  We derive analytical expressions for the flow of Newtonian and power law
fluids in elastic circularly-symmetric tubes based on a lubrication
approximation where the flow velocity profile at each cross section is assumed
to have its axially-dependent characteristic shape for the given rheology and
cross sectional size. Two pressure-area constitutive elastic relations for the
tube elastic response are used in these derivations. We demonstrate the
validity of the derived equations by observing qualitatively correct trends in
general and quantitatively valid asymptotic convergence to limiting cases. The
Newtonian formulae are compared to similar formulae derived previously from a
one-dimensional version of the Navier-Stokes equations.
