Velocity Profile? A large plate is pulled at a constant speed of U = 4 m/s over

Question

Velocity Profile?

A large plate is pulled at a constant speed of U = 4 m/s over a fixed plate on 5 - mm - thick engine oil film at 20degreeC. Because the gap is not small, linear velocity profile may not be applicable. Assuming a half - parabolic velocity profile (V = k y) in the oil film, as sketched Based on the boundary condition, determine the velocity profile in the oil film, Determine the shear stress developed on the upper plate. If a linear velocity profile was assumed, what will be the shear stress? Is it over - prediction or underprediction?

Explanation / Answer

Shear stress = mu*(du/dy)

At upper wall, assuming half-parabolic profile, we have du/dy = 0

Thus, shear stress = 0.

If a linear velocity profile were assumed, we'll have, at upper wall, du/dy = 4/0.005 = 800 /s

Viscosity of oil, mu = 0.31 Ns/m^2

Shear stress = 0.31*800 = 248 Pa

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