Question

The area between two infinite flat parallel sheets which are placed 10mm away

from each other is occupied with a fluid having dynamic viscosity 0.5Pa.s.

Through this distance between the sheets a plate with small thickness and cross

sectional area 0.1m2

is being pulled. Considering the plate is at 4mm distance from

one of the sheets and the velocity distribution is linear determine the amount of

force which is needed to pull the plate.

Answer 1

Since the velocity of thin plate moving over the fluid surface is not provided,

Therefore I assume the velocity to be $u\space m/s$

Viscosity, $\mu=0.5 \space Pa.s$

Area of plate, $A=0.1\space m^2$

On the upper surface of plate,

Shear stress,$\tau_1=\mu(\dfrac{du}{dy})_1$

Force, $F_1=$ $\tau_1A$ $=\mu(\dfrac{du}{dy})_1\times A$

$F_1=0.5(\dfrac{du}{0.004})\times0.1=12.5 du\space N$

Similarly, force on lower surface,

$F_2=8.333du\space N$

Total force required, $F=F_1+F_2=20.8du\space N$