Aerodynamics. — On the influence of gravity upon the expansion of a gas

Abstract

We consider a vertical column of gas, which before the instant t = 0 is limited by a horizontal plane wall at its upper end, whereas downwards the column extends indefinitely. Lateral motion of the gas is prevented (it may be assumed that the gas is enclosed in an infinite vertical cylinder with perfectly smooth walls, or that the lateral dimensions of the column are infinite). The gas originally is everywhere at rest. The pressure of the gas has a certain finite value p ₀ at the level where it is in contact with the boundary plane; downward the pressure rises in consequence of the weight of the gas, according to the law valid for an atmosphere in adiabatic (isentropic) equilibrium. Above the boundary plane is vacuum extending towards infinity.