Consider a thin square plate floating on a viscous liquid in a large tank. The height 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 . Which of the following statement

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 $μ_{0}$ . Which of the following statements is (are) true?} [2018]

Smart Achievers · Accepted Answer

(1, 3, 4)

$F = - η A (\frac{d v}{d x})$ or $| F |$ $= η A \frac{u_{0}}{h}$

where $\frac{u_{0}}{h} = velocity gradient (\frac{d v}{d x})$

$F \propto η; F \propto A; F \propto u_{0} and F \propto \frac{1}{h}$

Solution

Q.
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 $μ_{0}$ . Which of the following statements is (are) true} [2018]

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

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

3 The tangential (shear) stress on the floor of the tank increases with $μ_{0}$

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

Ans.
(1, 3, 4)

$F = - η A (\frac{d v}{d x})$ or $| F |$ $= η A \frac{u_{0}}{h}$

where $\frac{u_{0}}{h} = velocity gradient (\frac{d v}{d x})$

$F \propto η; F \propto A; F \propto u_{0} and F \propto \frac{1}{h}$

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Solution

Q. 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 μ0. Which of the following statements is (are) true} [2018]

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