A space 2.5 cm wide between two large plane surfaces is filled with oil. Force required to drag a very thin plate of area $0.5{\mathrm{m}}^2$ just midway the surfaces at a speed of $0.5{\mathrm{ms}}^{-1}$ is 1N. Find the coefficient of viscosity of oil $\text{ (in }\times {10}^{-3}\mathrm{kg}-{\mathrm{sm}}^{-2}\text{ ). }$

Velocity gradient $\frac{\mathrm{dV}}{\mathrm{dz}}=\frac{0.5}{\frac{2.5}{2}\times {10}^{-2}}=40$

As force on the plate due to viscosity is from upper as well as lower portion of the oil and both are equal using the expression for viscous

$\text{ force, }{\mathrm{F}}_{\mathrm{v}}=\eta \mathrm{A}\frac{\mathrm{dV}}{\mathrm{dz}}$

.Since there are two surfaces we get

$F_v=\eta 2A\frac{dV}{dz}$

$\therefore 1=\eta \times 2\times 0.5\times 40$

$\eta =2.5\times {10}^{-2}{\mathrm{kgsm}}^{-2}$