Question

A square plate of $1m$ side moves parallel to a second plate with velocity $4m/s$. A thin layer of water exists between plates. If the viscous force is $2N$ and the coefficient of viscosity is $0.01$ poise then find the distance between the plates in $mm$.

Answer 1

Given co-efficient of visco with $\eta =0.01$ of le $={10}^{-2}$ poise $={10}^{-3}kg/m$

Viscous to $ra=0.002N=2\times {10}^{-3}N$

Length of square plate $=0.1m$

Area of square plate $A=0.1\times 0.1={10}^{-2}{m}^2$

velocity $=0.1m/s={10}^{-1}m/s$

viscous force $=f=\eta A\frac{dv}{dx}$

$dx=\frac{\eta AV}{F}=\frac{{10}^{-3}\times {10}^{-2}\times {10}^{-1}}{2\times {10}^{-3}}=\frac{{10}^{-3}}{2}$

$=0.5\times {10}^{-3}=0.0005m$