Question

Two large vertical parallel plates separated by a gap of $d=1mm$ have a highly viscous liquid of density $800kg/m^3$ and viscosity coefficient $\eta =5poise$ flowing steadily under gravity in between the gap. Find the velocity gradient of the flow (in $s^{-1}$) near the plates surface. ($1-poise=0.1Ns/m^2)$.

Answer 1

Given, separation between the plates, $d=1mm$
Density of the liquid, $\rho =800kg/m^3$
Coefficient of viscosity of the liquid, $\eta =5poise=0.5Ns/m^2$
By force balance between the plates,
$\eta \frac{dv}{dx}=pA\frac{d}{2}g$
$\frac{dv}{dx}=\frac{pdg}{2\eta }$
$\frac{dv}{dx}=\frac{800\times 1\times {10}^{-3}\times 10}{2\times 0.5}$
$\frac{dv}{dx}=8s^{-1}$
Final answer: $\left(8\right)$