pressure and mass conservation -...
TRANSCRIPT
Today’s goals • Some definitions:
• Gravity. What is a shallow atomsphere
• Coordinates.
• The concept of a “parcel”
(or finite element in the fluid)
• Vertical variations in pressure
• Vertical variation in temperature (Seemingly obvious, but fascinating research topic)
Some initial things to remember • Newton’s second law: F = ma
“momentum concerned”
• Ideal gas law: p = rRT
expression of mass for air
• First law of thermodynamics
“energy conserved”
Gravity exists g
Earth is round a
There are days and nights
(Earth is rotating about once per day)
Alphabet soup is better in Greek
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Gravity
• Newton’s law of gravity 2r
mGMF e
Me mass of the Earth
m mass of the parcel
r Distance between center of the Earth and air parcel
So acceleration,
Directed exactly toward the
Earth’s center of gravity
20*r
GM
m
Fg e
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Me
m
dme
r
center of
mass
Integrating all mass
elements of, it can be
shown that the direction
vector r points to the
center of mass
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Earth is big, atmosphere is small
Radius of earth, a = 6371km
Depth of atmosphere ~30km
So we can use an approximation: r~ a
Thus,
Salby, Fundamentals of Atmospheric Physics, page 11.
Troposphere
Stratosphere
Mesosphere
Ionosphere
Thermosphere
Exosphere
Composition of the atmosphere
• Air is a mixture of various gases
• Particularly, nitrogen, oxygen, water vapor,
carbon dioxide
• We can assume air behaves like an ideal gas
Pressure is mass
• Pressure defined as force (imparted on
parcel walls by molecules) per units area
p=F/A
• For horizontal surface the force is weight
F = mg
• So, mass:
m = F/g = pA/g
Define some coordinates
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• Position x,y,x
But there are others!
Horizontal: Longitude, latitude
Vertical: Pressure, potential temperature,….
Velocity: u, v, w
(Change in position with time)
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The atmosphere is a fluid continuum
• Can be described atmosphere by a set field variables
that are continuous functions (in space and time)
e.g. temperature, pressure, wind, mass, water content
• It is convenient to consider these properties applying
to a “small” parcel of air
•Total mass of the atmosphere M = ∫globe dm
T, V, r,
p, q
x
y
z
Volume dV = dx dy dz
Mass dm = r dV
Pressure is mass
• Pressure defined as force (imparted on
parcel walls by molecules) per units area
p=F/A
• For horizontal surface the force is weight
F = mg
• So, mass:
m = F/g = pA/g
• What about change in forces on a parcel?
Pressure and mass
• Compute pressure at some height by integrating:
zp
zgpzp dd)(0
r
• Compute sea level pressure:
0
dzgps r
If the surface pressure is 1000hPa, what is the pressure with
half the atmospheric mass above? Half! (500hPa)