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Question

# Two horizontal plates placed 250 mm apart have an oil layer of viscosity 20 poise in between the plates. Calculate the shear stress on the oil layer, if the upper plate is moved with a velocity of 1250 mm/s.

A
20 N/m2
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B
2 N/m2
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C
10 N/m2
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D
None of the above mentioned.
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Solution

## The correct option is C 10 N/m2Shear stress is given by, σs=FvA=ηdvdz The velocity of the upper-most layer is v=1250 mm/s=1.25 m/s Velocity of the layer in contact with the bottom plate is, v=0 ⇒dv=1.25−0=1.25 m/s & dz=0.25 m Velocity gradient is, dvdz=1.250.25=5 s−1 Viscosity, η=20 Poise=2010=2 Pa.s From Eq.(i), σs=2×5=10 N/m2

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