Editing Navier–Stokes equations (section)

==Flow velocity==
The solution of the equations is a [[flow velocity]]. It is a [[vector field]]—to every point in a fluid, at any moment in a time interval, it gives a vector whose direction and magnitude are those of the velocity of the fluid at that point in space and at that moment in time. It is usually studied in three spatial dimensions and one time dimension, although two (spatial) dimensional and steady-state cases are often used as models, and higher-dimensional analogues are studied in both pure and applied mathematics. Once the velocity field is calculated, other quantities of interest such as [[pressure]] or [[temperature]] may be found using dynamical equations and relations. This is different from what one normally sees in [[classical mechanics]], where solutions are typically trajectories of position of a [[particle]] or deflection of a [[Continuum (theory)|continuum]]. Studying velocity instead of position makes more sense for a fluid, although for visualization purposes one can compute various [[Streamlines, streaklines, and pathlines|trajectories]]. In particular, the [[Streamlines, streaklines, and pathlines|streamlines]] of a vector field, interpreted as flow velocity, are the paths along which a massless fluid particle would travel. These paths are the [[integral curve]]s whose derivative at each point is equal to the vector field, and they can represent visually the behavior of the vector field at a point in time.