Abstract: This paper presents the law of maximum rate of energy dissipation in hydrodynamics and also in general continuum dynamics as an addition to the classical conservation laws expressed in the equation of continuity and the equations of motion. The corollary of the law is Belanger-Boss theorem of minimum reserved specific energy in applied hydraulics.The mechanical energy dissipated is transformed into heat reserved in the substance. The rate of energy dissipation at a time at a given temperature gives rise to the increase in entropy production. Hence the maximum rate of energy dissipation suggests itself the idea of reformulation of the second law of thermodynamics that the rate of entropy production in mechanical motion is always the maximum possible.The proposed extremity law in continuum dynamics has been derived from the variational principle and the reformulated second law of thermodynamics analyzed microscopically in the paper. The two laws together form the extremity laws of hydro-thermodynamics.