Discuss the coefficient of viscosity in terms of stress and strain.

(N/A) The figure shows the laminar flow of a fluid between two parallel plates.
The fluid is placed between two glass plates. The bottom plate is stationary,so the fluid layer in contact with it is also at rest.
The top plate moves with a velocity $v$,causing the fluid layer in contact with it to move with the same velocity $v$.
Due to this motion,the fluid initially in the shape $ABCD$ takes the shape $AEFD$ after a small time interval $\Delta t$.
During this process,the shear strain produced is $\frac{\Delta x}{l}$. As the top plate continues to move,this strain increases continuously with time.
In this case,the stress depends not on the strain itself,but on the rate of change of strain,which is $\frac{(\Delta x / l)}{\Delta t} = \frac{\Delta x}{l \Delta t} = \frac{v}{l}$ (where $\frac{\Delta x}{\Delta t} = v$ is the velocity).
Here,the shear stress is $\frac{F}{A}$,where $A$ is the area of the contact surface and $F$ is the tangential viscous force.
For a fluid,the coefficient of viscosity $\eta$ is defined as:
$\eta = \frac{\text{Shear Stress}}{\text{Rate of Shear Strain}}$
$\therefore \eta = \frac{(F / A)}{(v / l)} = \frac{Fl}{vA}$
Or,$F = \eta A \left(\frac{v}{l}\right)$.