  We make a consistent derivation, from the governing equations, of the
pressure transfer function in the small-amplitude Stokes wave regime and the
hydrostatic approximation in the small-amplitude solitary water wave regime, in
the presence of a background shear flow. The results agree with the well-known
formulae in the zero vorticity case,but they incorporate the effects of
vorticity through solutions to the Rayleigh equation. We extend the results to
permit continuous density stratification and to internal waves between two
constant-density fluids. Several examples are discussed.
