Transient flow of a viscous compressible fluid in a circular tube after a sudden point impulse

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis IS Studied on the basis of the linearized Navier-Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. Owing to the finite velocity of sound the flow behaviour differs qualitatively from that of an incompressible fluid. The flow velocity and the pressure disturbance at any fixed point different from the source point vanish at short time and decay at long times with a t(-3/2) power law.