Newton's Law of Viscosity

Simple shear in a fluid

When a fluid is subjected to a shear force, due to internal friction it produces an equal and opposing force against the applied force in the form of Shear Stress. The Shear Stress can be expressed as the product of Viscosity and it’s rate of shear.

$$\begin{array}{r}\frac{F}{A}={\tau }_{yx}=\mu \underset{\text{Shear rate}}{\underbrace{\left(-\frac{d{V}_x}{dy}\right)}}=\mu {\dot{\gamma }}_{yx}\end{array}$$

• Where, ${\tau }_{yx}\to$ Shear Stress, $\mu \to$ Viscosity, $\dot{\gamma }\to$ Shear rate, $V_x\to$ Velocity in $x$-direction.
• Note: The subscripts denote the directions normal and perpendicular to the forces respectively.
• It is observed that the shear rate is nothing but the gradient of $x$-velocity in $y$-direction.
• -ve sign implies that the shear stress acts in the direction opposite to the acting force.

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References

1. Definition of a non-Newtonian fluid