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A circular metal plate of radius 5 cm, r...

A circular metal plate of radius 5 cm, rests on a layer of castor oil 2mm thick, whose coeffeicient of viscosity os `15.5 dyn e cm^(-2)s`. Calculate the horizontal force required to move the plate with a speed of `5 cms^(-1)`. Also calculate strain rate and shearing stress.

Text Solution

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Here, `A= pi r^(2) = 22/7 xx 5^(2) = (550)/(7) cm^(2), dx = 2 mm = 0.2 cm, dupsilon = 5 cm//s, eta = 15.5" dyne "cm^(-2) s`.
Now, `F= eta A (d upsilon)/(dx) = 15.5 xx 550/7 xx 5/0.2 = 30446.4 dyne = 3.04 xx 10^(4) dyne`
starin rate = ` (d upsilon)/(dx) = (5 cm//s)/(0.2 cm) = 25 s^(-1)`
Shearing stress = `eta xx strai n rate = 15.5 xx 25 = 3.87.5" dyne "cm^(2)`.
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