Question

Consider a thin square plate floating on a viscous liquid in a large tank. The height h of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity u₀. Which of the following statements is (are) true? 

(A) The resistive force of liquid on the plate is inversely proportional to h 

(B) The resistive force of liquid on the plate is independent of the area of the plate 

(C) The tangential (shear) stress on the floor of the tank increases with u₀. 

(D) The tangential (shear) stress on the plate varies linearly with the viscosity η of the liquid.

Answer 1

Answer (A,C,D)

solution

Viscous force is given by F = - ηAdv/dy since h is very small therefore, magnitude of viscous force is given by

Since plate is moving with constant velocity, same force must be acting on the floor.