A curve that is tangent to the velocity vector at each point in the flow field is called a streamline. The streamline is a curve composed of different fluid particles at the same time, which gives the velocity direction of different fluid particles at that moment.
A curve that is tangent to the velocity vector at each point in the flow field is called a streamline.
The streamline is a curve composed of different fluid particles at the same time, which gives the velocity direction of different fluid particles at that moment.
Determine the differential equation of the streamline as: dr × v (r, t) = 0
Where v(r,t) and dr are the velocity vector and the arc element vector, respectively, t is time, and is regarded as a constant when integrating. The expression of the above equation in the Cartesian coordinate system is:
If C is a closed curve that is not streamlined in the fluid and does not self-intersect, and at each point through C at each point as a streamline, the surface formed by these streamlines is called a flow tube.
A trace is a curve drawn by a fluid particle as it moves through space. It gives the direction of velocity of the same fluid particle at different times. If the fluid motion is given in the form of Euler variables: v = v(r, t), where v is the velocity vector; r is the radial diameter, and t is the time, then the following differential equations are integrated:
And after the integration, the t in the resulting expression is eliminated to obtain the trace equation (see "Trace" entry). In the above formulas, t is an independent variable; the rectangular coordinates x, y, and z are functions of t; u, v, and w are components of the velocity vector on the x, y, and z axes, respectively.
Streamline nature
1. In the entire space of the moving fluid, a series of streamlines can be drawn, called streamline clusters. The degree of density of the streamline cluster reflects the difference in velocity in the flow field at that moment.
2. When it is unsteady, the shape of the streamline changes with time: for a constant stream, the shape and position of the streamline do not change with time.
3. The flow lines and traces of the constant current coincide.
4. Under normal circumstances, the streamlines cannot intersect, and cannot be folded. It can only be a smooth curve.
