Flow and Stream Lines

(1) The flow lines of a vector field p are lines at each point of which the tangent has the direction of the field vector at this point. The differential equations of flow lines have the form

dx/p₁ = dy/p₂ = dz/p₃

where x, y, and z are the coordinates of a point and P₁,P₂, and P₃ are the components of the field vector at the point.

(2) In hydrodynamics and aerodynamics, a stream line is a line at each point of which the tangent coincides in direction with the velocity of the flow particle at that point at a given moment. A set of stream lines make it possible to visualize the streaming of the fluid at any given moment, providing as it were a snapshot of the flow. Stream lines can be made visible with the help of suspended particles introduced into the stream (for example, aluminum powder in water, smoke in air). A short-exposure photographic picture of such a flow yields a visual picture of the stream lines.