Two large plane surface are 2.4 cm apart. The space between surface is filled with glycerin having viscosity `8.1**10^(-1)` Ns/`m^2`. What force is required to drag a thin plate of surface area 0.5 `m^2` between that large plane surface at speed of 0.6 m/s. If thin plate is at a distance of 0.8 m from one of plane surface.

SOLUTION:

Given,

Distance  of plate from one plane surface, `y_1=0.008 m`

Distance  of plate from another  plane surface`y_2=0.016 m`

Viscosity of liquid, `mu=8.1**10^(-1)`Ns/`m^2`

Cross sectional area of plate,`A=0.5 m^2`

Velocity of the plate, `V=0.6`m/s.

Since the thickness of the layer is  small, we can assume the velocity profile to be linear.

Now, 

Total force required to drag the plate=shear force due to fluid between the plate and upper plane + shear force due to fluid between the plate and lower plane

or, `F=F_1+F_2`

or, `F=A*(tau_1+tau_2)`

or, `F=A*mu*V*(1/y_1+1/y_2)`

or, `F=0.5**0.81**0.6**(1/0.008+1/0.016)`

or, `F=45.5625 N`

SOLUTION:

Given,

Distance  of plate from one plane surface, `y_1=0.008 m`

Distance  of plate from another  plane surface`y_2=0.016 m`

Viscosity of liquid, `mu=8.1**10^(-1)`Ns/`m^2`

Cross sectional area of plate,`A=0.5 m^2`

Velocity of the plate, `V=0.6`m/s.

Since the thickness of the layer is  small, we can assume the velocity profile to be linear.

Now, 

Total force required to drag the plate=shear force due to fluid between the plate and upper plane + shear force due to fluid between the plate and lower plane

or, `F=F_1+F_2`

or, `F=A*(tau_1+tau_2)`

or, `F=A*mu*V*(1/y_1+1/y_2)`

or, `F=0.5**0.81**0.6**(1/0.008+1/0.016)`

or, `F=45.5625 N`