conservation of momentum: this is newton's second law and it states that force = rate of change of momentum. momentum is mass times velocity. the momentum equations are the equations that make it hard to solve problems in fluid dynamics. there are a number of different versions that include a number of different effects. the navier-stokes equations are momentum equations, and the euler equations are the navier-stokes equations but with viscosity not included. there is one momentum equation in a 1d problem and three, one in each space direction, in 3d.