Question

Two plates are placed at a distance of 0.15 mm apart. The lower plate is fixed while the upper plate having surface area 1.0 m^2 is pulled at 0.3 m/s. Find the force and power required to maintain this speed, if the fluid separating them is having viscosity 1.5 poise.

Answer 1

Let force required be $F$

$$F=\nu\cdot(area)\cdot\dfrac{dv}{dz}$$

Putting all the values in SI unit

$$F=1.5\times(0.1Pa\cdot s)\cdot(1.0m^2)\cdot\dfrac{0.3\times10^{-3}m/s}{0.15\times10^{-3}m}=$$

$$=0.3N$$

The force is $0.3N.$

Let power required to maintain this speed be $P$

$$P=F\cdot v$$

$$P=0.3N\cdot0.3\times10^{-3}m/s=9\times10^{-5}W=90\mu W$$

Power required to maintain this speed is $9\times10^{-5}W=90\mu W.$