Table of Contents
Velocity components converted to meteorological direction
Equation 1.2a gives the following for determining wind direction from wind components:
To convert to Meteorological direction when U and V are positive
However, will this work when U is negative?
The term is included simply to convert the term from one set of units to another.
To convert from direction in degrees to U, V components
Static Pressure
Pressure is a Force/Area. Force = mass x acceleration
To convert from one set of units to another, use average sea level pressure in both units. See pg. 436.
Atmospheric pressure decreases nearly exponentially with height. (1.6a)
Temperature
Note: Stullís equation is: where, mw is molecular weight in grams/mole and
To use the Boltzman equation in its original form and the molecular weights given in Table 1-3, do the following:
Equation of State
Virtual Temperature
density dry air would have if it alone occupied volume, Vol.
Then the total pressure is:
PPT Slide
If we define
If we wish to define Tv in terms of mixing ratio, r, instead of vapor pressure, e, then since vapor pressure can be written:
If we multiply the numerator and denominator by Mw and divide both by md, and define r as:
Substituting in to the equation for Tv gives:
Multiplying the numerator and denominator by (1-r) gives:
This can be written as:
Note: the units of mixing ratio are normally given as grams of water/kilogram of dry air, or g/kg. For equation 1.13 be certain to convert to gram/gram.
Consider a situation where there is water vapor, liquid water droplets and ice crystals in a volume of air. The total water mixing ratio is given by: where, r = mixing ratio of vapor, rL = mixing ratio of liquid water, ri = mixing ratio of ice.
If there is no ice in the volume, but there is liquid water droplets, we assume the volume is holding all the water it can as vapor, so r = rs, saturation mixing ratio. But, when vapor condenses to form liquid water droplets, there is a decrease in the density of the air. The mass of vapor has decreased by the amount of water which was converted to liquid water. So, the density of the air changes.
Average density of air (which includes water vapor) is 1.225 kg/m3. Density of water = 1025 kg/m3. The ratio is roughly 1/1000. Then, for a volume of air containing liquid water droplets (which have converted from vapor to liquid): where, rs = saturation mixing ratio and rL is the liquid-water mixing ratio, (gliquid/gdry air)
Then, the General Gas Law should be written:
Gas Constants
For any particular gas, we can define a gas constant as:
For dry air containing 78% N2 and 21% O2, the gas constant becomes: For water vapor, the gas constant becomes:
If we take the ratio of the gas constant for dry air and water vapor we get:
Hydrostatic Equation
Consider the net vertical force upward due to pressure.
Force acting upward is:
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Author: Alcorn
Email: alcorn@ariel.met.tamu.edu
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