The study of the steady and unsteady flow through porous media and the interactions between fluids and particles is of utmost importance. In the present study, binomial and trinomial equations to calculate the changes in hydraulic gradient (i) in terms of flow velocity (V) were studied in the steady and unsteady flow conditions, respectively. According to previous studies, the calculation of drag coefficient (Cd) and consequently, drag force (Fd) is a function of coefficient of friction (f). Using Darcy-Weisbach equations in pipes, the hydraulic gradient equations in terms of flow velocity in the steady and unsteady flow conditions, and the analytical equations proposed by Ahmed and Sunada in calculation of the coefficients a and b of the binomial equation and the friction coefficient (f) equation in terms of the Reynolds number (Re) in the porous media, equations were presented for calculation of the friction coefficient in terms of the Reynolds number in the steady and unsteady flow conditions in 1D (one-dimensional) confined porous media. Comparison of experimental results with the results of the proposed equation in estimation of the drag coefficient in the present study confirmed the high accuracy and efficiency of the equations. The mean relative error (MRE) between the computational (using the proposed equations in the present study) and observational (direct use of experimental data) friction coefficient for small, medium and large grading in the steady flow conditions was equal to 1.913, 3.614 and 3.322%, respectively. In the unsteady flow condition, the corresponding values of 7.806, 14.106 and 10.506 % were obtained, respectively.

The study of the steady and unsteady flow through porous media and the interactions between fluids and particles is of utmost importance. In the present study, binomial and trinomial equations to calculate the changes in hydraulic gradient (i) in terms of flow velocity (V) were studied in the steady and unsteady flow conditions, respectively. According to previous studies, the calculation of drag coefficient (Cd) and consequently, drag force (Fd) is a function of coefficient of friction (f). Using Darcy-Weisbach equations in pipes, the hydraulic gradient equations in terms of flow velocity in the steady and unsteady flow conditions, and the analytical equations proposed by Ahmed and Sunada in calculation of the coefficients a and b of the binomial equation and the friction coefficient (f) equation in terms of the Reynolds number (Re) in the porous media, equations were presented for calculation of the friction coefficient in terms of the Reynolds number in the steady and unsteady flow conditions in 1D (one-dimensional) confined porous media. Comparison of experimental results with the results of the proposed equation in estimation of the drag coefficient in the present study confirmed the high accuracy and efficiency of the equations. The mean relative error (MRE) between the computational (using the proposed equations in the present study) and observational (direct use of experimental data) friction coefficient for small, medium and large grading in the steady flow conditions was equal to 1.913, 3.614 and 3.322%, respectively. In the unsteady flow condition, the corresponding values of 7.806, 14.106 and 10.506 % were obtained, respectively.