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Homework 7 - Ocean Currents
1. A modern container ship with a mass of 100,000 metric tons moves
with a speed of 20 knots from Los Angeles port southward. What is
the Coriolis force on the vessel at a latitude of 30oN , at the equator,
and at the southern latitude of 20oS!
2. A stormy wind of B=10 strength on the Beaufort scale on 40oS latitude
covering an area of A=10km2 drags the water in westerly direction.
Calculate the drag force the wind is exerting on the water.
3. Calculate the Ekman mass transport MEk at a very stormy day with the
wind stress reaching values of D = 104 N/m2 at the southern latitude
of 50oS. Calculate the wind velocity dragging the water and give the
corresponding wind speed on the Beaufort scale.
1. A modern container ship with a mass of 100,000 metric tons moves with a speed
of 20 knots from Los Angeles port southward. What is the Coriolis force on the
vessel at a latitude of 30oN , at the equator, and at the southern latitude of 20oS!
Fc  m  ac
Fc  2  m    v  sin 

0
360
rad
 2
 7.292 10 5 s 1
day
day
m  100,000,000 kg
v  20 1.852 km / h  37 km / h
Fc
Fc
Fc
Fc
Fc
Fc
3.7 10 4 m
 2 10 kg  7.292 10 s 
 sin 300
3600 s
kg  m
 7.5 105 2  7.5 105 N
s
4
9
5 1 3.7 10 m
 2 10 kg  7.292 10 s 
 sin 00
3600 s
kg  m
 0 2  0N
s
4
9
5 1 3.7 10 m
 2 10 kg  7.292 10 s 
  sin 200
3600 s
kg  m
 5.13 105 2  5.13 105 N
s
9
5
1






2. A stormy wind of B=10 strength on the Beaufort scale on 40oS latitude covering
an area of A=10km2 drags the water in westerly direction. Calculate the drag force
the wind is exerting on the water.
FD  C D  A   a  v 2
 a  1200
 
kg
m3
B  10  v  0.836  B 3 / 2  26.44
m
 C D  0.002
s
2
2
kg
m

FD  0.002 1200 3  10 4 m 2   26.44   1.68 1011 N
m
s

or FD A    1680 N m 2
3. Calculate the Ekman mass transport MEk at a very stormy day with the wind
stress reaching values of D = 104 N/m2 at the southern latitude of 50oS. Calculate
the wind velocity dragging the water and give the corresponding wind speed on
the Beaufort scale.
 D  z   f  M Ek
f  2    sin 500
  7.292 10 5 s 1
f  2  7.292 10 5 s 1  sin 500  1.117 10  4 s 1
M Ek
 D z 
10 4 N / m 2
7 kg



8
.
95

10
f
1.117 10  4 s 1
ms
v2 
f  M Ek
CD  a
v
v
f  M Ek
CD  a
1.117 10  4 s 1  8.95 107
0.002 1200
kg
m3
kg
m  s  64.54 m  232 km
s
h
2/3
m
 64.54 
v  0.836  B
 B
  18 quite a bit beyond the traditional Beaufort scale,
s
0
.
836


presently only reached as peak velocities in major category 5 hurricanes when the eye is passing!
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http://en.wikipedia.org/wiki/List_of_Category_5_Atlantic_hurricanes