Wave Propagation in Viscous Fluid Lines Including Higher Mode Effects

An analytical investigation of the symmetric modes of propagation for a viscous, compressible liquid in a cylindrical conduit is given in the form of an exact solution of the first-order Navier-Stokes equations. Boundary conditions for both rigid and elastic walls are imposed and the resulting characteristic equation is solved for the spatial attenuation-factor and phase velocity for several modes. The near-piston axial velocity profiles are found analytically for the case of a piston oscillating in a semi-infinite pipe and used to obtain the approximate state of shear stress near the piston. Experimental verification of this state of shear stress is made by viewing the action of a birefringent liquid in the neighborhood of an oscillating piston in a plexiglass tube. It is concluded that, in general, disturbances in a viscous fluid line consist of an infinite number of modes of propagation, the excitation of which depends upon the conduit end conditions, with the extent of spatial propagation being highly dependent upon the frequency and upon the type of conduit walls.