Question

The tangential force or viscous force on any layer of the liquid is directly proportional to velocity gradient $\left( {\dfrac{{dv}}{{dx}}} \right)$. Then the direction of velocity gradient is :
A. Perpendicular to the direction of the flow of liquid.
B. Parallel to the direction of the flow of liquid.
C. Opposite to the direction of flow of the liquid.
D. Independent of the direction of flow of the liquid

Answer 1

Hint – In order to solve this problem we need to understand velocity. A gradient is defined as the rate of change in velocity per unit of distance. And because the viscous force of the liquid which is in contact with the surface does not move and the liquid of the upper layer travels at a higher velocity, the velocity changes in the vertical direction. Doing this will solve your problem and will give you the right answer.

Complete answer
It is given in the question that tangential force on any of the layers of the liquid is directly proportional to the velocity gradient.
That is, ${F_t}\alpha \dfrac{{dv}}{{dx}}$.
So we can say that liquid which is in contact with the surface does not move and the liquid of the top layer moves with greater velocity, so there is velocity change in the vertical direction. Thus $\left( {\dfrac{{dv}}{{dx}}} \right)$​ is perpendicular to the direction of flow of liquid.
So, we can say that the correct answer is that the direction of the velocity gradient is directed perpendicular to the direction of the flow of liquid.
So, the right option is A.

Note: In this problem you need to know that the velocity gradient is the rate of change of velocity with respect to the length. The difference in velocity between the neighboring layers of the fluid is known as the velocity gradient and is defined by v / x, where v is the velocity difference and x is the distance between the layers. and the direction of the velocity gradient is perpendicular to the direction of the tangential force on the liquid due to other layers.