Question

Two horizontal plates placed $250\text{mm}$ apart have an oil layer of viscosity $20\text{poise}$ in between the plates. Calculate the shear stress on the oil layer, if the upper plate is moved with a velocity of $1250\text{mm/s}$.

• A. $20{\text{N/m}}^2$
• B. $2{\text{N/m}}^2$
• C. $10{\text{N/m}}^2$
• D. None of the above mentioned.

Answer 1

The correct option is C $10{\text{N/m}}^2$

Shear stress is given by,
${\sigma }_s=\frac{F_v}{A}=\eta \frac{dv}{dz}$
The velocity of the upper-most layer is $v=1250\text{mm/s}=1.25\text{m/s}$
Velocity of the layer in contact with the bottom plate is, $v=0$
$\Rightarrow dv=1.25-0=1.25\text{m/s}$
& $dz=0.25\text{m}$
Velocity gradient is,
$\frac{dv}{dz}=\frac{1.25}{0.25}=5{\text{s}}^{-1}$
Viscosity, $\eta =20\text{Poise}=\frac{20}{10}=2\text{Pa.s}$
From Eq.$\left(i\right)$,
${\sigma }_s=2\times 5=10{\text{N/m}}^2$