Question

A space $2.5cm$ wide between two large plane surfaces is filled with oil. Force required to drag a very thin plate of area $0.5m^2$ just midway the surfaces at a speed of $0.5m/$ sec is $1N$. The coefficient of viscosity in $kg-s/m^2$ is:

• A. $5\times 10^{-2}$
• B. $2.5\times 10^{-2}$
• C. $1\times 10^{-2}$
• D. $7.5\times 10^{-2}$

Answer 1

Answer: (B)

Velocity gradient $=\frac{0.5}{\frac{2.5}{2}\times 10^{-2}}$
As force on the plate due to viscosity is from upper as well as lower portion of the oil, equal from each part,
Then, $F=2\eta A\frac{dv}{dz}$
$=2\times \eta \times (0.5)\frac{0.5}{1.25\times 10^{-2}}$

$\Rightarrow \eta =2.5\times 10^{-2}kg-sec/m^2$