A hurricane is a tropical storm formed over the ocean by low atmospheric pressures. As a hurricane approaches land, inordinate ocean swells (very high tides) accompany the hurricane. A Class-5 hurricane features winds in excess of 155 mph, although the wind velocity at the center "eye" is very low.

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EXAMPLE 5–9
The Rise of the Ocean Due to a Hurricane
A hurricane is a tropical storm formed over the ocean by low atmospheric
pressures. As a hurricane approaches land, inordinate ocean swells (very
high tides) accompany the hurricane. A Class-5 hurricane features winds in
excess of 155 mph, although the wind velocity at the center "eye" is very
( Eye
Hurricane
low.
Calm
Figure 5-42 depicts a hurricane hovering over the ocean swell below. The
atmospheric pressure 200 mi from the eye is 30.0 in Hg (at point 1, gener-
ally normal for the ocean) and the winds are calm. The hurricane atmo-
spheric pressure at the eye of the storm is 22.0 in Hg. Estimate the ocean
оссan
O level
Оссan
swell at (a) the eye of the hurricane at point 3 and (b) point 2, where the
wind velocity is 155 mph. Take the density of seawater and mercury to be
64 Ibm/ft and 848 Ibm/ft?, respectively, and the density of air at normal
sea-level temperature and pressure to be 0.076 Ibm/ft.
FIGURE 5-42
Schematic for Example 5–9. The
vertical scale is greatly exaggerated.
SOLUTION A hurricane is moving over the ocean. The amount of ocean
swell at the eye and at active regions of the hurricane are to be determined.
Assumptions 1 The airflow within the hurricane is steady, incompressible,
and irrotational (so that the Bernoulli equation is applicable). (This is cer-
tainly a very questionable assumption for a highly turbulent flow, but it is jus-
tified in the solution.) 2 The effect of water drifted into the air is negligible.
Properties The densities of air at normal conditions, seawater, and mercury
are given to be 0.076 Ibm/ft, 64 Ibm/ft³, and 848 Ibm/ft?, respectively.
Analysis (a) Reduced atmospheric pressure over the water causes the water
to rise. Thus, decreased pressure at point 2 relative to point 1 causes the
ocean water to rise at point 2. The same is true at point 3, where the storm air
velocity is negligible. The pressure difference given in terms of the mercury
column height can be expressed in terms of the seawater column height by
AP = (pgh)Hg = (Pgh),w → hw
Psw
Transcribed Image Text:EXAMPLE 5–9 The Rise of the Ocean Due to a Hurricane A hurricane is a tropical storm formed over the ocean by low atmospheric pressures. As a hurricane approaches land, inordinate ocean swells (very high tides) accompany the hurricane. A Class-5 hurricane features winds in excess of 155 mph, although the wind velocity at the center "eye" is very ( Eye Hurricane low. Calm Figure 5-42 depicts a hurricane hovering over the ocean swell below. The atmospheric pressure 200 mi from the eye is 30.0 in Hg (at point 1, gener- ally normal for the ocean) and the winds are calm. The hurricane atmo- spheric pressure at the eye of the storm is 22.0 in Hg. Estimate the ocean оссan O level Оссan swell at (a) the eye of the hurricane at point 3 and (b) point 2, where the wind velocity is 155 mph. Take the density of seawater and mercury to be 64 Ibm/ft and 848 Ibm/ft?, respectively, and the density of air at normal sea-level temperature and pressure to be 0.076 Ibm/ft. FIGURE 5-42 Schematic for Example 5–9. The vertical scale is greatly exaggerated. SOLUTION A hurricane is moving over the ocean. The amount of ocean swell at the eye and at active regions of the hurricane are to be determined. Assumptions 1 The airflow within the hurricane is steady, incompressible, and irrotational (so that the Bernoulli equation is applicable). (This is cer- tainly a very questionable assumption for a highly turbulent flow, but it is jus- tified in the solution.) 2 The effect of water drifted into the air is negligible. Properties The densities of air at normal conditions, seawater, and mercury are given to be 0.076 Ibm/ft, 64 Ibm/ft³, and 848 Ibm/ft?, respectively. Analysis (a) Reduced atmospheric pressure over the water causes the water to rise. Thus, decreased pressure at point 2 relative to point 1 causes the ocean water to rise at point 2. The same is true at point 3, where the storm air velocity is negligible. The pressure difference given in terms of the mercury column height can be expressed in terms of the seawater column height by AP = (pgh)Hg = (Pgh),w → hw Psw
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