Question

A thin square plate of side, $l=10cm$ is dragged with constant velocity, $v$ = $3$ $cm/s$ in an oil. The width $d$ of the oil column is $2mm$. Square plate is placed symmetrically as shown in the figure. Assumed velocity of layer of oil at the end is negligible. The coefficient of viscosity is $150$ $poise$. Find the horizontal force (in $N$) required to move the square plate with constant velocity.

Answer 1

Since the plate moves with constant velocity, the net force acting on the plate must be zero.

Hence $F_a=2\times F_{vis}=2\eta A\frac{dv}{dy}$

$=2\eta \times l^2\times \frac{v}{d/2}$

$=\frac{4\eta l^{2}v}{d}$

$=\frac{4\times \frac{150}{10}\times {10}^{-2}\times 3\times {10}^{-3}}{2\times {10}^{-3}}$

$=9N$