Energy dissipation in circular tube

Energy dissipation distribution along the circular tube radius is important in solving such problems as calculation of heat transfer by the air flow through building envelope; calculation of pressure loss in spiral flows; calculation of cyclones with axial and tangential supply of dust-containing gas. Two types of one-dimensional radially axisymmetric flows in circular tube were considered: axial flow and rotation about the axis (Rankine vortex). Relying on two- and four-layer description of axial turbulent flow energy dissipation was calculated in each layer. Similar calculation for Rankine vortex with viscous sublayer at the tube surface was provided. By employing the dissipation minimum principle the boundary radius between rigid rotation and free vortex is calculated. Approximation of the velocity distribution in Rankine vortex is proposed.