A line with its tangent at any point in a fluid parallel to the instantaneous velocity of the fluid at that point. The differential equations of the streamline may be written dr × v = 0, where dr is an element of the streamline and v the velocity vector; or in Cartesian coordinates, dx/u = dy/v = dz/ w, where u, v, and w are the fluid velocities along the orthogonal x, y, and z axes, respectively. In steady-state flow the streamlines coincide with the trajectories of the fluid particles; otherwise, the streamline pattern changes with time. A two-dimensional wind-vector field may be completely specified by streamlines and isotachs. See free streamline; Compare trajectory.