Question

Streamline motion is that motion in which there is
(A) Only longitudinal velocity gradient
(B) Only radial velocity gradient
(C) Longitudinal as well as radial velocity gradient
(D) Neither longitudinal nor radial velocity gradient

Answer 1

Hint:Streamline flow can be assumed as the flow of layers.Generally, streamline flow is observed in the places where the cross-sectional area changes.A change in the cross-sectional area changes the flow velocity.

Complete step by step answer:

From the diagram, we can see the streamline line flow in the direction of A to B is happening due to the cross-sectional area change.
Let us consider the cross-section at point \[A{\text{ }}and{\text{ }}B\]
At any cross-section, the velocity gradient of the particles can be divided into two parts.
Longitudinal velocity gradient, which is the velocity along the flow direction.
Radial velocity gradient, which is along the cross-section.
Now, if we consider the longitudinal velocity gradient at the cross-section, A is \[{V_{AL}},\]and the radial velocity gradient is \[{V_{AR}}\] Similarly, the velocity gradients at cross-section B are \[{V_{BL}}and{\text{ }}{V_{BR}}.\]
But In any cross-section, the radial velocity gradient is the same. So there is no change in the radial velocity gradient, Whereas, if we see at the longitudinal velocity gradient, we will observe a change due to the reduced cross-sectional area at point
Hence we can say streamline motion is that motion in which only there is only a longitudinal velocity gradient.
So the correct answer is option(A) Only longitudinal velocity gradient.

Note:The longitudinal velocity gradient increases when the cross-sectional area decreases.We can consider water flowing in a pipe slowly as streamline flow.