Two horizontal plates are placed one above the other at a distance of 2 cm, the space between them being filled with an oil of viscosity 15 poises. What is the shear stress in oil if the upper plate is moved with a velocity of 2 m/s?
DSSSB JE - 2023,
Answer: D
For a Newtonian fluid the shear stress is \(\tau = \mu\,\dfrac{du}{dy}\). The viscosity is 15 poise, and 1 poise = 0.1 N s/m\(^2\), so \(\mu = 1.5\) N s/m\(^2\). The gap is 0.02 m and the velocity change across it is 2 m/s:
\[ \tau = 1.5 \times \frac{2}{0.02} = 150\ \text{N/m}^2 \]The smaller values of 120, 130 and 140 N/m\(^2\) would result from small arithmetic slips in the conversion of the viscosity or the gap, and do not follow from the data.
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