Shapiro1.00_Solution - MIT Department of Mechanical...

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Unformatted text preview: MIT Department of Mechanical Engineering 2.25 Advanced Fluid Mechanics Problem 1.00 This problem is from “2.25 Advanced Fluid Mechanics” by Ain Sonin Rate of change of properties measured by a probe moving through the earth’s atmosphere — plus some things about the earth and its atmosphere. The pressure distribution in a static, constant-temperature planetary atmosphere modeled as an ideal gas is given by p = p e- z/H (1.00a) where z is the altitude above a reference altitude z = 0, p is the absolute pressure at z = 0, and H = RT Mg (1.00b) is a length scale that characterizes the atmosphere. Its value is determined by the strength of the gravitational acceleration and the parameters that appear in the ideal-gas equation of state, p = ρ RT M ; (1.00c) R = 8 . 32 JK- 1 mol- 1 is the universal gas constant, T is the absolute temperature (taken as constant in this model of the atmosphere), M is the molar mass of the gas (0.029 kg/mol if the gas is air), and g is the acceleration of gravity at or near the surface of the planet. For the “Standard” isothermal model of the earth’s atmosphere, T = 288 K, p = 1 . 02 × 10 5 N/m 2 if z = 0 at sea level, and consequently H = 8 . 43 km....
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Shapiro1.00_Solution - MIT Department of Mechanical...

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