Two incompressible viscous fluids flow one on top of the other down an inclined plate at an angle 0. They both have the same density, p, but different viscosities μ₁ and μ2. The lower fluid has depth h₁ and the upper h₂. Assuming that viscous forces from the surrounding air is negligible and that the pressure on the free surface is atmospheric. Starting from continuity and Navier-Stokes, show that the fluid pressure P(y) = Pa + pg cos(0) (h₁ + h₂ − y) - 1 sin e Show that the fluid velocity in the bottom layer is vx = [(h₁ + h₂) y — — y²] pg si με x Inclined plate Ꮎ h₁ 1 h₂

Two incompressible viscous fluids flow one on top of the other down an inclined plate at an angle 0. They both have the same density, p, but different viscosities μ₁ and μ2. The lower fluid has depth h₁ and the upper h₂. Assuming that viscous forces from the surrounding air is negligible and that the pressure on the free surface is atmospheric. Starting from continuity and Navier-Stokes, show that the fluid pressure P(y) = Pa + pg cos(0) (h₁ + h₂ − y) - 1 sin e Show that the fluid velocity in the bottom layer is vx = [(h₁ + h₂) y — — y²] pg si με x Inclined plate Ꮎ h₁ 1 h₂