Consider the flow of an incompressible Newtonian fluid between two parallel plates that are 4 mm apart. If the upper plate moves to the right with u1 = 5 m/s, while the bottom one moves to the left with u2 = 1.5 m/s, what would be the net flow rate at a cross section between the two plates? Take the plate width to be 5 cm and the distance between the plates to be 4 mm.

Net flow rate = 0.00035 m³/s

Explanation:

The speed of plate 1, U₁ = 5 m/s

The speed of plate 2, U₂ = 1.5 m/s

The two plates are moving in different directions, the net speed will be gotten by taking the difference of the average of the two plates

The average speed due to the movement of plate 1 = U₁/2 = 5/2 = 2.5 m/s

The average speed due to the movement of plate 2 = U₂/2 = 1.5/2

= 0.75 m/s

The net average speed of the fluid = U₁/2 - U₂/2

The net average speed of the fluid = 2.5 - 0.75 = 1.75 m/s

Net flow rate = Net average speed * Area of the plate

Width of the plate, v = 5 cm = 0.05 m

Distance between the plates = 4 mm = 0.004 m

Area = 0.05 * 0.004

Area = 0.0002 m²

Net flow rate = 1.75 * 0.0002

Net flow rate = 0.00035 m³/s