The loop extrusion theory assumes that protein factors, such as cohesin rings, act as molecular motors that extrude chromatin loops. However, recent single molecule experiments have shown that cohesin does not show motor activity. To predict the physical mechanism involved in loop extrusion, we here theoretically analyze the dynamics of cohesin rings on a loop, where a cohesin loader is in the middle and unloaders at the ends. Cohesin monomers bind to the loader rather frequently and cohesin dimers bind to this site only occasionally. Our theory predicts that a cohesin dimer extrudes loops by the osmotic pressure of cohesin monomers on the chromatin fiber between the two connected rings. With this mechanism, the frequency of the interactions between chromatin segments depends on the loading and unloading rates of dimers at the corresponding sites.