In this paper, analytical expressions correlating the volumetric flow rate to
the pressure drop are derived for the flow of Carreau and Cross fluids through
straight rigid circular uniform pipes and long thin slits. The derivation is
based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to
obtain flow solutions for generalized Newtonian fluids through pipes and our
adaptation of this method to the flow through slits. The derived expressions
are validated by comparing their solutions to the solutions obtained from
direct numerical integration. They are also validated by comparison to the
solutions obtained from the variational method which we proposed previously. In
all the investigated cases, the three methods agree very well. The agreement
with the variational method also lends more support to this method and to the
variational principle which the method is based upon.Comment: 27 pages, 6 figure