Question

The space between two plates (20cm*20cm*1cm), 1 cm apart, is filled with a liquid of viscosity 1 Poise. The upper plate is dragged to the right with a force of 5N keeping the lower plate stationary. What will be the velocity in m/s of flow at a point 0.5 cm below the lower surface of the upper plate if the linear velocity profile is assumed for the flow?

Answer 1

Given:

Space between two plates = (20cm*20cm*1cm) which is 1 cm apart.

The viscosity of the fluid filled = 1 poise

Viscous force = 5N

to find:

The velocity of flow at a point 0.5cm below the lower surface of the upper plate.

Solution:

Fn = - μA$\frac{d_u}{d_x}$

Where,

Fn _______viscous force

A______area

$\frac{d_u}{d_x}$______velocity gradient

coefficient of viscosity (8.90* 10-4 pa.s)

Substituting the values we get,

Viscous force = -F = -5N

$\frac{d_u}{d_x}$ =  

(U_______velocity of upper plate

Х________distance between two plates)

-5 = 8.90* 10-4 x 450 x $\frac{u}{v}$

-5 = 0.4005 x U

U = 12.5m/s