

Click here to Order your Radar Equipment Online HYDROSTATIC EQUATION The hydrostatic equation incorporates pressure, temperature, density, and altitude. These are the factors that meteorologists must also deal with in any practical application of gas laws. The hydrostatic equation, therefore, has many applications in dealing with atmospheric pressure and density in both the horizontal and vertical planes. The hydrostatic equation itself will be used in future units and lessons to explain pressure gradients and vertical structure of pressure centers. Since the equation deals with pressure, temperature, and density, it is briefly discussed here. The hypsometric formula is based on the hydrostatic equation and is used for either determining the thickness between two pressure levels or reducing the pressure observed at a given level to that at some other level. The hypsometric formula states that the difference in pressure between two points in the atmosphere, one above the other, is equal to the weight of the air column between the two points. There are two variables that must be considered when applying this formula to the atmosphere. They are temperature and density. From Charles’ law we learned that when the temperature increases, the volume increases and the density decreases. Therefore, the thickness of a layer of air is greater when the temperature increases. To find the height of a pressure surface in the atmosphere (such as in working up an adiabatic chart), these two variables (temperature and density) must be taken into consideration. By working upward through the atmosphere, the height of that pressure surface can be computed by adding thicknesses together. Such a set of data is available in the AG2 Vol. 2, Unit 3. Since there are occasions when tables and SkewTs are not available, a simplified version of the hypsometric formula is presented here. This formula for computing the thickness of a layer is accurate within 2 percent; therefore, it is suitable for all calculations that the Aerographer’s Mate would make on a daily basis. The thickness of a layer can be determined by the following formula:
107 = A constant (representing density and mean virtual temperature) t = mean temperature in degrees Fahrenheit Po = pressure at the bottom point of the layer P = pressure at the top point of the layer For example, let us assume that a layer of air between 800 and 700 millibars has a mean temperature of 30°F. Applying the formula, we have

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