Lumped Parameter Description of Thermoviscous Acoustics in Tubes with Equilateral Triangular Cross-Sections

An accurate acoustic model of a tube in the millimeter or sub-millimeter size should include the losses that occur due to viscosity and thermal conduction, collectively termed thermoviscous losses. These losses are prominent in a boundary layer near the tube walls. Under the assumption that the boundary layer is thick compared to a characteristic geometry length, such as the radius for a circular cross-section, and fills out the entire cross-section, the tube can be described via a lumped parameter model. The lumped parameters have been known for several decades for a tube with circular cross-section, but the equilateral triangular tube has only been investigated in terms of transmission line parameters. The lumped parameters have here been established for the equilateral triangular tube as a truncated series solution of the transmission line parameters. One result observed is that the lumped parameter model for a triangular tube has 38% more viscous loss than a circular tube for a given area.