1. Tardigrade
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  3. Physics
  4. Two large vertical parallel plates separated by a gap of d=1 mm have a highly viscous liquid of density 800 kg / m 3 and viscosity coefficient η=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 .=0.1 N s m -2).

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Q. Two large vertical parallel plates separated by a gap of $d=1 \,mm$ have a highly viscous liquid of density $800 \,kg /$ $m ^{3}$ 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. $\left(1\right.$ poise $\left.=0.1 \,N \,s \, m ^{-2}\right)$.

Mechanical Properties of Fluids

Solution:

image
From force balance,
$\eta A \frac{d v}{d x}=\rho A \frac{d}{2} g$
$\therefore \frac{d v}{d x}=\frac{\rho d g}{2 \eta}$