A plate of area 0.20 m² moves at constant speed 0.10 m/s over a fixed surface. A Newtonian liquid film of thickness 2 mm and viscosity 1.5 Pa·s lies between the two surfaces. If the required force is N N, find N.
Physics · Properties of solid and fluid · viscosity and terminal velocity
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Question

A plate of area 0.20 m² moves at constant speed 0.10 m/s over a fixed surface. A Newtonian liquid film of thickness 2 mm and viscosity 1.5 Pa·s lies between the two surfaces. If the required force is N N, find N.

Physics · Properties of solid and fluid · viscosity and terminal velocity

G1 Physics · Accepted Answer

For a linear velocity profile, F = ηAv/d. Substitute: η = 1.5 Pa·s, A = 0.20 m², v = 0.10 m/s, d = 2 mm = 2×10⁻³ m. Therefore, F = 1.5×0.20×0.10/ [2×10⁻³]. The numerator is 0.03. Thus, F = 0.03/0.002 = 15 N. Hence, N = 15.