LU/ν=30 x 10-6
2. If it stops swimming, estimate the length scales it would take it to stop (Notice that
there are at least two length scales. Justify your choice.). Estimate how long of a time it
will take the cell to stop?
Answer: Stopping is caused by friction. Friction based time scale: t~L2/ν=10-6s. After this
amount of time the distance it covers is: L~Ut=30x10-12m.
12. What is the physical principle behind the Galileo thermometer (the one with the glass
balls partially filled with fluid that sink as the temperature gets warmer)?
Answer: The density of the water in the container decreases with temperature, thus the
ball become heavier relative to it and sink as the temperature rise.
13. Name the three mechanisms for heat transfer. How are they different from each
other?
Answer: Conduction-requires contact and is due to movement of molecules.
Convection- density differences within fluid (cold is denser) causes the fluid to move and
move the heat with it. Requires fluid to move heat.
Radiation-absorbed electromagnetic radiation causes heating of a material and material of
given temperature radiates energy based on its temperature. Can propagate in void (e.g.
between sun and earth) .
14. Water coming out a faucet has a tendency to reduce its cross sectional area. Why?
Answer: The water accelerate due to gravity and since the flux of water coming out is
constant the cross sectional area of the water is reduced (v x A = const.)
15. An iceberg is floating on the ocean. Its density is 920 kg m-3 while the density of the
ocean is 1030 kg m-3. How much of the iceberg's volume is above water (in percent)?
Answer: (Archimedes’ principle) V x 920 = Vin water x 1030
Vout of water= V- Vin water = V(1-920/1030)~0.1xV
16. You are asked by the US Geological Survey to measure the volume of water flowing
per hour down the Penobscot River near Bangor. How would you go about determining
how much water flows downstream? What properties do you need to measure?
Answer: Cross sectional area and velocity of flow at several places of the river to
compute a meaningful spatially averaged velocity. Water flux= A x average velocity
17. The diffusion coefficient of CO2 in water is 1.77*10-9 m2 s-1. Based on dimensional
analysis, how far (on average) would a molecule of CO2 move in 1 d (~105 s)?
Answer: L={1.77*10-9 m2 s-1 x 105 s}1/2~10-2m
18. What are the dimensions of the Re number?
Answer: Re has no dimensions.
19. A tsunami is generated by an earthquake near Japan. How long will it take it to cross
the pacific (assume an average depth of 4000 m and a distance of 8000 kmÅ notice, this
is much too short. EB).
Answer: The speed of propagation is the group speed. Tsunami is a shallow water wave
Æ cg={gH}1/2~200m/s. T=8000000m/200=40000s~0.5day.
20. Two similar fish with different lengths are swimming in water (Reynolds number
nearly 100,000). Do they experience the same drag force? If you answer no, please
specify the fish that is likely to experience more drag.
Answer: The larger fish is likely to have a larger surface area and therefore is likely to
experience a larger drag force. It is also likely to be able to swim faster (in general, larger
organisms do swim faster), increasing the drag force it experiences.
21. What is the steepness of a wave of amplitude = 0.4 m, wavelength = 2 m, and period
of 1s. Is this wave likely to break?
Steepness: 2x0.4/2=0.4>1/7 this wave IS likely to break.
22. What causes waves that do not break in the deep ocean to break when they arrive on a
shallow beach?
Answer: wave get steeper due to slowing of speed as the water in which they propagate
becomes shallower.
----------------------------------------------------------------------------------------------------------A. Treating fluids as a continua or non-discrete media is justified because:
c. it is impossible to keep track of all the molecules in the fluid;
B. When we calculate the pressure at the base of a fluid column:
a. the width of the column does not matter;
C. You are asked to evaluate whether a water-tight, rectangular container will float or
sink in fresh water at room temperature. What measurements do you need to do in order
to be able to answer this question?
a. weight of the container;
b. volume of the container;
c. temperature of the container;
d. a and b; Å this is the right answer
e. a, b, and c.
D. Ice floats on water because:
it is solid;
it is colder than the water;
it is denser than the water;
all of the above;
e. none of the above.
