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 $\eta =5$ poise 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

Answer: 8

From force balance,
$\eta A\frac{dv}{dx}=\rho A\frac{d}{2}g$
$\therefore \frac{dv}{dx}=\frac{\rho dg}{2\eta }$