Two immiscible Newtonian liquids flow steadily between two large parallel plates under the influence of an applied pressure gradient. The lower plate is fixed while the upper one is pulled with a constant velocity of U = 10 m/s. The thickness, h, of each layer of fluid is 0.5 m. The velocity profile for each layer is given by

1. V₁ = 6 + ay - 3y², 0 ‰¤ y ‰¤ 0.5

2. V₂ = b + cy - 9y², -0.5 ‰¤ y ‰¤ 0

3. Where a, b, and c are constants.

(a) Determine the values of constants a, b, and c.

(b) Develop an expression for the viscosity ratio, for example, μ₁/μ₂ = ?

(c) Determine the forces and their directions exerted by the liquids on both plates if μ₁ = 10^-3 Paˆ™s and each plate has a surface area of 4 m².

U= 10 m/s Liquid 1 Liquid interface Liquid 2