Our study is motivated by the first experimental results on pion production and stopping obtained in pA collisions in E910 experiment at BNL. The effect of stopping is the deceleration of an incident high energy proton traversing the target nucleus. It appears due to the energy losses relevant to the production of secondary particles in the inelastic interactions with nucleons. A hydrodynamic effective model of stopping is proposed that is based on the consideration of the nuclear matter as a liquid and by the introduction of an effective stopping force acting on a fast-moving proton. With this force, we obtain a differential equation that describes the relativistic motion of a proton in a nucleus. Calculations in the framework of this analytical model are performed for the correlation between the mean multiplicity of charged pions and a number of binary collisions.