Question

A Newtonian fluid fills the clearance between a shaft and a sleeve. When a force of $800N$ is applied to the shaft, parallel to the sleeve, the shaft speed of $1.5cm/sec$. If a force of $2.4kN$ is applied instead, the shaft would move with a speed of

• A. $1.5cm/sec$
• B. $13.5cm/sec$
• C. $4.5cm/sec$
• D. None

Answer 1

Answer: (C)

$4.5cm/sec$

Using the relation $\tau =\mu \frac{du}{dy}$. Here $\tau$ is the shear stress between the layers of the liquid which is equal to $\frac{F}{A}$. $du$ is the change of velocity=$u-0=u$ and $dy$ is the clearance which is equal to $y$.
Thus we get
$\frac{F}{A}=\mu \frac{u}{y}$
or
$F=\frac{A\mu u}{y}\propto u$
Thus we get
$\frac{F_1}{u_1}=\frac{F_2}{u_2}$
Substituting the values we get
$\frac{800}{1.5}=\frac{2400}{u_2}$
Thus we get $u_2=4.5cm/s$