It is very important to study the steady and unsteady flow through porous media and fluid- particle interactions. In the present study, using the experimental data obtained from experiments performed in a steel cylinder on small, medium and large materials, using Particle Swarm Optimization (PSO) algorithm was first used to optimize the coefficients of binomial equations (a, b) and three parameter equations (a, b, c) to calculate changes of hydraulic gradient (i) versus flow velocity (V) in the steady and unsteady flow conditions, respectively. If, using experimental results of unsteady flow, three parameter equation is used to calculate the hydraulic gradient in the unsteady flow condition instead of the binomial equation (by assuming a negligible value for the third term), the mean relative error (MRE) of the above mentioned gradations is improved by 22, 38 and 19%, respectively. Since the Drag coefficient (C_d) and consequently the Drag force (F_d) is a function of the coefficient of friction (f), in the present study, using Darcy-Weisbach equations binomial and three parameter equations were presented for the steady and unsteady flow conditions, respectively. In addition, using the analytical equations proposed by Ahmed and Sunada for coefficients a and b, high accuracy equations were presented to calculate coefficient of friction (f) in terms of the Reynolds number (Re) in the steady and especially unsteady flow conditions in the porous media with all gradation types and Reynolds numbers. As a results, MRE between the calculated (using the proposed equations in the present study) and observed (using experimental data) coefficients of friction for the small, medium and large materials in the steady flow condition was calculated as 1.913, 3.614 and 3.322%, respectively. The corresponding values of 7.806, 14.106 and 10.506% were calculated in the unsteady flow condition, respectively.

研究通过多孔介质的稳态和非稳态流动和流体-颗粒相互作用是非常重要的。在本研究中，利用在钢筒中对小、中、大材料进行的实验获得的实验数据，首先使用粒子群优化 (PSO) 算法优化二项式方程 ( a , b ) 和三个方程的系数。参数方程 ( a , b , c ) 计算水力梯度 ( i ) 与流速 ( V ) 的变化) 分别在稳态和非稳态流动条件下。如果使用非定常流动的实验结果，而不是使用二项式方程（假设第三项的值可以忽略），使用三参数方程计算非定常流动条件下的水力梯度，则平均相对误差（MRE）上述灰度分别提高了 22%、38% 和 19%。由于阻力系数 ( C _d ) 和因此阻力 ( F _d ) 是摩擦系数 ( f)，在本研究中，使用 Darcy-Weisbach 方程二项式和三个参数方程分别提出了稳态和非稳态流动条件。此外，使用 Ahmed 和 Sunada 为系数 a 和 b 提出的解析方程，提出了高精度方程来计算摩擦系数 ( f) 表示在具有所有级配类型和雷诺数的多孔介质中稳态和特别是非稳态流动条件下的雷诺数 (Re)。结果，计算的（使用本研究中提出的方程）和观察到的（使用实验数据）摩擦系数在稳定流动条件下的小、中和大材料之间的 MRE 计算为 1.913、3.614 和 3.322% ， 分别。7.806、14.106 和 10.506% 的相应值分别在非定常流动条件下计算。