A thin plate moves between two parallel horizontal stationary flat plates at a c

Question

A thin plate moves between two parallel horizontal stationary flat plates at a constant velocity of 5 m/s.The two stationary surfaces are spaced 4 cm apart and the medium is oil with viscosity 0.9 Pa.s. The area of the plate in contact with the fluid at any given time is 2m long and 0.5m wide. If the plate moves through the mid plane between the surfaces, the force, F required to maintain this motion is?

Assume the velocity distribution in the oil is linear. A thin plate moves between two parallel horizontal stationary flat plates at a constant velocity of 5 m/s.The two stationary surfaces are spaced 4 cm apart and the medium is oil with viscosity 0.9 Pa.s. The area of the plate in contact with the fluid at any given time is 2m long and 0.5m wide. If the plate moves through the mid plane between the surfaces, the force, F required to maintain this motion is?

Assume the velocity distribution in the oil is linear.

Explanation / Answer

du / dy = 5 / 0.02 since change in speed = 5 m/s from stationary plates to the middle plate located at 0.02 m from stationary plate

The force acting due to viscosity on each side of plate = viscosity * Area * du/dy

= 0.9 * 2 * 0.5 * 5 / (0.02) = 225 N

Total force required to move the plate = 2*225 = 450 N

It is twicesince there are 2 surfaces where viscous forces act.

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