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 $kgs/m^2$ 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)

$2.5\times {10}^{-2}$

Velocity gradient $\frac{dV}{dz}=\frac{0.5}{\frac{2.5}{2}\times {10}^{-2}}=40$
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 force,
$F_{viscous}=\eta A\frac{dV}{dz}$
Since there are two surfaces, we get
$F_{viscous}=\eta \times 2A\frac{dV}{dz}$
$\therefore 1N=\therefore \eta \times 2\times 0.5\times 40$
$\therefore \eta =2.5\times {10}^{-2}kgsec{m}^{-2}$