For compressible flow with friction in a cylindrical pipe the momentum, continuity, and heat-transfer equations are examined to determine whether an increase in Mach number ("thermal" Laval nozzle) is obtainable through heat conduction from the gas through the pipe walls. The analysis is based on the assumption that the wall temperature is negligibly small in comparison with the stagnation temperature of the gas. The analysis leads to a negative result. When the gas cooling is increased by also considering radiation to the wall, a limited region at high temperatures is obtained where Mach number increases were theoretically possible. Obtaining this condition practically is considered impossible.

It is shown that the ordinary Joukowski formula for lift force of cascade blades in incompressible flow can be applied to the case of subsonic compressible flow with sufficient accuracy, provided that the density in the formula is taken as the arithmetic mean of the densities far ahead of and behind the cascade.

A method of computing the resistance of a cascade of airfoils in a viscous compressible gas flow is described. The investigation occurred in subsonic velocities only because of the required assumption of isentropic flow.