Question 408: Properties of Matter

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 place is pulled horizontally with a constant velocity $${\mu _{0.}}$$ Which of the following statements is (are) true?

Accepted Answer

Force of viscosity can be written as follows:
$$f = \eta A{{dv} \over {dy}}$$
Here $$\eta $$ is coefficient of viscosity, A is face area of plate and dv / dy is velocity gradient. We can assume that velocity of fluid at the bottom (h depth below) is zero; hence $${{dv} \over {dy}} = {{{u_0}} \over h}$$; hence force of viscocity can be written as follows:
$$f = \eta A{{{u_0}} \over h}$$
We can see that force of viscosity is inversely proportional to h; hence option (a) is correct.
We can see that force of viscosity is proportional to area of plate; hence option (b) is wrong.
Tangential stress can be written as $${f \over A} = \eta {{{u_0}} \over h}$$.
We can see that options (c) and (d) are also correct.

Answer

The resistive force of liquid on the plate is inversely proportional to $$h$$

Answer

The resistive force of liquid on the plate is independent of the area of the plate

Answer

The tangential (shear) stress on the floor of the tank increases with $${\mu _0}$$

Answer

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

Properties of Matter

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h of the liquid in the tank is much less than the width of the tank. The floating place is pulled horizontally with a constant velocity {\mu _{0.}}$ Which of the following statements is (are) true?

Choose the correct answer: