Acoustic power balance in lined ducts

It is shown that the two common definitions of acoustic energy density and intensity in uniform unlined ducts carrying uniform flow are compatible to the extent that both energy densities can be used in an appropriate variational principle to derive the convected wave equation. When the duct walls are lined both energy densities must be modified to account for the wall energy density. This results in a new energy conservation equation which utilizes a modified definition of axial power and accounts for wall dissipation. Computations in specific cases demonstrate the validity of the modified acoustic energy relation.