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Values of ρ b of b = 1 through b = 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when h = h b+1. [ 2 ] In these equations, g 0 , M and R * are each single-valued constants, while ρ , L , T and h are multi-valued constants in accordance with the table below.
A trivial example. In mathematics, the mountain climbing problem is a mathematical problem that considers a two-dimensional mountain range (represented as a continuous function), and asks whether it is possible for two mountain climbers starting at sea level on the left and right sides of the mountain to meet at the summit, while maintaining equal altitudes at all times.
at each geopotential altitude, where g is the standard acceleration of gravity, and R specific is the specific gas constant for dry air (287.0528J⋅kg −1 ⋅K −1). The solution is given by the barometric formula. Air density must be calculated in order to solve for the pressure, and is used in calculating dynamic pressure for moving vehicles.
From 11 km up to 20 km (65,620 ft or 12.4 mi), the constant temperature is −56.5 °C (−69.7 °F), which is the lowest assumed temperature in the ISA. The standard atmosphere contains no moisture. Unlike the idealized ISA, the temperature of the actual atmosphere does not always fall at a uniform rate with height.
For an airliner cruising at 755 feet per second (828 km/h) at an altitude of 33,000 feet (10 km) (where the air density is about 0.0258 pounds per cubic foot (0.413 kg/m 3)), the dynamic pressure on the front of the plane is 1.586 pounds per square inch (109.4 hPa), about 41% of the static pressure (3.84 pounds per square inch (265 hPa)).
These figures should be compared with the temperature and density of Earth's atmosphere plotted at NRLMSISE-00, which shows the air density dropping from 1200 g/m 3 at sea level to 0.125 g/m 3 at 70 km, a factor of 9600, indicating an average scale height of 70 / ln(9600) = 7.64 km, consistent with the indicated average air temperature over ...
The increase in altitude necessary for P or ρ to drop to 1/e of its initial value is called the scale height: H = R T M g 0 {\displaystyle H={\frac {RT}{Mg_{0}}}} where R is the ideal gas constant, T is temperature, M is average molecular weight, and g 0 is the gravitational acceleration at the planet's surface.
The gravity g′ at depth d is given by g′ = g(1 − d/R) where g is acceleration due to gravity on the surface of the Earth, d is depth and R is the radius of the Earth. If the density decreased linearly with increasing radius from a density ρ 0 at the center to ρ 1 at the surface, then ρ(r) = ρ 0 − (ρ 0 − ρ 1) r / R, and the ...