Q.State Newton's law of viscosity, writing it as an equation, and explain the physical meaning and SI unit of the coefficient of viscosity of a fluid. How does the viscosity of a liquid generally change as its temperature is raised, and how does this differ from the way the viscosity of a gas changes with temperature?

Newton's law of viscosity states that the tangential (viscous) force $F$ needed to maintain a steady relative velocity between two adjacent layers of a fluid is directly proportional to the area of contact $A$ between the layers and to the velocity gradient $dv/dx$ set up between them:

The constant of proportionality, $\eta$, is the coefficient of viscosity. Physically, $\eta = \dfrac{F/A}{dv/dx}$ is the tangential force per unit area required to maintain a unit velocity gradient in the fluid -- a fluid with a large $\eta$ (such as glycerine or honey) needs a much larger force to shear it at a given rate than a fluid with a small $\eta$ (such as water or air). Since $F/A$ is in $\text{Pa}$ and $dv/dx$ is in $\text{s}^{-1}$, $\eta$ has SI unit $\text{Pa·s}$ (also called the poiseuille).

Effect of temperature: for a liquid, viscosity arises mainly from intermolecular cohesive forces between neighbouring molecules; raising the temperature gives the molecules more thermal energy, weakening the effectiveness of these cohesive forces, so the liquid's viscosity decreases. For a gas, viscosity arises mainly from the transfer of momentum as molecules dart between adjacent layers; raising the temperature increases the average molecular speed, increasing this rate of momentum transfer, so the gas's viscosity increases -- the opposite trend to a liquid.

State Newton's law as the proportionality between viscous force and the product of area and velocity gradient, identify $\eta$ as the constant of proportionality with unit $\text{Pa·s}$, then contrast the molecular reason viscosity falls with temperature for a liquid against the reason it rises with temperature for a gas.

• Stating that viscosity always decreases with temperature, without distinguishing the opposite behaviour of gases.
• Quoting the unit of $\eta$ as $\text{N/m}^2$ alone (that is only the unit of $F/A$, i.e. stress) rather than $\text{Pa·s}$, forgetting the extra factor of time that comes from dividing by the velocity gradient's unit of $\text{s}^{-1}$.