Momentum motion. The first use of "momentum" in its proper mathematical sense is not clear but by the time of Jenning's "Miscellanea" in 1721, five years before the final edition of Newton's "Principia Mathematica", momentum or "quantity of motion" was being defined for students as "a rectangle", the product of and , where is "quantity of material" and is "velocity", . Momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If is
Derivation of the Navier–Stokes equations where it's assumed that all body forces are describable as gradients (for example it is true for gravity), and density has been divided so that viscosity becomes kinematic viscosity. The second vector calculus identity above states that the divergence of the curl of a vector field is zero. Since the (incompressible) mass continuity equation specifies the divergence of flow velocity being zero, we can replace the flow velocity with the curl of some vector formula_84 so that mass continuity is always satisfied: So, as long as flow velocity is represented through formula_86, mass continuity is unconditionally satisfied. With this new