عنوان مقاله [English]
Darcy's law is valid for laminar flow and its application is not recommended for turbulent flow. The turbulent flow equations are derived based on hydrodynamics principals with introducing turbulence effects. The purpose of this research is to derive the relationship between discharge and hydraulic potential in radial flow in unconfined aquifers under steady state. The basis of the relationship is fractional derivative approach of the velocity flow related to the hydraulic gradient. The previous study data was used for the verification of the derived equation. The profile of the water level was computed and plotted for different porous media with non-Darcy flow in unconfined aquifer for different discharges based on the extracted equation and compared with the results of the Darcy's law. The results showed with increasing the discharge values the highest and lowest increament of water level were 10 and 1.48% related to Darcy flow respectively. These values for increasing of hydraulic conductivity were 19 and 9.8% respectively. Overall, the difference between the Darcy and non Darcy flow in water level estimation increased with increasing discharge and hydraulic conductivity as well as the increase of both parameters, which water level was higher in Darcy flow than non Darcy flow in all water profile profiles.