Nature of fluid flow :
When a fluid flows through a tunnel or tube, the nature of motion of the fluid may be classified with respect to the nature of the flow.
If the flow velocity at a particular point remains constant with time then the flow of fluid is said to be steady and if it changes with time at that particular point then the flow is said to be unsteady.
Streamline Motion :
Consider an incompressible, non-viscous fluid which is flowing through a tube.
Let us take a line A-B-C-D-E through which the fluid particles are successively following each preceding particle to move from A to E.
The velocity of the fluid particles at A, B, C, D and E are, respectively, vA→, vB→, vC→, vD→ and vE→
The flow is considered to be steady if these velocities at A , B , C , D and E are constant with time. When a fluid particle is coming towards A , just reaches A and then it acquires the velocity vA→ . The same fluid particle, attains the velocity vB→ at the point B though it had velocity vA→ at A.
In this way the fluid particle successively reaches C, D & E and acquires the respective velocities at those positions. This reveals two things – line of motion of a stream of fluid particles is fixed and the velocities at different points are fixed with respect to time.
This path of motion of the fluid particles is called a streamline and the motion is called streamline flow. The velocity of a particle in streamline flow is a function of position only.