Analytical solutions for Bingham plastic fluids in laminar regime
An analytical approach is used to develop true solutions for calculating the friction factor, and pipe diameter under laminar ﬂow conditions of Bingham plastic ﬂuids in pipe networks. For this, governing equations have been converted to suitable quartic equations. In the next step, each of the quartic equations has been converted to a resolvent cubic equation and two quadratic equations. This research shows these steps clearly to reach acceptable physical analytic solutions for calculating the friction factor and pipe diameter. Proposed true analytical solutions aim at reducing the computational time and effort and eliminate the need for iterative solutions. The propagation of errors for nonlinear systems should be accounted for when the intensive computation of the friction factor (e.g. in optimization problems) is required. Proposed solution of the friction factor will be a suitable computational tool for implementing these nonlinear models.