Question

A flat plate that is 0.3m wide and 1m long is pulled over a film of water that is 0.2mm thick. The water is at 20 C. If the pulling force is 20N, what is the velocity of the plate?

Answer 1

The velocity of the pulling plate is 14.98 m/s.

Step-by-step explanation:

The shear stress caused by the 20 Newton force on the plate is given by

`\tau =(20)/(Area)=(20)/(0.3* 1.0)=66.66N/m^2`

Now by newton's law of viscosity we have

`\tau =\mu\cdot (\Delta u)/(\Delta y)`

where

`\mu` is the dynamic viscosity of the water at 20 degree

`(\Delta u)/(\Delta y)` is the velocity gradient

Applying values we get

`66.66=8.90* 10^(-4)* (U)/(0.2* 10^-3)\\\\\therefore u=14.98m/s`