Question

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 5.5 cm and the distance between the plates to be 4 mm.

Answer 1

`3.85*10^(-5)m^3/a`

Step-by-step explanation:

We need to find the average velocity of each plate,
`u_1` and
`u_2`.

So substituting,

`\bar{V_1} = (1)/(2)*u_1=(1)/(2)*5m/s=2.5m/s`

`\bar{V_2} = (1)/(2)*u_2 = (1)/(2)*1.5m/s=0.75m/s`

The net velocity is:
`\bar{V_1}-\bar{V_2}=2.5-0.75=1.75m/s`

The flow rate =
`\bar{V}_(net)A = 1.75m/s * 5.5*10^(-3) * 4*10^(-3)`

The flow rate
`= \bar{V}_(net)A = 3.85*10^(-5)m^3/a`