Download Pressure and mass conservation

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Newton's laws of motion wikipedia, lookup

Atomic theory wikipedia, lookup

Fluid dynamics wikipedia, lookup

Modified Newtonian dynamics wikipedia, lookup

Inertia wikipedia, lookup

Pressure wikipedia, lookup

Relativistic mechanics wikipedia, lookup

Seismometer wikipedia, lookup

Gravity wikipedia, lookup

Center of mass wikipedia, lookup

Transcript
Pressure and mass conservation
1
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:
“momentum concerned”
• Ideal gas law:
expression of mass for air
• First law of thermodynamics
“energy conserved”
F = ma
Gravity exists
Earth is round
There are days and nights
(Earth is rotating about once per day)
g
a
Alphabet soup is better in Greek
p = rRT

Forces?
• Fg, Gravity
• Fv, Viscosity
• Fp, Pressure gradient
F=ma
All have the same units, N
4
Gravity
• Newton’s law of gravity
Me
m
r
GM e m
F 
r2
mass of the Earth
mass of the parcel
Distance between center of the Earth and air parcel
So acceleration,
Directed exactly toward the
Earth’s center of gravity
GM e
F
g0 *    2
m
r
5
r
m
dme
Me
center of
mass
Integrating all mass
elements of, it can be
shown that the direction
vector r points to the
center of mass
6
Earth is big, atmosphere is small
Radius of earth, a = 6371km
Depth of atmosphere ~30km
So we can use an approximation: r~
a
Thus,
7
Exosphere
Ionosphere
Thermosphere
Mesosphere
Stratosphere
Troposphere
Salby, Fundamentals of Atmospheric Physics, page 11.
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
Definition:
Lapse rate
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
• Position x,y,x
But there are others!
Horizontal: Longitude, latitude
Vertical: Pressure, potential temperature,….
Velocity: u, v, w
(Change in position with time)
13
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
Volume dV = dx dy dz
T, V, r,
p, q
x
z
Mass dm = r dV
y
•Total mass of the atmosphere M = ∫globe dm
14
Special look at mass….err pressure
• What is pressure?
NCEP Reanalysis: http://www.cdc.noaa.gov/
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:
p
z
p( z )   dp   g  rdz

0
• Compute sea level pressure:
0
ps   g  rdz

If the surface pressure is 1000hPa, what is the pressure with
half the atmospheric mass above?
Half! (500hPa)
Relationship
between
temperature,
pressure and
density
The
hydrostatic
equation
Exercises
Practice question:
• Holton 1.13, 1.16, 1.17, 1.18
Reading to next week
• Holton2.6
• Holton 2.7
• Start on RY CH1