Title: Unsteady Flow in a Porous, Elastic, Circular Tube : Part 2. The Tube Contracting or Expanding in Radial Directions
Abstract: A linear theory for unsteady flow of a viscous, incompressible fluid in a semi-infinite circular tube with a porous, elastic wall is developed. The tube radially contracts or expands keeping its axial length constant. The fluid is assumed to pass through the porous wall under a certain defined condition of injection. Laminar similar solutions with respect to space and time are obtained. Velocities, pressures, frictional drags, powers and works of fluid are analyzed. A rapid contracting motion of a tube results in separating the flow into a core region and the boundary layer, while a rapid expanding motion brings about a remarkable compensating flow in the center of the tube. The conditions of elastic motions together with the conditions of injection give a classification of pumping action of a porous, elastic tube.