Question

A plate having an area of 0.6m2 is sliding down the inclined plane at 30° to the horizontal with a velocity of 0.36m/s. There is a cushion of fluid 1.8 mm thick between the plane and the plate. Find the viscosity of the fluid if the weight of the plate is 280N.

Answer 1

To find the viscosity of the fluid, we use the formula

$F = \eta\frac{\Delta v}{\Delta x}\times A$

implying that $\eta = F \div\frac{\Delta v}{\Delta x} A$

where $F = mgsin30^{o}$

$mgsin30^{o} \div \frac{\Delta v}{\Delta x}\times A$

$= 280sin30\div \frac{0.36}{1.8\times10^{-3}}\times0.6$

$140 \div 120 = 1.17 (Pa . s)$