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 $u_0$. 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 $u_0$
• D. The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid

Answer 1

Answer: (A), (C), (D)

Viscous force is given by $F=-\eta A\frac{dv}{dy}$ since h is very small therefore, magnitude of viscous force is given by
$F=\eta A\frac{\Delta v}{\Delta y}$
$\therefore F=\frac{\eta A{u}_0}{h}\Rightarrow F\propto \eta \&F\propto u_0;F\propto \frac{1}{h},F\propto A$
Since plate is moving with constant velocity, same force must be acting on the floor.