PFC / JA - 95 - 5 Theory of Low Mach Number Compressible Flow

The properties of a relatively uncommon regime of fluid dynamics, low Mach number compressible flow are investigated. This regime, which is characterized by an exceptionally large tube aspect ratio L/d ~ 106 leads to highly subsonic flows in which friction dominates inertia. Even so, because of the large aspect ratio, finite pressure, temperature, and density gradients are required, implying that compressibility effects are also important. Analytic results are presented for both the laminar and turbulent regimes. Perhaps the most interesting result is that in forced flow situations steady state solutions exist only below a critical value of heat input. Above this value the flow reverses against the direction of the applied pressure gradient causing fluid to leave both the inlet and outlet implying that the related concepts of a steady state friction factor and heat transfer coefficient have no validity.