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  4. The tangential force (or) viscous force on any layer of the liquid is directly proportional to velocity gradient ((dv/dx)) . Then the direction of velocity gradient is :

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Q. The tangential force (or) viscous force on any layer of the liquid is directly proportional to velocity gradient $\left(\frac{dv}{dx}\right)$ . Then the direction of velocity gradient is :

Mechanical Properties of Fluids

Solution:

According to question tangential force, $F _{ T } \propto \frac{ dV }{ dX }$
Now, because of viscous force, 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 vertical direction. Thus $\frac{ dV }{ dX }$ is perpendicular to the direction of flow of liquid.