Question

The space between two plates (20cm*20cm*1cm), 1 cm apart, is filled with a liquid of viscosity 1 Poise. The upper plate is dragged to the right with a force of 5N keeping the lower plate stationary.

What will be the velocity in m/s of flow at a point 0.5 cm below the lower surface of the upper plate if linear velocity profile is assumed for the flow?

(a) 1.25

(b) 2.5

(c) 12.5

(d) 0.25

This question was addressed to me in an international level competition.

This intriguing question originated from Viscosity topic in section Properties of Fluids of Fluid Mechanics

Answer 1

The correct option is (c) 12.5

The best explanation: where Fν = viscous force, A = area, du ⁄ dx = velocity gradient, μ = co-effcient of viscosity. If linear velocity profile is assumed, du⁄dx = U/x, where U = velocity of the upper plate and x = distance between the two plates. Now, the viscous force Fv = -F= -5N. Substituting all the values in the equation, U becomes 12.5 m/s.