Water flow through porous media is involved with physical factors such as size and configuration of pores, contact angle of grain surface, and connectivity of pores. To deal with these factors, pore-scale modeling is essential. Pore aggregate referred to as pore-network is extracted from randomly packed spherical grains with the modified Delaunay tessellation method. Water flow in a pore-network is formulated in terms of a network flow problem in hydraulics, in which friction and local losses such as contraction and enlargement of pipes are explicitly treated, while those are implicitly included in the hydraulic conductance of capillary tubes in existing works. Through the numerical experiments, it was confirmed that the effect of the local loss on the hydraulic conductivity could be negligible. Furthermore, the relative permeabilities of porous media with mixed wettabilities along the primary drainage and imbibition processes were estimated.