Two large parallel plates of area A are separated by a Newtonian liquid layer of thickness d. The lower plate is fixed and the upper plate moves parallel to itself with constant speed v. Assuming a linear velocity gradient across the liquid, what force is required to maintain the motion?
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Question

Two large parallel plates of area A are separated by a Newtonian liquid layer of thickness d. The lower plate is fixed and the upper plate moves parallel to itself with constant speed v. Assuming a linear velocity gradient across the liquid, what force is required to maintain the motion?

Options

G1 Physics · Accepted Answer

For a Newtonian liquid, shear stress is proportional to the velocity gradient: τ = η(dv/dy). For a linear velocity profile between the plates, dv/dy = v/d. Therefore, τ = ηv/d. Since τ = F/A, we obtain F/A = ηv/d. Hence, F = ηAv/d. Correct option: B.