# Viscosity

## Table of Contents

The formula relating viscosity and shear deformation rate in a fluid, also known as Newton’s law of viscosity is given by the following equation:

$$ \tau = \mu \frac{\partial u}{\partial y} $$

Where

- \( \small \tau\ \) is the applied shear stress,
- \( \small \mu \) is the dynamic viscosity, with units of pressure \( \cdot \) time,
- \( \small \frac{\partial u}{\partial y} \) is shear deformation rate, and
- \( \small y \) is the perpendicular distance from the surface.

In the case where velocity varies linearly with y, the equation simplifies to:

$$ \tau = \mu \frac{u}{y} $$