Abstract
This study investigates the Hagen–Poiseuille pipe flow of viscoplastic fluids, focusing on analytical predictions of concrete pumping using the shear-stress-dependent parabolic model. Research highlights encompass solving the steady laminar pipe flow for viscoplastic fluids described by the parabolic model, extending analytical studies to a nonlinear rheological model with easily accessible experimental parameters, presenting detailed results for the two-fluid parabolic model, and introducing computational apps implementing theoretical findings. The parabolic model outperforms linear models, such as the Bingham model, in accuracy by accounting for the nonlinearity in the shear stress and shear rate relations. The influence of rheological parameters on these relations is analyzed, and their versatility is demonstrated by a Wolfram Mathematica-based application program. This approach is adaptable for other models with shear stress as the independent variable, offering valuable insights into viscoplastic fluid flows.