5. Two immiscible fluids of equal density are flowing down a surface inclined at a 30° angle. The two fluid layers are of equal thickness h 2.5 mm; the kinematic viscosity of the upper fluid is twice that of the lower fluid, which is Viower=2x104 m s. Find the velocity at the interface and the velocity at the free surface. Plot the velocity distribution.

2. Consider a flow with the velocity profile given by the equation below. The fluid surface is located at y = 0. Here, U∞ is called the freestream velocity and 8 is called the boundary layer thickness. Calculate the boundary layer thickness at a point where the shear stress is 36 mPa if the freestream velocity is 40 m/s and the fluid's dynamic viscosity 1.81.105 Pa.s. U.. ( 2 (²) - (²) ²) u(y) = U∞o

Please solve following problem. Especially I cannot understand how to get flow rate.

4. Consider a viscous flow inside an annular pipe. The inner surface of the pipe is located at r = R₁ and is stationary. The outer surface is located at r = Ro and moves to the right with speed Upipe. The pressure inside the pipe is constant. The fluid inside the pipe has dynamic viscosity μ. Assume that the flow is steady, incompressible, fully-developed, axisymmetric, non-rotating, and has negligible body forces. Starting from the differential form of the conservation of mass and momentum equations: a. Derive an equation for the velocity inside the pipe in terms of Upipe, R₁, Ro, and r. b. Determine the average velocity inside the pipe in terms of Upipe, R₁, and Ro. C. Determine the shear stress acting on the inner annulus in terms of Upipe, Ri, Ro, and u. Upipe er R₁ fluid