Question

A square plate with 1.5 m of each side moves through a space filled with oil . Take the viscosity of the oil as 0.07801N-s/m2. If the velocity of the plate is to be maintained constant at V m/s, with the given data below calculate:Total force required to pull the plate

Answer 1

(The diagram missing in the question is given below)

Given :

Length of side of a square plate = 1.5 m

Viscocity of oil = 0.0780 N-s/m²

To Find :

The total force required to pull the plate

Solution :

• As the plate moves with constant velocity, the net force acting on the plate should be zero

                $F_{a} = F_{vis}$    

• Force of viscocity is different on both the plates as the width of the oil between the plates is different

               $F_{a} = F_{vis1} +F_{vis2}$

               $F_{a}=\eta A\frac{dv}{dy_{1} } + \eta A\frac{dv}{dy_{2} }$

               $F_{a}=\eta Adv(\frac{1}{dy_{1}}+\frac{1}{dy_{1}} ]$

               $F_{a} = 0.0780\times (1.5)^{2}\times2.5(\frac{1}{23} +\frac{1}{35} )\times 10^{2}$

               $F_{a} =3.16N$

The force required to pull the plate is 3.16N