The motion of fluids and gases, studied macroscopically as continuous material is the heart of fluid dynamics. Properties such as density, pressure, temperature, and velocity are taken to be well-defined at infinitely small points, and are assumed to vary continuously from one point to another. The discrete, molecular nature of a fluid is ignored. each of the variables such as velocity, pressure, and density are continuous functions of space and time. This continuum hypothesis permits us to mathematically model fluid flow using calculus. Navier-Stokes equations dictate not position but rather velocity. A solution of the Navier-Stokes equations is called a velocity field or flow field, which is a description of the velocity of the fluid at any given point in space and time.
Brandon, K. R. (2011). The Navier-Stokes Equations (Undergraduate honors thesis, University of Redlands). Retrieved from http://inspire.redlands.edu/cas_honors/16