  Slender tubes constituted of hyperelastic materials undergoing large
deformations and conveying inertialess flow of Newtonian fluids at steady state
are a model representations of complex systems in both biomechanics and
bio-inspired technology. In this paper, we undertake a systematic study of this
system. The tube's hyperelastic behavior is modeled by five (5) different
constitutive laws: neo Hookean, Mooney Rivlin, Fung, Gent and Ogden. Invoking
the principles of finite elasticity, we delineate the local pressure -
deformation relationship for the tube for each of the hyperelastic models. The
structural mechanical field of the tube is then coupled with fluid flow field,
which is simplified using the tenets of lubrication approximation. The
resultant fluid-structure interaction problem then throws up a cohort of
interesting results including the deformation and pressure profile across the
tube, and tube laws for five ($5$) hyperelastic models. Analysing these
results, we posit that the behavior of neo Hookean and Mooney Rivlin tubes us
converse of Fung's and Gent's tubes; the latter show a strain hardening
behavior whilst the former exhibit a strain softening one. A sensitivity
analysis which underscores the relative importance of geometrical nonlinearity
in the problem then follows.
