A cylinder with diameter 100mm and length 0.25m slides vertically down inside a hollow cylindrical tube of diameter 102mm. The space between the cylindrical body and the tube wall is filled with thick lubricating oil with a dynamic viscosity of 2.5 Ns/m2 . Calculate the terminal velocity of the cylinder if its weight is 20N.

2.0366 m/s

Explanation:

Terminal velocity can be calculated form newton law of viscosity

Dc ( diameter of cylinder ) = 100 mm = 0.1 m

L = 0.25 m

Dh ( diameter of hollow tube ) = 102 mm = 0.102 m

μ ( viscosity ) = 2.5 Ns/m2

h ( the difference between the diameters / 2 ) = Dh - Dc / 2

 = ( 0.102 - 0.1 ) / 2 = 0.002 m

The drag force of the cylinder is equal to the weight of the cylinder = 20 N expressed as

     W = μ * A

     20 = ( 2.5 ) * * ( π * d * L )

      20 = (2.5 ) * *  ( π * 0.1 * 0.25 )

therefore V = (20 / 0.1964) * 0.02

                 V = 2.0366 m/s

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