Question

a circular metal plate of radius 5cm rest on a layer of Castrol oil to 2mm thick whose coefficient of viscosity is15.5 poise. Calculate the horizontal force required to move the plate with the speed of 5 cm per second

Answer 1

Answer:

Explanation: as we know that F=eata

×A×dv by DX so the solution is give below

Answer 2

Given:

The radius of the metallic plate is $5cm$ that is $r=5cm$.

The thickness of the Castrol oil is $2mm$ that is $dx=0.2cm$.

The coefficient of viscosity is η$=15.5Ncm^{-2} s$.

To Find:

To find the horizontal force and the shearing stress that is required to move the metallic plate with the speed of $5cm$ per second.

Step by step explanation:

• The area of Castrol oil goes by,

        $A$= π$r^{2}$.

• This is the total surface Area.

• Substitute the values in the given formula,

        $A=\frac{22}{7} ( 25)cm^{2}$.

• The formula to find the horizontal force that is required is given by,  

        $F=A(\frac{dv}{dx})$η.

• By substituting the surface area and the other corresponding values in the formula we get,

        $F=(15.5)(\frac{22}{7} )(25)(25)$.

• By solving the above equation we the get required horizontal force to move the plate as,

       $F=30446.42dyne.$

• Shearing stress is given by,

        $Shearing stress=Shearing strain$(η).

• Solve the above equation by substituting the values in the equation.

        $shearing stress=(15.5)(25)$.

• By solving the above equation we get,$shearing stress=387.5dyne/cm^2$.

Final answer:

The horizontal force required to move the plate is, $F=30446.42dyne.$

The shearing stress is $387.5dyne/cm^2$.