A horizontal plate of surface area A 1m2 is pulled to the r

A horizontal plate of surface area A = 1m^2, is pulled to the right with velocity 5 m/s in oil whose dynamic viscosity Mu = 1.2 Pa.s. Determine the force, F. required to maintain this motion if h_1 = h_2 = 2cm h_1 - 1cm and h_2 = 3cm. (Assume linear velocity profiles in the oil)

Solution

Given data:

V=5m/s

A=1m²

µ=1.2 Pa

F=A

=µV/b

b=distance between plates

Solution:

a) h1=h2=2cm

₁=µV/b₁

b₁=h1=h2= 2X10^-2m

=(1.2X5)/2X10^-2

=300N/m²

F₁=₁XA

=300X1=300N

F₂=2XA

=300X1=300N

F=F₁+F2

=600N

b)h1=1, h2=3

₁=µV/b₁

b1=h1=1X10^-2m

=(1.2X5)/1X10-2

=600N/m²

F₁=₁XA

=600X1

=600N

2=µV/b2

b2=h2=3X10^-2m

₂=(1.2X5)/3X10^-2

=200N/m²

F2=2XA

=200N

Therefore total force applied is F₁+F₂=800N