Question

A Newtonian fluid with a viscosity of 50 cP is placed between two large parallel separated by a distance of 8 mm. Each plate has an area of 2 m^2, The upper plate the positive x-direction with a velocity of 0.4 m/s while the lower plate is kept stationary Calculate the steady force applied to the upper plate. The fluid in part (a) is replaced with another Newtonian fluid of viscosity 5 cP.. If a steady force applied to the upper plate is the same as that of part(a), calculate the velocity of the upper plate.

Answer 1

F= 5 N

V= 4 m/s

Step-by-step explanation:

Given that fluid is Newtonian fluid .As we know that for Newtonian fluid the shear stress given as

`\tau =\mu (du)/(dy)`

We also know that

Force = shear stress x area of plate

Now by putting the values

`\tau =\mu (du)/(dy)`

Here velocity of fluid profile is linear.

`\tau =\mu (U)/(h)`

`\tau =50* 10^(-2)* 0.1* (0.4)/(0.008)`

τ= 2.5 Pa

So force = 2.5 x 2

F= 5 N

Now when fluid is replaced by another fluid but force is constant.The height of plate is also constant.

Lets take velocity of fluid is V in the new condition

So we can say that

`\mu_1U=\mu_2V`

Now by putting the value

50 x 0.4 = 5 x V

V= 4 m/s