A streamline is a line the tangent to which at each point coincides with the direction in velocity of fluid particles at the point at a given moment of time. In a steady flow, the streamlines are the trajectories of particles. In a nonstationary flow, the streamlines vary with time and do not coincide with their trajectories. The differential equations in the Cartesian system have the form
If a certain flow has a stream function y, then the equation for a family of streamlines in this flow is = const. The set of streamlines allows us to present a vivid picture of the motion. In such illustrations, the streamlines are usually represented so that the fluid flow rate between the adjacent streamlines is the same for the whole figure. In this case, the density of streamlines is proportional to the flow velocity in the given section of the flow. Through a given point in space filled with liquid or gas, we can draw the streamlines at a given moment. The exceptions are provided by singular points at which the fluid velocity is zero or infinite.
In visualizing the streamlines experimentally, the flow of separate particles of liquid or gas is made visible by introducing fine light particles, jets of paint or smoke. When photographing such a flow with short exposure a picture called the aerodynamic flow spectrum is obtained.