Explain velocity gradient and coefficient of viscosity and give their units.

(N/A) $1$. Velocity Gradient: When a fluid flows over a fixed surface,the velocity of the fluid layers increases with distance from the surface. The rate of change of velocity $(v)$ with respect to the perpendicular distance $(z)$ from the fixed surface is called the velocity gradient. It is given by $\frac{dv}{dz}$. Its $SI$ unit is $s^{-1}$.
$2$. Coefficient of Viscosity: According to Newton's law of viscosity,the viscous force $(F)$ acting between two layers of a fluid is directly proportional to the area of contact $(A)$ and the velocity gradient $(\frac{dv}{dz})$. Thus,$F = \eta A \frac{dv}{dz}$,where $\eta$ is the coefficient of viscosity. It is defined as the tangential force per unit area required to maintain a unit velocity gradient between two parallel layers of fluid. Its $SI$ unit is $Pa \cdot s$ or $N \cdot s/m^2$ (also known as Poiseuille).