E. When is a lake coldest (has the least heat)?
b. Near the date in winter when the heat flux to the lake is nearly zero.
F. Two particle made of the same material are settling in water and the Re<<1. One has a
diameter which is three times larger than the other. Which is true:
b. The smaller one will sink 9 times slower than the other.
G. The Doppler Effect refers to:
b. the observation that sound changes frequency depending on the movement of
source relative to a receiver.
H. Resonance refers to:
b.Forcing a physical system to oscillate at its natural frequency.
I. For water:
b. It takes less energy to thaw ice than to evaporate the same mass of water.
J. Water has a dampening effect on climate because:
a. It has a high specific heat capacity.
K. The greenhouse effect is due to:
b.The presence of an atmosphere that absorbs infra-red radiation.
L. Sound, light and surface waves all have the following in common:
They are periodic phenomena in space and time.
They propagate well in water.
Have speeds that depend on the density of water.
d.All of the above.
---------------------------------------------------------------------------------------------------------a. When a fluid is subjected to a shear stress, it will reach a state of equilibrium in which
no further motion occurs.
F
b. Pressure and shear stress are two examples of force per unit area.
T
c. The density of water is approximately 1000 kg m-3 and the gravitational acceleration is
T
9.81 m s-2
d. The atmospheric pressure in the classroom equals nearly 100,000 kg m-1 s-2 (N m2
)
T
e. Kinematic viscosity = dynamic viscosity/density, with units m2 s-1.
T
f. Force = rate of change of momentum
T
g. Work = Force*distance
T
h. In a fluid at rest, pressure at a point is isotropic (equal in any direction).
T
i. In a fluid at rest pressure decreases with depth.
F
j. A solid object completely immersed in oil will experience the same upward buoyant
force as when it is immersed in water.
F
k. An object that floats on water on Earth may sink if the gravitational acceleration is
changed.
F
l. To avoid the no-slip condition we make surfaces immersed in fluid very smooth. F
m. The no-slip condition causes momentum to pass from the boundary of the fluid into
the fluid itself.
T
n. The no-slip condition implies that right next to a body the fluid and the body move at
the same speed.
T
o. The pressure at the base of the atmosphere is similar to the pressure due to a column of
water of 1 m depth.
F
p. A boat is most stable when its center of gravity is as high as possible above its center
of buoyancy.
F
T
q. At high Reynolds number, the drag force on an object is proportional to U2.
r. The phase and group speeds of shallow water gravity waves are the same.
T
s. Longer sail boats can, in principle, go faster than short sail boats.
T
t. The amplitude of particle motion due to surface waves decays with depth.
T
v. In the absence of other forces, water flows from low pressure to high pressure. F
w. On the moon one would expect gravity waves to propagate faster than on Earth. F
x. Settling speed increases with viscosity.
F
y. Particles will settle in fluids slower on the moon relative to Earth.
T
z. The warmer something is the more heat it has.
T
aa. The greenhouse gases absorb primarily UV light.
F
ab. When water is evaporated from the ocean the ocean looses heat.
T
ac. Maximum of blackbody radiation occurs at increasing wavelength with increasing
temperature.
F
ad. The height a fluid climbs in a capillary tube increases with the tube’s diameter F
ae. Jet propulsion is a low Re swimming strategy.
F
af. The reason the poles gets less sun heat than the equatorial regions is that the sun’s
radiation is spread over a larger area than near the equator.
T
---------------------------------------------------------------------------------------------------------Explain what physical phenomena are exhibited in the following figures:
Flux=velocity x cross section. If cross
section changes velocity changes to
conserve the product.
Black body radiation; higher
temperature implies shorter
wavelength.
By Bernoulli’s principle, changes of velocity is
accompanied by opposite change in pressure.
Fluid that is accelerated due to disturbance is
associated with reduced pressure where the
velocity is maximum.
Turbulent flow in pipes have
smaller boundary layer but
have reduced flux for the
same pressure gradient due to
increase dissipation.