A plate of metal 10 cm sq. rests on a layer of caster oil 2mm thick whose coefficient of viscosity is `15.5 dyn e cm^(-2)s`. Calculate the horizontal force required to move the plate with a speed of `3 cm s^(-1)`. Also calculate strain rate and shearing strees.

Explanation

Here, `A = 10 xx10 sq cm`
`= 100 sq cm`
`eta - 15.5" dyne "cm^(-2) s`,
Thickness of oil = distance of plate from fixed layer
i.e., `dx=2 mm = 0.2 cm, d upsilon = 3 cms^(-10), F=?`
Now, `F= eta A (dupsilon)/(dx) = 15.5 xx 100 xx 3/0.2`
`=23250 dyn e`
Strain rate = `(dupsilon)/(dx) = 3/0.2 = 15 s^(-1)`
Shearing stress = `eta xx "shearing strain"`
`=15.5 xx 15`
`= 232.5 dyn e cm^(-2)`