Question

The viscous drag is:
A. inversely proportional to the velocity gradient.
B. directly proportional to the surface area of layers in contact.
C. independent of the nature of liquid.
D. perpendicular to the direction of liquid flow.

Answer 1

Hint: Viscous drag is a force between any two layers of flowing liquid, when there is a relative motion between the two layers. The viscous drag opposes the relative motion between the two layers. The magnitude of the viscous drag is given as $F=\eta A\dfrac{dv}{dy}$. Use this formula to select the correct option.
Formula used:
$F=\eta A\dfrac{dv}{dy}$

Complete answer:
Like we have friction between two surfaces when there is a relative motion between the two surfaces, in liquids also there is a frictional force. This frictional force in liquids is called viscosity or viscous drag.
Consider that a liquid is made up of many layers. When the liquid flows, these layers slide on one another. Hence, there is a relative motion between any two layers of the liquid. This when the viscous drag comes into play.

The viscous force opposes the relative motion between the layers of the liquid that are in contact.
Consider the flowing water of a river. The top layer will have the maximum velocity. As we go down to the ground, the velocity of the layers of water decreases and eventually the velocity of the water layer in contact with ground is zero. This change in velocity with respect to the depth is called velocity gradient.

The magnitude of the viscous drag between layers of a liquid is given as $F=\eta A\dfrac{dv}{dy}$ ….(i).
Here, $\eta $ is called the coefficient of viscosity, A is the area of layers in contact and $\dfrac{dv}{dy}$ is the velocity gradient.

If we see equation (i), we get that the viscous drag is directly proportional to the area of the layers in contact.

So, the correct answer is “Option B”.

Note:
The viscous drag is directly proportional to the velocity gradient.
The coefficient of viscosity depends on the nature of the liquid. Hence, the viscous drag is dependent on the nature of the liquid.
The viscous force acts parallel to layers. Therefore, the direction of the viscous drag is along the direction of the flow of the liquid.