This paper presents a determination of the effective viscosity in the Brinkman equation by a numerical simulation of an imaginary physical experiment with a viscometer. The model of a porous medium and the applied method of solution are very simple. In the idealized problem, we consider axial flow through an infinite array of cylindrical rods. Assuming that the flow in such a porous medium is described by the Brinkman filtration equation, the effective viscosity can be calculated as a function of the porosity. In this paper, a relation between the volume fraction and the effective viscosity is given for triangular and square arrays of rods.