math in the news: 8/1/11
DESCRIPTION
In this issue of Math in the News we look at the science and math of heat waves.TRANSCRIPT
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8/1/11
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Heat Waves
A Bermuda High is a
high-pressure air system
that starts, and stays,
along the East Coast.
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Heat Waves
Think of the draft of air
created by a helicopter’s
propellers.
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Heat Waves
A similar phenomenon
happens with the
swirling air of the high
pressure front.
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Heat Waves
The downward force
comes, in part, from the
torque created by the
force of the wind (F) and
the radius (r) of the high-
pressure system.
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Heat Waves
The direction of torque
is always
perpendicular to the
plane formed by the
radius and the force.
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Heat Waves
You can think of the
high-pressure system
as a rotating cylinder
of humid air.
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Heat Waves
Torque is a force and
this force is applied
over the column of air.
Since pressure is force
divided by area, then
the overall effect is to
increase the air
pressure.
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Heat Waves
The downward pressure
pushes out cooler air,
and this persists during
the high-pressure
system. This causes a
temperature increase.
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Heat Waves
The downward pressure
also keeps cooler air
fronts from breaking
through the high-
pressure system. This
keeps temperatures
warm.
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Heat Waves
A continual flow of
warm, moist air from
the Caribbean keeps
the high-pressure
system intact. This
prolongs the heat.
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Heat Waves
The warm, moist air
from Caribbean is
heavier than cool, dry
air. This causes an
increase in pressure
and temperature.
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Heat Waves
But how much pressure
does the high-pressure
system add to the
regions affected by this
system?
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Heat Waves
Pressure is the ratio of
the downward force
and the area of the
high-pressure system.
For a cylinder the
pressure formula
changes to this.
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Heat Waves
As we saw earlier, the
downward force from
the pressure system is
the torque. Express
torque in force units.
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Heat Waves
Torque is the product
of angular momentum
(I) and angular
acceleration (α). For a
rotating disk, the
torque formula is as
shown here.
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Heat Waves
Use this formula for
torque in the pressure
equation.
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Heat Waves
We cannot directly
measure the mass but
we can estimate mass
using the density of air
and volume of the
cylinder.
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Heat Waves
Inputting the mass
equation into the
pressure equation and
simplifying yields a
fairly simple equation.
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Heat Waves
This graph shows the
pressure as a function
of radius, with
parameters for h, α,
and ρ. The horizontal
graph shows standard
pressure.
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Heat Waves
As the radius
increases, so does the
air pressure, and as a
result, so does the
temperature.