# What is viscous force?

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**Hint:**When a fluid layer slips or tends to slip on neighboring layers in contact in a steady flow of fluid, the two layers apply tangential force on one other, aiming to eliminate the relative motion between them. The property of a material that resists the displacement between its different layers is known as viscosity. Also, the force that opposes the relative motion between the layers is known as viscous force.

**Complete answer:**

**Viscous force:**It is the resistance (internal) force provided by a fluid when it is subjected to tangential force on its surface (shear).

When a fluid flows across a surface, the particles of the flow near the surface adhere to it. As a result, the fluid's relative velocity about the surface is zero. In other words, the fluid molecules at the surface have the same velocity as the surface.

Consider a tangential force acting on the fluid's free surface. As a result, the fluid-free surface molecules move at a given velocity, say $V$ , under the influence of this external force.

The velocity of the fluid molecules at a zero-perpendicular distance (directly next to the surface) from the surface, on the other hand, is equal to that of the surface and not equal to the velocity of the fluid molecules at the fluid free surface ($V$). As a result, the velocity of distinct layers varies at different sites. A velocity gradient exists across the flow mathematically.

Back to viscous force, it is caused by cohesive forces in the fluid itself. These layers of fluid dragged when they subjected to an uneven force. As a result of the forces of attraction, the layer attempts to drag the descending layer.

This disparity in velocity is caused by the presence of a force opposing the fluid's motion (or flow). This resistant force is referred to as viscous force.

Additional information:

Viscous force formula:

The viscous force can be estimated by multiplying the surface shear stress by the fluid and the area. The shear stress induced by fluid viscosity is directly proportional to the material viscosity coefficient and the velocity gradient.

$F = \mu A\dfrac{u}{y}$

$F$- Force

$\mu $-the fluid's viscosity

$A$-each plate's area

$\dfrac{u}{y}$-shear deformation rate

**Note:**A measure of a fluid's flow resistance. The viscosity of a fluid is related to the rate at which its velocity changes in space; the proportionality constant is the viscosity. The extensional viscosity to shear viscosity ratio for Newtonian liquids (liquids with no viscosity fluctuation with shear or extension rate) is \[3\]. Trouton's ratio is represented by this figure. Trouton's ratio can range from \[3\] in more complex liquids, such as polymer solutions, and can vary with shear or extension rate.