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1976 US Standard Atmosphere U.S. Standard Atmosphere One of several models of the atmosphere. Provides dependence of temperature, pressure and density on altitude. Temperature is tabulated at 8 specific altitudes and temperatures at other altitudes, pressure and density computed from those data.

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1976 US Standard Atmosphere2 For Incompressible Fluid (like Water) P1P1 P [Pascal = N/m 2 ] z Known as “hydrostatic equation” The difference in pressure at the two depth is due to the weight of the column of water between them.

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1976 US Standard Atmosphere3 Atmosphere – Compressible Fluid First consider an isothermal (constant temperature) atmosphere and assume a perfect gas: Rearrange: (Perfect gas) Apply limits:

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4 Atmosphere – Compressible Fluid So for isothermal (constant temperature) atmosphere: i.e., express pressure at one point in terms of that at a different altitude You can also handle (integrate) the case where the temperature is a linear function of altitude (constant “lapse rate”).* These are the two options in the VBA coding that goes with the USStandAtmos.xls spreadsheet on webpage (www.people.virginia.edu/~rjr/modules/xls) Note exponential drop of pressure with altitude, vs. linear with depth in an incompressible fluid like water. *See, e.g., D.G. Shepherd, Elements of Fluid Mechanics, Harcourt, Brace and World, 1965.

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1976 US Standard Atmosphere5 Red circles indicate the limits of the 7 layers. Intermediate values are computed from them.

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1976 US Standard Atmosphere6 U.S. Standard Atmosphere 1976 Seven layers between sea level and ~85 km Decrease of “g” with altitude is included in the calculation by use of “geopotential” altitude. –h = Altitude * R earth / (Altitude + R earth ) Two layers are isothermal Five layers have constant “lapse rate” (dT/dz) Pressure tabulated at base of each layer and change computed between there and the point of interest. –Use equation we just derived for isothermal layer, similar equation for constant lapse rate layers. Density found from P and T and perfect gas law.

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1976 US Standard Atmosphere7 Dependence of Density and Pressure On Altitude. Handy numbers to remember: 1.Density of air at sea level [kg/m3], 2.Pressure at sea level [kPa], 3.Depth of troposphere [km]. Handy numbers to remember: 1.Density of air at sea level [kg/m3], 2.Pressure at sea level [kPa], 3.Depth of troposphere [km].

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1976 US Standard Atmosphere8 Other notes: Most sunlight comes through atmosphere (it’s largely transparent), hits surface of earth and the air in contact is heated up. That’s why the peak air temperature is at surface. The other temperature peak at ~50 km is due to absorption of UV rays by ozone (and there isn’t much atmosphere there to heat up).

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